{"id":58,"date":"2022-03-16T22:31:48","date_gmt":"2022-03-16T22:31:48","guid":{"rendered":"https:\/\/www.dm.unipi.it\/research\/mathematical-physics\/"},"modified":"2026-01-23T10:11:51","modified_gmt":"2026-01-23T09:11:51","slug":"mathematical-physics","status":"publish","type":"page","link":"https:\/\/www.dm.unipi.it\/research\/areas\/mathematical-physics\/","title":{"rendered":"Mathematical Physics"},"content":{"rendered":"\n<p>The research areas of the Mathematical Physics group are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Celestial Mechanics:<\/strong> mathematical theory and applications to real problems in astronomy and astrodynamics.<\/li>\n\n\n\n<li><strong>Dynamical Systems:<\/strong> general theory, statistical and stochastic properties, applications to other disciplines.<\/li>\n\n\n\n<li><strong>Geometrical structure of the spacetime continuum:<\/strong> low regularity Lorentzian geometry, mathematical relativity, causality, and topological ordered spaces.<\/li>\n\n\n\n<li><strong>Many-body quantum systems:<\/strong> analytic methods for the study of emergent effects.<\/li>\n\n\n\n<li><strong>Topological solitons: <\/strong>study of behaviour of localised, particle-like solutions of non-linear PDEs, which are particularly stable due to their non-trivial topological properties.<\/li>\n<\/ul>\n\n\n\n<p>More specific research topics investigated by this group are described below.<\/p>\n\n\n\n<p>The group manages the spin-off <a href=\"http:\/\/www.spacedys.com\/\" target=\"_blank\" rel=\"noreferrer noopener\">SpaceDyS s.r.l.<\/a> (Polo Tecnologico di Navacchio).<\/p>\n\n\n\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h4 class=\"wp-block-heading\">Research Topics<\/h4>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h5 id=\"at-580\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Celestial Mechanics<\/h5><div id=\"ac-580\" class=\"c-accordion__content\">\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-581\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Members<\/h6><div id=\"ac-581\" class=\"c-accordion__content\"><div class=\"d-flex row justify-content-between px-2 pb-4\">\n\n\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7ca\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nGiulio Ba\u00f9\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:giulio.bau@unipi.it\">giulio.bau@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63cef8880570144d28d41c52\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nMiriam Falletta\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:miriam.falletta@phd.unipi.it\">miriam.falletta@phd.unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c800\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nClara Grassi\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:clara.grassi@dm.unipi.it\">clara.grassi@dm.unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7cd\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nGiovanni Federico Gronchi\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:giovanni.federico.gronchi@unipi.it\">giovanni.federico.gronchi@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7cf\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nGiacomo Lari\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:giacomo.lari@unipi.it\">giacomo.lari@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63cef8880570144d28d41c50\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nMaddalena Mochi\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:maddalena.mochi@phd.unipi.it\">maddalena.mochi@phd.unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63c562f159df1b118b33faa7\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nRoberto Paoli\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:roberto.paoli@dm.unipi.it\">roberto.paoli@dm.unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7c7\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nGiacomo Tommei\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:giacomo.tommei@unipi.it\">giacomo.tommei@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<p>Below is the list of the specific topics studied in this research area, each of them with a detailed description and the lists of members and collaborators.<\/p>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h5 id=\"at-582\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Mathematical models and methods for the analysis of interplanetary tracking data<\/h5><div id=\"ac-582\" class=\"c-accordion__content\">\n<p>The Celestial Mechanics Group is involved in three research projects, linked to the space missions BepiColombo (ESA), Juno (NASA), and Hera (ESA). The BepiColombo mission was launched in 2018 and will arrive in orbit around Mercury in 2025: it aims to study the planet&#8217;s gravity field, its composition, its state of rotation, and carry out tests on theories of gravitation. The Celestial Mechanics group will analyze the data from the radio science experiment with the dedicated software Orbit14, developed with ASI funding in 2007. Simulations and cruise data analysis are currently being carried out. The Juno mission was launched in 2011 and has been in orbit around Jupiter since 2016: it aims to study the origin and evolution of the planet. The Celestial Mechanics Group is responsible for analyzing the data from the radio science experiment with the dedicated software Orbit14 with the aim of estimating Jupiter&#8217;s physical parameters, including gravitational and tidal coefficients. These parameters are necessary to improve the internal structure models of the planet. The Hera mission will be launched in 2024 and the goal will be the binary asteroid Didymos which it will reach in 2026, a few years after the moon of Didymos, called Dimorphos, was impacted by DART probe of NASA. Hera&#8217;s purpose is to characterize the post-impact environment of the asteroid through different tools. The Celestial Mechanics group will develop software, based on Orbit14, to analyze radio science data and will also conduct an analysis of the non-gravitational perturbations acting on the system (Yarkovsky-YORP-BYORP effects).<\/p>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-583\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Members<\/h6><div id=\"ac-583\" class=\"c-accordion__content\"><div class=\"d-flex row justify-content-between px-2 pb-4\">\n\n\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63cef8880570144d28d41c52\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nMiriam Falletta\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:miriam.falletta@phd.unipi.it\">miriam.falletta@phd.unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7cf\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nGiacomo Lari\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:giacomo.lari@unipi.it\">giacomo.lari@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63cef8880570144d28d41c50\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nMaddalena Mochi\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:maddalena.mochi@phd.unipi.it\">maddalena.mochi@phd.unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63c562f159df1b118b33faa7\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nRoberto Paoli\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:roberto.paoli@dm.unipi.it\">roberto.paoli@dm.unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7f1\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nGiulia Schettino\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:giulia.schettino@unifi.it\">giulia.schettino@unifi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7c7\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nGiacomo Tommei\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:giacomo.tommei@unipi.it\">giacomo.tommei@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-584\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Collaborators<\/h6><div id=\"ac-584\" class=\"c-accordion__content\"><div class=\"d-flex row justify-content-between px-2 pb-4\">\n\n\n\n<\/div>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h5 id=\"at-585\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Solar system dynamics and astrodynamics<\/h5><div id=\"ac-585\" class=\"c-accordion__content\">\n<ul class=\"wp-block-list\">\n<li>Long-term evolution of satellites\u2019 dynamics driven by tidal dissipation. Dissipative effects due to tidal forces between satellites and their hosting planet influence greatly the dynamics and the interior of the moons. For example, the volcanism of the moon Io is due to the coupling between tides and resonances with the other satellites of the Jovian system. We develop dynamical models that we use to investigate the orbital history of the moons of our solar system.<\/li>\n\n\n\n<li>Long-term evolution of planets\u2019 obliquity. The planets of our solar system are characterized by very different inclinations of their spin axis (or obliquities). For example, Jupiter has an obliquity of just 3\u00b0, Saturn 27\u00b0, and Uranus even 98\u00b0. We develop dynamical models that we use to explain the current obliquity of the gas giants of the solar system.<\/li>\n\n\n\n<li>New formulations of the perturbed two-body problem based on non-singular orbital elements: these are obtained by regularization of the equations of motion or via a purely geometrical approach. Such formulations can substantially improve the accuracy in the propagation of the state and associated uncertainty of Earth&#8217;s artificial satellites as well as of natural small bodies in the Solar system.<\/li>\n\n\n\n<li>Patched dynamics: it is used as a first approximation of more complex models. The solutions of the simpler problem can be used as a starting guess to compute the solutions of the more difficult ones, or sometimes they can be used to obtain the qualitative behavior of the more complex system. We apply patched dynamics to study close approaches of asteroids with the Earth and the passage through shadow for an Earth satellite.<\/li>\n<\/ul>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-586\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Members<\/h6><div id=\"ac-586\" class=\"c-accordion__content\"><div class=\"d-flex row justify-content-between px-2 pb-4\">\n\n\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7ca\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nGiulio Ba\u00f9\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:giulio.bau@unipi.it\">giulio.bau@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c800\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nClara Grassi\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:clara.grassi@dm.unipi.it\">clara.grassi@dm.unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7cd\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nGiovanni Federico Gronchi\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:giovanni.federico.gronchi@unipi.it\">giovanni.federico.gronchi@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7cf\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nGiacomo Lari\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:giacomo.lari@unipi.it\">giacomo.lari@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-587\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Collaborators<\/h6><div id=\"ac-587\" class=\"c-accordion__content\"><div class=\"d-flex row justify-content-between px-2 pb-4\">\n\n\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nClaudio Bombardelli (Universidad Polit\u00e9cnica de Madrid)\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:claudio.bombardelli@upm.es\">claudio.bombardelli@upm.es<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"https:\/\/www.unipi.it\/ateneo\/organizzazione\/persone\/giordana-bucchioni-176300\/\" target=\"_blank\" rel=\"noopener noreferrer\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nGiordana Bucchioni (Universit\u00e0 di Pisa)\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:giordana.bucchioni@ing.unipi.it\">giordana.bucchioni@ing.unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nIrene Cavallari (Universit\u00e0 di Pisa)\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:irene.cavallari@dm.unipi.it\">irene.cavallari@dm.unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nJavier Hernando-Ayuso (ISpace)\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:j-hernando@ispace-inc.com\">j-hernando@ispace-inc.com<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nMelaine Saillenfest (LTE -- Observatoire de Paris)\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:melaine.saillenfest@obspm.fr\">melaine.saillenfest@obspm.fr<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nGiovanni Valsecchi (Istituto di Astrofisica e Planetologia Spaziali (IAPS-INAF))\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:Giovanni.Valsecchi@iaps.inaf.it\">Giovanni.Valsecchi@iaps.inaf.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h5 id=\"at-588\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Orbit determination (OD)<\/h5><div id=\"ac-588\" class=\"c-accordion__content\">\n<p>The Celestial Mechanics Group (CMG) boasts more than thirty years of experience in the dynamics and orbit determination of minor bodies of the solar system, e.g. Main Belt Asteroids (MBAs) and Near-Earth Asteroids (NEAs). Such work led to the realization of the online services AstDyS (it contains data about numbered and multi-opposition asteroids, including for example their orbital elements with the related uncertainties and proper elements) and NEODyS (it contains data about NEAs, including close approaches information, and probabilities of impact with the Earth). Since 2006 the CMG has also been involved in research in the field of space debris. In these broad fields of research, a non-exhaustive list of sub-topics is the following.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>New initial OD methods for very short arcs of observations: this problem arises from the fact that the next-generation surveys (e.g. Pan-STARRS, LSST) will be able to gather a huge number of observations of small celestial bodies per night.<\/li>\n\n\n\n<li>Classification of the asteroid families in the Main Belt.<\/li>\n\n\n\n<li>Impact Monitoring (IM) of NEAs: the goal of IM is to establish, starting from observations, if a given NEA could have a chance to impact the Earth in the future. Such algorithms have been implemented in the CLOMON2 software (since 2002), which daily processes observational data from observers around the world by calculating the orbits of objects and their uncertainty. In the last ten years the NEOScan software has been developed: it analyzes the NEOCP data (where there are objects with very few observations) to determine the type of object and, in the case of a NEA, evaluate possible imminent impacts.<\/li>\n\n\n\n<li>Chaotic OD: it is the problem of determining the state and the associated uncertainty of a chaotic dynamical system from a set of observations. In particular, we want to understand the behavior of the uncertainty as the number of observations grows and how it changes if a dynamical parameter is included among the variables to be determined; such analysis is applied to celestial bodies that undergo several close encounters with planets or planets&#8217; satellites.<\/li>\n\n\n\n<li>Correlation and OD for space debris.<\/li>\n\n\n\n<li>Collision avoidance of space debris: we study the problem of finding in a given time interval (usually a few days) which pairs of space debris orbiting around the Earth can become sufficiently close to each other, providing also the probability of this event. Due to the big number of space debris present in the catalog, filters are necessary to quickly discard many pairs of objects. One of these filters consists of a new procedure to speed up the computation of the minimum distance between two confocal comics.<\/li>\n<\/ul>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-589\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Members<\/h6><div id=\"ac-589\" class=\"c-accordion__content\"><div class=\"d-flex row justify-content-between px-2 pb-4\">\n\n\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7ca\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nGiulio Ba\u00f9\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:giulio.bau@unipi.it\">giulio.bau@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c800\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nClara Grassi\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:clara.grassi@dm.unipi.it\">clara.grassi@dm.unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7cd\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nGiovanni Federico Gronchi\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:giovanni.federico.gronchi@unipi.it\">giovanni.federico.gronchi@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7cf\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nGiacomo Lari\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:giacomo.lari@unipi.it\">giacomo.lari@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7c7\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nGiacomo Tommei\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:giacomo.tommei@unipi.it\">giacomo.tommei@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-5810\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Collaborators<\/h6><div id=\"ac-5810\" class=\"c-accordion__content\"><div class=\"d-flex row justify-content-between px-2 pb-4\">\n\n\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nRobert Jedicke (University of Hawaii)\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:jedicke@hawaii.edu\">jedicke@hawaii.edu<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nZoran Kne\u017eevi\u0107 (Astronomical Observatory Belgrade)\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:zoran@aob.rs\">zoran@aob.rs<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nErica Scantamburlo (Universit\u00e0 di Torino)\n\n<\/span><br>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nFederica Spoto (Center for Astrophysics | Harvard & Smithsonian)\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:federica.spoto@cfa.harvard.edu\">federica.spoto@cfa.harvard.edu<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nGiovanni Valsecchi (Istituto di Astrofisica e Planetologia Spaziali (IAPS-INAF))\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:Giovanni.Valsecchi@iaps.inaf.it\">Giovanni.Valsecchi@iaps.inaf.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h5 id=\"at-5811\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Variational methods to study periodic orbits of the $N$-body problem<\/h5><div id=\"ac-5811\" class=\"c-accordion__content\">\n<p>We search for new periodic orbits of the Newtonian $N$-body problem as minimizers of the Lagrangian action functional in a set of symmetric loops, imposing also topological constraints. We also search for periodic motions with the same symmetries and topological constraints in the case of non-Newtonian forces, with interaction potentials of the form $1\/r^\\alpha$ ($\\alpha&gt;1$), where $r$ is the distance between the two bodies. The linear stability of such orbits is also investigated.<\/p>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-5812\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Members<\/h6><div id=\"ac-5812\" class=\"c-accordion__content\"><div class=\"d-flex row justify-content-between px-2 pb-4\">\n\n\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7cd\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nGiovanni Federico Gronchi\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:giovanni.federico.gronchi@unipi.it\">giovanni.federico.gronchi@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-5813\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Collaborators<\/h6><div id=\"ac-5813\" class=\"c-accordion__content\"><div class=\"d-flex row justify-content-between px-2 pb-4\">\n\n\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nMarco Fenucci (Near-Earth Object Coordination Centre - ESA)\n\n<\/span><br>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nMaria Giovanna Fusco (Universit\u00e0 degli Studi dell'Aquila)\n\n<\/span><br>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h5 id=\"at-5814\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Dynamical Systems<\/h5><div id=\"ac-5814\" class=\"c-accordion__content\">\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-5815\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Members<\/h6><div id=\"ac-5815\" class=\"c-accordion__content\"><div class=\"d-flex row justify-content-between px-2 pb-4\">\n\n\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7da\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nClaudio Bonanno\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:claudio.bonanno@unipi.it\">claudio.bonanno@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7db\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nCarlo Carminati\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:carlo.carminati@unipi.it\">carlo.carminati@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63822bbf7942943d6350d693\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nGianluigi Del Magno\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:gianluigi.delmagno@unipi.it\">gianluigi.delmagno@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63822bbf7942943d6350d691\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nStefano Galatolo\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:stefano.galatolo@unipi.it\">stefano.galatolo@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=638f8389c48db50bbcd31b30\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nPaolo Giulietti\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:paolo.giulietti@unipi.it\">paolo.giulietti@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<p>Below is the list of the specific topics studied in this research area, each of them with a detailed description and the lists of members and collaborators.<\/p>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h5 id=\"at-5816\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Complexity of time series<\/h5><div id=\"ac-5816\" class=\"c-accordion__content\">\n<p>The methods of nonlinear dynamical systems have been applied to the study of time series since the 90s. These applications have included time series of different origins, biomedical, economic, physical, etc. In particular, it is by now clear that one useful method is the classification of the time series in terms of some notion of entropy and complexity. We collaborate with Centro Piaggio of the University of Pisa to study the complexity of biomedical time series and the effects of noise on their classification.<\/p>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-5817\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Members<\/h6><div id=\"ac-5817\" class=\"c-accordion__content\"><div class=\"d-flex row justify-content-between px-2 pb-4\">\n\n\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7da\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nClaudio Bonanno\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:claudio.bonanno@unipi.it\">claudio.bonanno@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-5818\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Collaborators<\/h6><div id=\"ac-5818\" class=\"c-accordion__content\"><div class=\"d-flex row justify-content-between px-2 pb-4\">\n\n\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"https:\/\/www.unipi.it\/ateneo\/organizzazione\/persone\/martina-bianco-197184\/\" target=\"_blank\" rel=\"noopener noreferrer\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nMartina Bianco (Universit\u00e0 di Pisa)\n\n<\/span><br>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"https:\/\/www.unipi.it\/ateneo\/organizzazione\/persone\/vincenzo-catrambone-147179\/\" target=\"_blank\" rel=\"noopener noreferrer\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nVincenzo Catrambone (Universit\u00e0 di Pisa)\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:vincenzo.catrambone@unipi.it\">vincenzo.catrambone@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"https:\/\/www.unipi.it\/ateneo\/organizzazione\/persone\/andrea-scarciglia-205042\/\" target=\"_blank\" rel=\"noopener noreferrer\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nAndrea Scarciglia (Universit\u00e0 di Pisa)\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:andrea.scarciglia@centropiaggio.unipi.it\">andrea.scarciglia@centropiaggio.unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"https:\/\/www.unipi.it\/ateneo\/organizzazione\/persone\/gaetano-valenza-95977\/\" target=\"_blank\" rel=\"noopener noreferrer\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nGaetano Valenza (Universit\u00e0 di Pisa)\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:gaetano.valenza@unipi.it\">gaetano.valenza@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h5 id=\"at-5819\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Dynamical systems with singularities and billiards<\/h5><div id=\"ac-5819\" class=\"c-accordion__content\">\n<p><strong>Hyperbolic Systems with Singularities.<\/strong> A hyperbolic dynamical system is characterized by the presence of expanding and contracting directions. This property produces a complex behavior that in many ways appears stochastic despite the deterministic nature of the system. We are interested in hyperbolic dynamical systems with piecewise regular dynamics (systems with singularities). They represent natural models for mechanical systems with collisions such as billiards. The main aim of the project is the study of the ergodic properties of hyperbolic systems with singularities. In particular, we want to study the existence and properties of special invariant measures called SRB that describe the statistical properties of most of the system\u2019s orbits. We are also interested in the construction of hyperbolic billiards and the analysis of their ergodic properties. Conditions on the geometry of the billiard table and on the law of reflection that guarantee the hyperbolicity of billiard tables in the plane are well known. The goal is to weaken these conditions and extend them to billiards in Euclidean spaces of any dimension.<\/p>\n\n\n\n<p><strong>Generic Properties of Convex Billiards.<\/strong> We investigate generic properties of billiards in convex regions of any size with a regular border (Birkhoff billiards). A property of particular interest is the positivity of the topological entropy which guarantees the existence of a non-trivial hyperbolic set (Smale\u2019s horseshoe). The genericity of this property is known for Birkhoff billiards in the plane. The extension of this result to Birkhoff billiards in arbitrary dimensions is the main objective of this project.<\/p>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-5820\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Members<\/h6><div id=\"ac-5820\" class=\"c-accordion__content\"><div class=\"d-flex row justify-content-between px-2 pb-4\">\n\n\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63822bbf7942943d6350d693\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nGianluigi Del Magno\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:gianluigi.delmagno@unipi.it\">gianluigi.delmagno@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-5821\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Collaborators<\/h6><div id=\"ac-5821\" class=\"c-accordion__content\"><div class=\"d-flex row justify-content-between px-2 pb-4\">\n\n\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nMario Bessa (Universidade da Beira Interior)\n\n<\/span><br>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nPaulo Duarte (Universidade de Lisboa)\n\n<\/span><br>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nJo\u00e3o Lopes Dias (ISEG - Universidade de Lisboa)\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:jldias@iseg.ulisboa.pt\">jldias@iseg.ulisboa.pt<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nJos\u00e9 Pedro Romana Gaiv\u00e3o (ISEG - Universidade de Lisboa)\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:jpgaivao@iseg.ulisboa.pt\">jpgaivao@iseg.ulisboa.pt<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nMaria Joana Torres (Centro de Matematica (CMAT) - Universidade do Minho)\n\n<\/span><br>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h5 id=\"at-5822\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Statistical properties of dynamical systems<\/h5><div id=\"ac-5822\" class=\"c-accordion__content\">\n<p>Our group is interested in the study of the statistical properties of discrete and continuous group actions describing physical phenomena at different scales. We are mostly interested in spectral methods, which have interesting applications in other contexts. The dynamical systems we study are divided into three classes: uniformly hyperbolic systems; non-uniformly hyperbolic and infinite-measure systems; parabolic systems.<\/p>\n\n\n\n<p><strong>Uniformly hyperbolic systems.<\/strong> We are interested in the statistical properties of single and coupled systems. The main properties we study are the existence of rare events and their frequency, and the robustness of the system to small perturbations.<\/p>\n\n\n\n<p><strong>Non-uniformly hyperbolic and infinite-measure systems.<\/strong> In this case, many of the classical results fail. We are interested in studying the asymptotic behaviour of Birkhoff sums (i.e. the sum of an observable along the orbits of the system), the notion of mixing (i.e. the speed of the loss of memory along the orbits of the system), the analytical properties of the transfer operator and the dynamical zeta function (tools of the so-called thermodynamic formalism approach). In particular, we consider dynamical systems related to regular and multi-dimensional continued fractions algorithms, and to the geodesic and horocycle flows on modular surfaces.<\/p>\n\n\n\n<p><strong>Parabolic systems. <\/strong>These systems are characterised by slow convergence for the Birkhoff sums of the observables along the orbits of the system. The main idea is to accelerate the system or decompose it by looking at observables in suitable anisotropic spaces of functions. By these techniques, one obtains information on the speed of convergence to the equilibrium state and identifies eventual deviations from the typical behaviour or obstructions to it.<\/p>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-5823\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Members<\/h6><div id=\"ac-5823\" class=\"c-accordion__content\"><div class=\"d-flex row justify-content-between px-2 pb-4\">\n\n\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7da\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nClaudio Bonanno\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:claudio.bonanno@unipi.it\">claudio.bonanno@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7db\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nCarlo Carminati\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:carlo.carminati@unipi.it\">carlo.carminati@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63822bbf7942943d6350d691\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nStefano Galatolo\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:stefano.galatolo@unipi.it\">stefano.galatolo@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=638f8389c48db50bbcd31b30\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nPaolo Giulietti\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:paolo.giulietti@unipi.it\">paolo.giulietti@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-5824\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Collaborators<\/h6><div id=\"ac-5824\" class=\"c-accordion__content\"><div class=\"d-flex row justify-content-between px-2 pb-4\">\n\n\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nMauro Artigiani (Universidad Nacional de Colombia)\n\n<\/span><br>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nOliver Butterley (Universit\u00e0 degli Studi di Roma Tor Vergata)\n\n<\/span><br>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nRoberto Castorrini (Universit\u00e0 degli Studi della Tuscia)\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:roberto.castorrini@gmail.com\">roberto.castorrini@gmail.com<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nGiampaolo Cristadoro (Universit\u00e0 degli Studi di Milano-Bicocca)\n\n<\/span><br>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nThomas Garrity (Williams College)\n\n<\/span><br>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nStefano Isola (Universit\u00e0 di Camerino)\n\n<\/span><br>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nMarco Lenci (Universit\u00e0 di Bologna)\n\n<\/span><br>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nDavide Ravotti (Universit\u00e9 de Lille)\n\n<\/span><br>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nTanja Schindler (University of Exeter)\n\n<\/span><br>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nMatteo Tanzi (King's College London)\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:matteo.tanzi@kcl.ac.uk\">matteo.tanzi@kcl.ac.uk<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nSandro Vaienti (CNRS, Universit\u00e9 de Toulon, Aix-Marseille Universit\u00e9)\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:vaienti@cpt.univ-mrs.fr\">vaienti@cpt.univ-mrs.fr<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h5 id=\"at-5825\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Stochastic dynamical systems and applications<\/h5><div id=\"ac-5825\" class=\"c-accordion__content\">\n<p><strong>Stochastic Dynamical Systems for Climate Studies.<\/strong> We are interested in applying transfer operator techniques and results obtained in the case of abstract dynamical systems to certain climate models. Once a model flow has been constructed, it is possible to construct operators close in spirit to the transfer operator associated to the time-one map of the flow. The statistical properties of such a system can then be investigated through the functional analytic properties of the operator. We are particularly interested in three aspects of such a study. First, when we interpret the response of the system to the perturbations, we investigate how the invariant measure changes, i.e., the so-called \u201clinear response\u201d of the system (or its absence). Second, we compare our abstract asymptotic results with the existence of appropriate time scales, we do so by scouting for metastable observables, i.e., for example, the system might not be in equilibrium but might stay very close to a periodic cycle for a very long time. Last, we study the appearance and distribution of extreme climatic events. This can be done by exploring recurrence properties to special sets of the phase space on which chosen observables are above\/below certain thresholds, which encode the extreme event.<\/p>\n\n\n\n<p><strong>Thermodynamic Formalism, Stochastic Filter and Stochastic Billiards.<\/strong> We study the ergodic properties of stochastic dynamical systems generated by transformations with hyperbolic behaviour on average through the analysis of the spectrum of the transfer operator (thermodynamic formalism). This approach has interesting applications to the problem of the stability of the stochastic filter in probability theory. The problem consists in obtaining an optimal estimate of the state of the system starting from a sequence of observations affected by noise and showing that such an estimate loses memory of its initial condition. We are also interested in the study of stochastic billiards that are obtained from a deterministic billiard by replacing the law of specular reflection with a stochastic reflection law. An orbit of a stochastic billiard table is a Markov chain with transition probability depending on the geometry of the billiard table and the law of reflection. The goal is to show the existence of stationary measures for a large family of billiards with stochastic reflection. Of particular interest is the comparison between the statistical properties of a stochastic billiard and those of the corresponding deterministic billiard.<\/p>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-5826\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Members<\/h6><div id=\"ac-5826\" class=\"c-accordion__content\"><div class=\"d-flex row justify-content-between px-2 pb-4\">\n\n\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63822bbf7942943d6350d693\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nGianluigi Del Magno\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:gianluigi.delmagno@unipi.it\">gianluigi.delmagno@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=63822bbf7942943d6350d691\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nStefano Galatolo\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:stefano.galatolo@unipi.it\">stefano.galatolo@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=638f8389c48db50bbcd31b30\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nPaolo Giulietti\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:paolo.giulietti@unipi.it\">paolo.giulietti@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-5827\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Collaborators<\/h6><div id=\"ac-5827\" class=\"c-accordion__content\"><div class=\"d-flex row justify-content-between px-2 pb-4\">\n\n\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nJochen Broecker (University of Reading)\n\n<\/span><br>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nJo\u00e3o Lopes Dias (ISEG - Universidade de Lisboa)\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:jldias@iseg.ulisboa.pt\">jldias@iseg.ulisboa.pt<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nJos\u00e9 Pedro Romana Gaiv\u00e3o (ISEG - Universidade de Lisboa)\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:jpgaivao@iseg.ulisboa.pt\">jpgaivao@iseg.ulisboa.pt<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nSandro Vaienti (CNRS, Universit\u00e9 de Toulon, Aix-Marseille Universit\u00e9)\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:vaienti@cpt.univ-mrs.fr\">vaienti@cpt.univ-mrs.fr<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h5 id=\"at-5828\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Geometrical structure of the spacetime continuum<\/h5><div id=\"ac-5828\" class=\"c-accordion__content\">\n<p>We are interested in understanding the deep nature of spacetime taking inspiration from several tools provided by the mathematical sciences. This includes Lorentzian geometry under low regularity assumptions on the metric and connection, the theory of cone structures over manifolds, including Finslerian approaches, the theory of Lorentzian metric\/length spaces and, at an even deeper fundamental level, the theory of topological ordered spaces with measure. The goal is to prepare the ground for the understanding of a foreseeable quantization of spacetime where we shall need to describe it with a structure more general than the smooth Lorentzian manifold. We are also interested in global aspects of Lorentzian geometry in a traditional smooth setting and in Finslerian extensions of Einstein&#8217;s gravity.<\/p>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-5829\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Members<\/h6><div id=\"ac-5829\" class=\"c-accordion__content\"><div class=\"d-flex row justify-content-between px-2 pb-4\">\n\n\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=66e9b3e4ed270fad8e175af6\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nEttore Minguzzi\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:ettore.minguzzi@unipi.it\">ettore.minguzzi@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-5830\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Collaborators<\/h6><div id=\"ac-5830\" class=\"c-accordion__content\"><div class=\"d-flex row justify-content-between px-2 pb-4\">\n\n\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nAleksei Bykov (Universit\u00e0 degli Studi di Firenze)\n\n<\/span><br>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nAlfonso Garcia Parrado (Universidad de Cordoba)\n\n<\/span><br>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nStefan Suhr (Ruhr Universit\u00e4t Bochum)\n\n<\/span><br>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h5 id=\"at-5831\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Many-body quantum systems<\/h5><div id=\"ac-5831\" class=\"c-accordion__content\">\n<p>We consider quantum mechanical systems composed of many-particles. In this context, the relevant Schr\u00f6dinger equation lives in spaces of very high dimension, precluding any exact analysis or efficient numerical approach. However, when we look at the same systems at a larger scale, we observe emergent phenomena, such as phase transitions, universality, nonlinear effects. We focus on understanding the emergent behavior by methods of functional analysis, both from the dynamical as well as the spectral point of view.<\/p>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-5832\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Members<\/h6><div id=\"ac-5832\" class=\"c-accordion__content\"><div class=\"d-flex row justify-content-between px-2 pb-4\">\n\n\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=65ff16a8282479bbfbba78ad\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nChiara Boccato\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:chiara.boccato@unipi.it\">chiara.boccato@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=66753aac39cf57c129b5fea6\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nUmberto Morellini\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:umberto.morellini@dm.unipi.it\">umberto.morellini@dm.unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-5833\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Collaborators<\/h6><div id=\"ac-5833\" class=\"c-accordion__content\"><div class=\"d-flex row justify-content-between px-2 pb-4\">\n\n\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nSerena Cenatiempo (Gran Sasso Science Institute)\n\n<\/span><br>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nAndreas Deuchert (Virginia Tech)\n\n<\/span><br>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nDomenico Monaco (Sapienza Universit\u00e0 di Roma)\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:monaco@mat.uniroma1.it\">monaco@mat.uniroma1.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nBenjamin Schlein (Universit\u00e4t Z\u00fcrich)\n\n<\/span><br>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nRobert Seiringer (IST Austria)\n\n<\/span><br>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h5 id=\"at-5834\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Topological solitons<\/h5><div id=\"ac-5834\" class=\"c-accordion__content\">\n<p>We study the behaviour of localised, particle-like solutions of non-linear PDEs which are particularly stable due to their non-trivial topological properties. These type of objects arise naturally in high-energy theories and are of intrinsic mathematical interest. Examples include vortices, monopoles, instantons and gravitational instantons. Besides looking for exact solutions, we investigate the properties of the spaces of solutions (moduli spaces), as well as the behaviour of linear objects (such as spinors or electromagnetic fields) coupled to topological solitons.<\/p>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-5835\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Members<\/h6><div id=\"ac-5835\" class=\"c-accordion__content\"><div class=\"d-flex row justify-content-between px-2 pb-4\">\n\n\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<a href=\"\/en\/scheda-personale\/?person_id=66b22d2a07603ae95c6ed9f1\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a>\n<span class=\"card-title ml-2 h5\">\nGuido Franchetti\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:guido.franchetti@unipi.it\">guido.franchetti@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-5836\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Collaborators<\/h6><div id=\"ac-5836\" class=\"c-accordion__content\"><div class=\"d-flex row justify-content-between px-2 pb-4\">\n\n\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nDerek Harland (University of Leeds)\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:d.g.harland@leeds.ac.uk\">d.g.harland@leeds.ac.uk<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nCalum Ross (Edge Hill University)\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:Calum.Ross@edgehill.ac.uk\">Calum.Ross@edgehill.ac.uk<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"col-lg-6 col-12 py-2\">\n<div class=\"card h-100 m-2 shadow-sm\">\n<div class=\"card-body\">\n<i class=\"fas fa-id-card fa-fw\"><\/i>\n<span class=\"card-title ml-2 h5\">\nBernd Schroers (University of Edinburgh)\n\n<\/span><br>\n<i class=\"fas fa-at mr-3\"><\/i><a href=\"mailto:B.Schroers@ed.ac.uk\">B.Schroers@ed.ac.uk<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h4 class=\"wp-block-heading\">People<\/h4>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h5 id=\"at-5837\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Faculty<\/h5><div id=\"ac-5837\" class=\"c-accordion__content\">\n<!-- QUERY_STRING [https:\/\/manage.dm.unipi.it\/api\/v0\/staff?_sort=person&qualification__in=PO%7CPA%7CRTDa%7CRTDb%7CRIC&isInternal=1&SSD=MAT%2F07&startDate__lte_or_null=today&endDate__gte_or_null=today] -->\n<!-- 200 OK -->\n<table class=\"peopletable\">\n<thead><tr>\n<th>Name<\/th>\n<th class=\"enable-sort\">Surname<\/th>\n<th>Email<\/th>\n<th>Personal Card<\/th>\n<\/tr><\/thead><tbody>\n<tr>\n<td>Giulio<\/td>\n<td>Ba\u00f9<\/td>\n<td><a href=\"mailto:giulio.bau@unipi.it\"><i class=\"far fa-envelope fa-fw\"><\/i><span class=\"d-none d-lg-inline\">giulio.bau@unipi.it<\/span><\/a><\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7ca\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a><\/td>\n<\/tr>\n<tr>\n<td>Chiara<\/td>\n<td>Boccato<\/td>\n<td><a href=\"mailto:chiara.boccato@unipi.it\"><i class=\"far fa-envelope fa-fw\"><\/i><span class=\"d-none d-lg-inline\">chiara.boccato@unipi.it<\/span><\/a><\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=65ff16a8282479bbfbba78ad\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a><\/td>\n<\/tr>\n<tr>\n<td>Claudio<\/td>\n<td>Bonanno<\/td>\n<td><a href=\"mailto:claudio.bonanno@unipi.it\"><i class=\"far fa-envelope fa-fw\"><\/i><span class=\"d-none d-lg-inline\">claudio.bonanno@unipi.it<\/span><\/a><\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7da\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a><\/td>\n<\/tr>\n<tr>\n<td>Gianluigi<\/td>\n<td>Del Magno<\/td>\n<td><a href=\"mailto:gianluigi.delmagno@unipi.it\"><i class=\"far fa-envelope fa-fw\"><\/i><span class=\"d-none d-lg-inline\">gianluigi.delmagno@unipi.it<\/span><\/a><\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=63822bbf7942943d6350d693\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a><\/td>\n<\/tr>\n<tr>\n<td>Guido<\/td>\n<td>Franchetti<\/td>\n<td><a href=\"mailto:guido.franchetti@unipi.it\"><i class=\"far fa-envelope fa-fw\"><\/i><span class=\"d-none d-lg-inline\">guido.franchetti@unipi.it<\/span><\/a><\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=66b22d2a07603ae95c6ed9f1\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a><\/td>\n<\/tr>\n<tr>\n<td>Paolo<\/td>\n<td>Giulietti<\/td>\n<td><a href=\"mailto:paolo.giulietti@unipi.it\"><i class=\"far fa-envelope fa-fw\"><\/i><span class=\"d-none d-lg-inline\">paolo.giulietti@unipi.it<\/span><\/a><\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=638f8389c48db50bbcd31b30\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a><\/td>\n<\/tr>\n<tr>\n<td>Giovanni Federico<\/td>\n<td>Gronchi<\/td>\n<td><a href=\"mailto:giovanni.federico.gronchi@unipi.it\"><i class=\"far fa-envelope fa-fw\"><\/i><span class=\"d-none d-lg-inline\">giovanni.federico.gronchi@unipi.it<\/span><\/a><\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7cd\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a><\/td>\n<\/tr>\n<tr>\n<td>Giacomo<\/td>\n<td>Lari<\/td>\n<td><a href=\"mailto:giacomo.lari@unipi.it\"><i class=\"far fa-envelope fa-fw\"><\/i><span class=\"d-none d-lg-inline\">giacomo.lari@unipi.it<\/span><\/a><\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7cf\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a><\/td>\n<\/tr>\n<tr>\n<td>Ettore<\/td>\n<td>Minguzzi<\/td>\n<td><a href=\"mailto:ettore.minguzzi@unipi.it\"><i class=\"far fa-envelope fa-fw\"><\/i><span class=\"d-none d-lg-inline\">ettore.minguzzi@unipi.it<\/span><\/a><\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=66e9b3e4ed270fad8e175af6\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a><\/td>\n<\/tr>\n<tr>\n<td>Giacomo<\/td>\n<td>Tommei<\/td>\n<td><a href=\"mailto:giacomo.tommei@unipi.it\"><i class=\"far fa-envelope fa-fw\"><\/i><span class=\"d-none d-lg-inline\">giacomo.tommei@unipi.it<\/span><\/a><\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7c7\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a><\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h5 id=\"at-5838\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Affiliate Members<\/h5><div id=\"ac-5838\" class=\"c-accordion__content\">\n<!-- QUERY_STRING [https:\/\/manage.dm.unipi.it\/api\/v0\/staff?_sort=person&qualification__in=Collaboratore%7CProfessore+Emerito&isInternal=1&SSD=MAT%2F07&startDate__lte_or_null=today&endDate__gte_or_null=today] -->\n<!-- 200 OK -->\n<table class=\"peopletable\">\n<thead><tr>\n<th>Name<\/th>\n<th class=\"enable-sort\">Surname<\/th>\n<th>Email<\/th>\n<th>Personal Card<\/th>\n<\/tr><\/thead><tbody>\n<tr>\n<td>Giulia<\/td>\n<td>Schettino<\/td>\n<td><a href=\"mailto:giulia.schettino@unifi.it\"><i class=\"far fa-envelope fa-fw\"><\/i><span class=\"d-none d-lg-inline\">giulia.schettino@unifi.it<\/span><\/a><\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7f1\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a><\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h5 id=\"at-5839\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Former Members<\/h5><div id=\"ac-5839\" class=\"c-accordion__content\">\n<!-- QUERY_STRING [https:\/\/manage.dm.unipi.it\/api\/v0\/staff?_sort=person&qualification__in=ex+Docente&SSD=MAT%2F07&startDate__lte_or_null=today&endDate__gte_or_null=today] -->\n<!-- 200 OK -->\n<table class=\"peopletable\">\n<thead><tr>\n<th>Name<\/th>\n<th class=\"enable-sort\">Surname<\/th>\n<\/tr><\/thead><tbody>\n<tr>\n<td>Gianfranco<\/td>\n<td>Capriz<\/td>\n<\/tr>\n<tr>\n<td>Andrea<\/td>\n<td>Milani Comparetti<\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h5 id=\"at-5840\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Postdoctoral Fellows<\/h5><div id=\"ac-5840\" class=\"c-accordion__content\">\n<!-- QUERY_STRING [https:\/\/manage.dm.unipi.it\/api\/v0\/staff?_sort=person&qualification__in=Assegnista&isInternal=1&SSD=MAT%2F07&startDate__lte_or_null=today&endDate__gte_or_null=today] -->\n<!-- 200 OK -->\n<table class=\"peopletable\">\n<thead><tr>\n<th>Name<\/th>\n<th class=\"enable-sort\">Surname<\/th>\n<th>Email<\/th>\n<th>Personal Card<\/th>\n<\/tr><\/thead><tbody>\n<tr>\n<td>Clara<\/td>\n<td>Grassi<\/td>\n<td><a href=\"mailto:clara.grassi@dm.unipi.it\"><i class=\"far fa-envelope fa-fw\"><\/i><span class=\"d-none d-lg-inline\">clara.grassi@dm.unipi.it<\/span><\/a><\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c800\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a><\/td>\n<\/tr>\n<tr>\n<td>Umberto<\/td>\n<td>Morellini<\/td>\n<td><a href=\"mailto:umberto.morellini@dm.unipi.it\"><i class=\"far fa-envelope fa-fw\"><\/i><span class=\"d-none d-lg-inline\">umberto.morellini@dm.unipi.it<\/span><\/a><\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=66753aac39cf57c129b5fea6\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a><\/td>\n<\/tr>\n<tr>\n<td>Roberto<\/td>\n<td>Paoli<\/td>\n<td><a href=\"mailto:roberto.paoli@dm.unipi.it\"><i class=\"far fa-envelope fa-fw\"><\/i><span class=\"d-none d-lg-inline\">roberto.paoli@dm.unipi.it<\/span><\/a><\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=63c562f159df1b118b33faa7\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a><\/td>\n<\/tr>\n<tr>\n<td>Sharvari<\/td>\n<td>Tikekar<\/td>\n<td><a href=\"mailto:sharvari.tikekar@dm.unipi.it\"><i class=\"far fa-envelope fa-fw\"><\/i><span class=\"d-none d-lg-inline\">sharvari.tikekar@dm.unipi.it<\/span><\/a><\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=65e74bd5c2019549bdd8ae9e\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a><\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h5 id=\"at-5841\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Ph.D. Students at the Department of Mathematics<\/h5><div id=\"ac-5841\" class=\"c-accordion__content\">\n<!-- QUERY_STRING [https:\/\/manage.dm.unipi.it\/api\/v0\/staff?_sort=person&qualification__in=Dottorando+in+Matematica&isInternal=1&SSD=MAT%2F07&startDate__lte_or_null=today&endDate__gte_or_null=today] -->\n<!-- 200 OK -->\n<table class=\"peopletable\">\n<thead><tr>\n<th>Name<\/th>\n<th class=\"enable-sort\">Surname<\/th>\n<th>Email<\/th>\n<th>Personal Card<\/th>\n<\/tr><\/thead><tbody>\n<tr>\n<td>Nicola<\/td>\n<td>Bertozzi<\/td>\n<td><a href=\"mailto:nicola.bertozzi@phd.unipi.it\"><i class=\"far fa-envelope fa-fw\"><\/i><span class=\"d-none d-lg-inline\">nicola.bertozzi@phd.unipi.it<\/span><\/a><\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=63cef8880570144d28d41c58\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a><\/td>\n<\/tr>\n<tr>\n<td>Anargyros<\/td>\n<td>Dogkas<\/td>\n<td><a href=\"mailto:anargyros.dogkas@phd.unipi.it\"><i class=\"far fa-envelope fa-fw\"><\/i><span class=\"d-none d-lg-inline\">anargyros.dogkas@phd.unipi.it<\/span><\/a><\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=6543b9f5370d65c031a31584\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a><\/td>\n<\/tr>\n<tr>\n<td>Miriam<\/td>\n<td>Falletta<\/td>\n<td><a href=\"mailto:miriam.falletta@phd.unipi.it\"><i class=\"far fa-envelope fa-fw\"><\/i><span class=\"d-none d-lg-inline\">miriam.falletta@phd.unipi.it<\/span><\/a><\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=63cef8880570144d28d41c52\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a><\/td>\n<\/tr>\n<tr>\n<td>Francesco<\/td>\n<td>Geroni<\/td>\n<td><a href=\"mailto:francesco.geroni@phd.unipi.it\"><i class=\"far fa-envelope fa-fw\"><\/i><span class=\"d-none d-lg-inline\">francesco.geroni@phd.unipi.it<\/span><\/a><\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=6543bbf8370d65c031a3195c\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a><\/td>\n<\/tr>\n<tr>\n<td>Maddalena<\/td>\n<td>Mochi<\/td>\n<td><a href=\"mailto:maddalena.mochi@phd.unipi.it\"><i class=\"far fa-envelope fa-fw\"><\/i><span class=\"d-none d-lg-inline\">maddalena.mochi@phd.unipi.it<\/span><\/a><\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=63cef8880570144d28d41c50\"><i class=\"fas fa-id-card fa-fw\"><\/i><\/a><\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h5 id=\"at-5842\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Ph.D. Students at other departments of the University of Pisa<\/h5><div id=\"ac-5842\" class=\"c-accordion__content\">\n<!-- QUERY_STRING [https:\/\/manage.dm.unipi.it\/api\/v0\/staff?_sort=person&qualification__in=Dottorando+Esterno&SSD=MAT%2F07&startDate__lte_or_null=today&endDate__gte_or_null=today] -->\n<!-- 200 OK -->\n<table class=\"peopletable\">\n<thead><tr>\n<th>Name<\/th>\n<th class=\"enable-sort\">Surname<\/th>\n<\/tr><\/thead><tbody>\n<tr>\n<td>Martina<\/td>\n<td>Bianco<\/td>\n<\/tr>\n<tr>\n<td>Siming<\/td>\n<td>Li<\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h4 class=\"wp-block-heading\">Ph.D. Theses supervised by members of the group<\/h4>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h5 id=\"at-5843\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">awarded by the University of Pisa<\/h5><div id=\"ac-5843\" class=\"c-accordion__content\"><!-- QUERY_STRING [https:\/\/manage.dm.unipi.it\/api\/v0\/thesis?_sort=-date&SSD=MAT%2F07&institutions=641b8b0b840928dc5b8da2e3] -->\n<!-- 200 OK -->\n<table>\n<thead><tr>\n<th>Year<\/th>\n<th>Name<\/th>\n<th class=\"enable-sort\">Surname<\/th>\n<th>Title of the Thesis<\/th>\n<th> Supervisor(s)<\/th>\n<\/tr><\/thead><tbody>\n<tr>\n<td>2025<\/td>\n<td>Andrea<\/td>\n<td>Scarciglia<\/td>\n<td>Physiological noise in complex neuro-cardiovascular systems<\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7da\">Claudio  Bonanno<\/a> and Gaetano  Valenza<\/td>\n<\/tr>\n<tr>\n<td>2024<\/td>\n<td>Clara<\/td>\n<td>Grassi<\/td>\n<td>Orbits, encounters and collisions: applications to asteroids and artificial satellites<\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7cd\">Giovanni Federico  Gronchi<\/a><\/td>\n<\/tr>\n<tr>\n<td>2023<\/td>\n<td>Irene<\/td>\n<td>Cavallari<\/td>\n<td>Patched dynamics and perturbation theory in some problems of Celestial Mechanics<\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7ca\">Giulio  Ba\u00f9<\/a> and <a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7cd\">Giovanni Federico  Gronchi<\/a><\/td>\n<\/tr>\n<tr>\n<td>2020<\/td>\n<td>Marco<\/td>\n<td>Fenucci<\/td>\n<td>Variational methods and Hamiltonian perturbation theory applied to the N-body problem: a theoretical and computational approach<\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7cd\">Giovanni Federico  Gronchi<\/a><\/td>\n<\/tr>\n<tr>\n<td>2018<\/td>\n<td>H\u00e9l\u00e8ne<\/td>\n<td>Ma<\/td>\n<td>On the determination of preliminary orbits and detection of possible conjunctions for space debris<\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7cd\">Giovanni Federico  Gronchi<\/a> and Andrea  Milani Comparetti<\/td>\n<\/tr>\n<tr>\n<td>2018<\/td>\n<td>Alessio<\/td>\n<td>Del Vigna<\/td>\n<td>On Impact Monitoring of Near-Earth Asteroids<\/td>\n<td>Andrea  Milani Comparetti<\/td>\n<\/tr>\n<tr>\n<td>2018<\/td>\n<td>Giacomo<\/td>\n<td>Lari<\/td>\n<td>The Galilean satellites' dynamics and the estimation of the Jovian system's dissipation from JUICE data<\/td>\n<td>Andrea  Milani Comparetti<\/td>\n<\/tr>\n<tr>\n<td>2017<\/td>\n<td>Melaine<\/td>\n<td>Saillenfest<\/td>\n<td>Secular theories and orbital dynamics beyond Neptune<\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7c7\">Giacomo  Tommei<\/a><\/td>\n<\/tr>\n<tr>\n<td>2016<\/td>\n<td>Daniele<\/td>\n<td>Serra<\/td>\n<td>Satellite Geodesy of other planets<\/td>\n<td>Andrea  Milani Comparetti<\/td>\n<\/tr>\n<tr>\n<td>2012<\/td>\n<td>Stefano<\/td>\n<td>Cical\u00f2<\/td>\n<td>On theoretical and experimental aspects of the rotation of celestial bodies<\/td>\n<td>Andrea  Milani Comparetti<\/td>\n<\/tr>\n<tr>\n<td>2012<\/td>\n<td>Davide<\/td>\n<td>Farnocchia<\/td>\n<td>Population orbit determination: Algorithms and Simulations<\/td>\n<td>Andrea  Milani Comparetti<\/td>\n<\/tr>\n<tr>\n<td>2006<\/td>\n<td>Giacomo<\/td>\n<td>Tommei<\/td>\n<td>Impact monitoring of Near-Earth Objects: theoretical and computational\nresults<\/td>\n<td>Andrea  Milani Comparetti<\/td>\n<\/tr>\n<tr>\n<td>2002<\/td>\n<td>Giovanni Federico<\/td>\n<td>Gronchi<\/td>\n<td>Theoretical and computational aspects of collision singularities in the N\u2013body problem<\/td>\n<td>Andrea  Milani Comparetti<\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h5 id=\"at-5844\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">awarded by another institution<\/h5><div id=\"ac-5844\" class=\"c-accordion__content\"><!-- QUERY_STRING [https:\/\/manage.dm.unipi.it\/api\/v0\/thesis?_sort=-date&SSD=MAT%2F07&institutions__ne=641b8b0b840928dc5b8da2e3] -->\n<!-- 200 OK -->\n<table>\n<thead><tr>\n<th>Year<\/th>\n<th>Name<\/th>\n<th class=\"enable-sort\">Surname<\/th>\n<th>Title of the Thesis<\/th>\n<th> Institution<\/th>\n<th> Supervisor(s)<\/th>\n<\/tr><\/thead><tbody>\n<tr>\n<td>2017<\/td>\n<td>Davide<\/td>\n<td>Amato<\/td>\n<td>Advanced orbit propagation methods applied to asteroids and space debris<\/td>\n<td>Universidad Polit\u00e9cnica de Madrid<\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7ca\">Giulio  Ba\u00f9<\/a> and Claudio  Bombardelli<\/td>\n<\/tr>\n<tr>\n<td>2015<\/td>\n<td>Imen<\/td>\n<td>Chouari<\/td>\n<td>Op\u00e9rateurs de transfert en Th\u00e9orie Ergodique associ\u00e9s \u00e0 la transformation de Farey<\/td>\n<td>Universit\u00e9 de Tunis El Manar<\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7da\">Claudio  Bonanno<\/a><\/td>\n<\/tr>\n<tr>\n<td>2010<\/td>\n<td>Linda<\/td>\n<td>Dimare<\/td>\n<td>Problems of Celestial Mechanics<\/td>\n<td>Sapienza Universit\u00e0 di Roma<\/td>\n<td><a href=\"\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7cd\">Giovanni Federico  Gronchi<\/a> and Piero  Negrini<\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h4 class=\"wp-block-heading\">Grants<\/h4>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h5 id=\"at-5845\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Current<\/h5><div id=\"ac-5845\" class=\"c-accordion__content\"><!-- QUERY_STRING [https:\/\/manage.dm.unipi.it\/api\/v0\/grant?_sort=-endDate&startDate__lte_or_null=today&endDate__gte_or_null=today&SSD=MAT%2F07] -->\n<!-- 200 OK -->\n<ul>\n<li class=\"mb-2 currentmat\/01, mat\/02, mat\/03, mat\/04, mat\/05, mat\/06, mat\/07, mat\/08, mat\/09 National\">\n<h5 class=\"mb-0 font-weight-bold\">\n<a href=\"\/research\/grant-details\/?grant_id=651c0fd9a1e7fa876c5c8720\">\nDipartimento di Eccellenza 2023-2027\n<small class=\"text-muted\">(Progetto Ministeriale Nazionale)<\/small>\n<\/a><\/h5>\n<p class='mb-0'>Coordinator of the Research Unit: <a href='\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7be'>Matteo Novaga<\/a><\/p>\n<p>Project period: <em>Jan 01, 2023 &ndash; Dec 31, 2027<\/em><\/p>\n<\/li>\n<li class=\"mb-2 currentmat\/07 National\">\n<h5 class=\"mb-0 font-weight-bold\">\n<a href=\"\/research\/grant-details\/?grant_id=63860dd5f6c76fe5b717c7fb\">\nAttivit\u00e0 scientifiche per la Missione HERA\n<small class=\"text-muted\">(ASI Project)<\/small>\n<\/a><\/h5>\n<p class='mb-0'>Principal Investigator: <em>Paolo Tortora<\/em><\/p>\n<p class='mb-0'>Coordinator of the Research Unit: <a href='\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7c7'>Giacomo Tommei<\/a><\/p>\n<p>Project period: <em>Apr 06, 2022 &ndash; Jun 30, 2027<\/em><\/p>\n<\/li>\n<li class=\"mb-2 currentmat\/07 National\">\n<h5 class=\"mb-0 font-weight-bold\">\n<a href=\"\/research\/grant-details\/?grant_id=65fbf8b47d04ff8cbb4b33af\">\nStudio preliminare dei payloads per la missione URANUS flagship di NASA\n<small class=\"text-muted\">(ASI Project)<\/small>\n<\/a><\/h5>\n<p class='mb-0'>Principal Investigator: <em>Paolo Tortora<\/em><\/p>\n<p class='mb-0'>Coordinator of the Research Unit: <a href='\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7cf'>Giacomo Lari<\/a><\/p>\n<p>Project period: <em>Mar 21, 2024 &ndash; Sep 21, 2026<\/em><\/p>\n<\/li>\n<li class=\"mb-2 currentmat\/07 National\">\n<h5 class=\"mb-0 font-weight-bold\">\n<a href=\"\/research\/grant-details\/?grant_id=6780da6d9ac406d089fb105f\">\nRadio scienza: attivit\u00e0 scientifiche per la fase E della missione Bepi Colombo e per la missione estesa Juno\n<small class=\"text-muted\">(ASI Project)<\/small>\n<\/a><\/h5>\n<p class='mb-0'>Principal Investigator: <em>Luciano Iess<\/em><\/p>\n<p class='mb-0'>Coordinator of the Research Unit: <a href='\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7c7'>Giacomo Tommei<\/a><\/p>\n<p>Project period: <em>Aug 02, 2024 &ndash; Aug 01, 2026<\/em><\/p>\n<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h5 id=\"at-5846\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Past<\/h5><div id=\"ac-5846\" class=\"c-accordion__content\"><!-- QUERY_STRING [https:\/\/manage.dm.unipi.it\/api\/v0\/grant?_sort=-endDate&endDate__lt=today&SSD=MAT%2F07] -->\n<!-- 200 OK -->\n<ul>\n<li class=\"mb-2 currentmat\/07 National\">\n<h5 class=\"mb-0 font-weight-bold\">\n<a href=\"\/research\/grant-details\/?grant_id=65114e4f5eb7c4792bdd088b\">\nStochastic properties of dynamical systems CUP I53D23002380006\n<small class=\"text-muted\">(Prin 2022)<\/small>\n<\/a><\/h5>\n<p class='mb-0'>Principal Investigator: <em>Carlangelo Liverani<\/em><\/p>\n<p class='mb-0'>Coordinator of the Research Unit: <a href='\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7da'>Claudio Bonanno<\/a><\/p>\n<p>Project period: <em>Sep 28, 2023 &ndash; Feb 28, 2026<\/em><\/p>\n<\/li>\n<li class=\"mb-2 currentmat\/07 National\">\n<h5 class=\"mb-0 font-weight-bold\">\n<a href=\"\/research\/grant-details\/?grant_id=651299d75eb7c4792bdd3844\">\nMagnetic skyrmions, skyrmionic bubbles and domain walls for spintronic applications\n<small class=\"text-muted\">(Prin 2022 PNRR)<\/small>\n<\/a><\/h5>\n<p class='mb-0'>Principal Investigator: <a href='\/en\/scheda-personale\/?person_id=63cef8880570144d28d41c66'>Cyrill Muratov<\/a><\/p>\n<p>Project period: <em>Sep 28, 2023 &ndash; Feb 28, 2026<\/em><\/p>\n<\/li>\n<li class=\"mb-2 currentmat\/07 National\">\n<h5 class=\"mb-0 font-weight-bold\">\n<a href=\"\/research\/grant-details\/?grant_id=6641d95cb370b355eab243c9\">\nInteracting Quantum Systems: Topological Phenomena and Effective Theories - CUP G53D23001760001\n<small class=\"text-muted\">(Prin 2022)<\/small>\n<\/a><\/h5>\n<p class='mb-0'>Principal Investigator: <em>Domenico Monaco<\/em><\/p>\n<p class='mb-0'>Coordinator of the Research Unit: <a href='\/en\/scheda-personale\/?person_id=65ff16a8282479bbfbba78ad'>Chiara Boccato<\/a><\/p>\n<p>Project period: <em>Sep 28, 2023 &ndash; Feb 28, 2026<\/em><\/p>\n<\/li>\n<li class=\"mb-2 currentmat\/07 National\">\n<h5 class=\"mb-0 font-weight-bold\">\n<a href=\"\/research\/grant-details\/?grant_id=69b7deef2c76f400f2169a7f\">\nContemporary perspectives on geometry and gravity - CUP B53D23009340006\n<small class=\"text-muted\">(PRIN 2022)<\/small>\n<\/a><\/h5>\n<p class='mb-0'>Principal Investigator: <em>Nicola Gigli<\/em><\/p>\n<p class=\"mb-0\">Coordinator of the Research Unit: <em>Federico Talamucci<\/em><\/p>\n<p>Project period: <em>Oct 10, 2024 &ndash; Feb 28, 2026<\/em><\/p>\n<\/li>\n<li class=\"mb-2 currentmat\/07 National\">\n<h5 class=\"mb-0 font-weight-bold\">\n<a href=\"\/research\/grant-details\/?grant_id=641ce5e96bec133a94f4f741\">\nMonitoraggio Asteroidale (MONitoring ASTERoids)\n<small class=\"text-muted\">(ASI Project)<\/small>\n<\/a><\/h5>\n<p class='mb-0'>Principal Investigator: <a href='\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7c7'>Giacomo Tommei<\/a><\/p>\n<p>Project period: <em>Dec 05, 2022 &ndash; Dec 04, 2025<\/em><\/p>\n<\/li>\n<li class=\"mb-2 currentmat\/07 National\">\n<h5 class=\"mb-0 font-weight-bold\">\n<a href=\"\/research\/grant-details\/?grant_id=63860dd5f6c76fe5b717c845\">\nRadio scienza: attivit\u00e0 scientifiche per la fase E della missione Bepi Colombo e per la missione estesa Juno\n<small class=\"text-muted\">(ASI Project)<\/small>\n<\/a><\/h5>\n<p class='mb-0'>Principal Investigator: <em>Luciano Iess<\/em><\/p>\n<p class='mb-0'>Coordinator of the Research Unit: <a href='\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7c7'>Giacomo Tommei<\/a><\/p>\n<p>Project period: <em>Aug 02, 2022 &ndash; Aug 01, 2024<\/em><\/p>\n<\/li>\n<li class=\"mb-2 currentmat\/07 National\">\n<h5 class=\"mb-0 font-weight-bold\">\n<a href=\"\/research\/grant-details\/?grant_id=63860dd5f6c76fe5b717c802\">\nI-CELMECH \"New frontiers of Celestial Mechanics: theory and applications\"\n<small class=\"text-muted\">(Prin 2017)<\/small>\n<\/a><\/h5>\n<p class='mb-0'>Principal Investigator: <em>Massimiliano Guzzo<\/em><\/p>\n<p class='mb-0'>Coordinator of the Research Unit: <a href='\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7ca'>Giulio Ba\u00f9<\/a><\/p>\n<p>Project period: <em>Aug 01, 2019 &ndash; Aug 19, 2023<\/em><\/p>\n<\/li>\n<li class=\"mb-2 currentmat\/07 National\">\n<h5 class=\"mb-0 font-weight-bold\">\n<a href=\"\/research\/grant-details\/?grant_id=63860dd5f6c76fe5b717c807\">\nRegular and stochastic behaviour in dynamical systems\n<small class=\"text-muted\">(Prin 2017)<\/small>\n<\/a><\/h5>\n<p class='mb-0'>Principal Investigator: <em>Carlangelo Liverani<\/em><\/p>\n<p class='mb-0'>Coordinator of the Research Unit: <a href='\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7da'>Claudio Bonanno<\/a><\/p>\n<p>Project period: <em>Aug 01, 2019 &ndash; Aug 19, 2023<\/em><\/p>\n<\/li>\n<li class=\"mb-2 currentmat\/01, mat\/03, mat\/07 National\">\n<h5 class=\"mb-0 font-weight-bold\">\n<a href=\"\/research\/grant-details\/?grant_id=63860dd5f6c76fe5b717c7d2\">\nSistemi dinamici in logica, geometria, fisica matematica e scienza delle costruzioni\n<small class=\"text-muted\">(Progetti di Ricerca di Ateneo (PRA) 2020 - 2021)<\/small>\n<\/a><\/h5>\n<p class='mb-0'>Principal Investigator: <a href='\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7c7'>Giacomo Tommei<\/a><\/p>\n<p>Project period: <em>Jul 07, 2020 &ndash; Dec 31, 2022<\/em><\/p>\n<\/li>\n<li class=\"mb-2 currentmat\/07 International\">\n<h5 class=\"mb-0 font-weight-bold\">\n<a href=\"\/research\/grant-details\/?grant_id=63860dd5f6c76fe5b717c7e8\">\nStardust Reloaded\n<small class=\"text-muted\">(MSCA-ITN-2018 - Innovative Training Networks)<\/small>\n<\/a><\/h5>\n<p class='mb-0'>Coordinator of the Research Unit: <a href='\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7cd'>Giovanni Federico Gronchi<\/a><\/p>\n<p>Project period: <em>Nov 21, 2018 &ndash; Dec 31, 2022<\/em><\/p>\n<\/li>\n<li class=\"mb-2 currentmat\/07 National\">\n<h5 class=\"mb-0 font-weight-bold\">\n<a href=\"\/research\/grant-details\/?grant_id=63ad640ce91c8d0f758ad4f7\">\nDeterministic and stochastic dynamical systems for climate studies\n<small class=\"text-muted\">(Progetto Giovani GNFM)<\/small>\n<\/a><\/h5>\n<p class='mb-0'>Principal Investigator: <a href='\/en\/scheda-personale\/?person_id=638f8389c48db50bbcd31b30'>Paolo Giulietti<\/a><\/p>\n<p>Project period: <em>Feb 01, 2021 &ndash; Jul 31, 2022<\/em><\/p>\n<\/li>\n<li class=\"mb-2 currentmat\/07 National\">\n<h5 class=\"mb-0 font-weight-bold\">\n<a href=\"\/research\/grant-details\/?grant_id=63860dd5f6c76fe5b717c7f2\">\nRadio scienza per BepiColombo e Juno: prosecuzione attivit\u00e0 scientifiche\n<small class=\"text-muted\">(ASI Project)<\/small>\n<\/a><\/h5>\n<p class='mb-0'>Principal Investigator: <em>Luciano Iess<\/em><\/p>\n<p class='mb-0'>Coordinator of the Research Unit: <a href='\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7c7'>Giacomo Tommei<\/a><\/p>\n<p>Project period: <em>Apr 21, 2020 &ndash; Apr 20, 2022<\/em><\/p>\n<\/li>\n<li class=\"mb-2 currentmat\/07 National\">\n<h5 class=\"mb-0 font-weight-bold\">\n<a href=\"\/research\/grant-details\/?grant_id=63860dd5f6c76fe5b717c7f3\">\nRadio scienza per BepiColombo e Juno: prosecuzione attivit\u00e0 scientifiche\n<small class=\"text-muted\">(ASI Project)<\/small>\n<\/a><\/h5>\n<p class='mb-0'>Principal Investigator: <em>Luciano Iess<\/em><\/p>\n<p class='mb-0'>Coordinator of the Research Unit: <a href='\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7c7'>Giacomo Tommei<\/a><\/p>\n<p>Project period: <em>Dec 21, 2017 &ndash; Mar 20, 2020<\/em><\/p>\n<\/li>\n<li class=\"mb-2 currentmat\/01, mat\/03, mat\/05, mat\/07 National\">\n<h5 class=\"mb-0 font-weight-bold\">\n<a href=\"\/research\/grant-details\/?grant_id=63860dd5f6c76fe5b717c7dc\">\nSistemi dinamici in analisi, geometria, logica e meccanica celeste\n<small class=\"text-muted\">(Progetti di Ricerca di Ateneo (PRA) 2017 - 2018)<\/small>\n<\/a><\/h5>\n<p class='mb-0'>Principal Investigator: <a href='\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7c8'>Marco Abate<\/a><\/p>\n<p>Project period: <em>Apr 10, 2017 &ndash; Apr 09, 2019<\/em><\/p>\n<\/li>\n<li class=\"mb-2 currentmat\/07 National\">\n<h5 class=\"mb-0 font-weight-bold\">\n<a href=\"\/research\/grant-details\/?grant_id=63860dd5f6c76fe5b717c7f5\">\nRadioscienza per BepiColombo e Juno - fasi B2\/C\/D - Attivit\u00e0 scientifiche\n<small class=\"text-muted\">(ASI Project)<\/small>\n<\/a><\/h5>\n<p class='mb-0'>Principal Investigator: <em>Luciano Iess<\/em><\/p>\n<p class=\"mb-0\">Coordinator of the Research Unit: <em>Andrea Milani Comparetti<\/em><\/p>\n<p>Project period: <em>Dec 23, 2009 &ndash; Jul 20, 2017<\/em><\/p>\n<\/li>\n<li class=\"mb-2 currentmat\/07 International\">\n<h5 class=\"mb-0 font-weight-bold\">\n<a href=\"\/research\/grant-details\/?grant_id=63860dd5f6c76fe5b717c7e3\">\nITN Stardust - Workpackage Close-Range Navigation and Manipulation of Space Debris and Asteroids\n<small class=\"text-muted\">(FP7 Marie Curie Initial Training Networks (ITN) scheme)<\/small>\n<\/a><\/h5>\n<p class='mb-0'>Coordinator of the Research Unit: <a href='\/en\/scheda-personale\/?person_id=63860dd5f6c76fe5b717c7cd'>Giovanni Federico Gronchi<\/a><\/p>\n<p>Project period: <em>Feb 01, 2013 &ndash; Jan 31, 2017<\/em><\/p>\n<\/li>\n<li class=\"mb-2 currentmat\/07 National\">\n<h5 class=\"mb-0 font-weight-bold\">\n<a href=\"\/research\/grant-details\/?grant_id=63860dd5f6c76fe5b717c7f6\">\nRadioscienza per BepiColombo e Juno - fasi B2\/C\/D - Attivit\u00e0 scientifiche\n<small class=\"text-muted\">(ASI Project)<\/small>\n<\/a><\/h5>\n<p class='mb-0'>Principal Investigator: <em>Luciano Iess<\/em><\/p>\n<p class=\"mb-0\">Coordinator of the Research Unit: <em>Andrea Milani Comparetti<\/em><\/p>\n<p>Project period: <em>Jan 12, 2007 &ndash; Jan 11, 2009<\/em><\/p>\n<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h4 class=\"wp-block-heading\">Visitors<\/h4>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h5 id=\"at-5847\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Prospective<\/h5><div id=\"ac-5847\" class=\"c-accordion__content\"><!-- QUERY_STRING [https:\/\/manage.dm.unipi.it\/api\/v0\/visit?_sort=person&startDate__gt=today&SSD=MAT%2F07] -->\n<!-- 200 OK -->\n<table class=\"peopletable\">\n<thead><tr>\n<th>First Name<\/th>\n<th class=\"enable-sort\">Last Name<\/th>\n<th> Affiliation<\/th>\n<\/tr><\/thead><tbody>\n<tr>\n<td>Matteo<\/td>\n<td>Gallone<\/td>\n<td>Universit\u00e0 degli Studi di Milano (La Statale)<\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h5 id=\"at-5848\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Current<\/h5><div id=\"ac-5848\" class=\"c-accordion__content\"><!-- QUERY_STRING [https:\/\/manage.dm.unipi.it\/api\/v0\/visit?_sort=person&startDate__lte_or_null=today&endDate__gte_or_null=today&SSD=MAT%2F07] -->\n<!-- 200 OK -->\n<table class=\"peopletable\">\n<thead><tr>\n<th>First Name<\/th>\n<th class=\"enable-sort\">Last Name<\/th>\n<th> Affiliation<\/th>\n<th> Building<\/th>\n<th> Floor<\/th>\n<th> Office<\/th>\n<\/tr><\/thead><tbody>\n<tr>\n<td>Siming<\/td>\n<td>Li<\/td>\n<td>Dalian University<\/td>\n<td>Building A<\/td>\n<td>First floor<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h5 id=\"at-5849\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Grouped by year<\/h5><div id=\"ac-5849\" class=\"c-accordion__content\">\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-5850\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">2026<\/h6><div id=\"ac-5850\" class=\"c-accordion__content\"><!-- QUERY_STRING [https:\/\/manage.dm.unipi.it\/api\/v0\/visit?_sort=person&startDate__lte_or_null=2026-12-31&endDate__gte_or_null=2026-01-01&SSD=MAT%2F07] -->\n<!-- 200 OK -->\n<table class=\"peopletable\">\n<thead><tr>\n<th>First Name<\/th>\n<th class=\"enable-sort\">Last Name<\/th>\n<th> Affiliation<\/th>\n<th> From<\/th>\n<th> To<\/th>\n<\/tr><\/thead><tbody>\n<tr>\n<td>Riccardo<\/td>\n<td>Adami<\/td>\n<td>Politecnico di Torino<\/td>\n<td>Feb 09, 2026<\/td>\n<td>Feb 12, 2026<\/td>\n<\/tr>\n<tr>\n<td>Jean-Bernard<\/td>\n<td>Bru<\/td>\n<td>Basque Center for Applied Mathematics (BCAM)<\/td>\n<td>Feb 09, 2026<\/td>\n<td>Feb 13, 2026<\/td>\n<\/tr>\n<tr>\n<td>Lucrezia<\/td>\n<td>Cossetti<\/td>\n<td>UPV\/EHU<\/td>\n<td>Feb 08, 2026<\/td>\n<td>Feb 11, 2026<\/td>\n<\/tr>\n<tr>\n<td>Daniele<\/td>\n<td>Ferretti<\/td>\n<td>Gran Sasso Science Institute<\/td>\n<td>Feb 08, 2026<\/td>\n<td>Feb 12, 2026<\/td>\n<\/tr>\n<tr>\n<td>Matteo<\/td>\n<td>Gallone<\/td>\n<td>Universit\u00e0 degli Studi di Milano (La Statale)<\/td>\n<td>Apr 20, 2026<\/td>\n<td>Apr 30, 2026<\/td>\n<\/tr>\n<tr>\n<td>Filippo<\/td>\n<td>Girardi<\/td>\n<td>SNS, Pisa<\/td>\n<td>Feb 08, 2026<\/td>\n<td>Feb 12, 2026<\/td>\n<\/tr>\n<tr>\n<td>Ian<\/td>\n<td>Jauslin<\/td>\n<td>Rutgers, The State University of New Jersey<\/td>\n<td>Jan 14, 2026<\/td>\n<td>Jan 15, 2026<\/td>\n<\/tr>\n<tr>\n<td>Lucas<\/td>\n<td>Jougla<\/td>\n<td>Constructor University<\/td>\n<td>Feb 08, 2026<\/td>\n<td>Feb 12, 2026<\/td>\n<\/tr>\n<tr>\n<td>Bernhard<\/td>\n<td>Kepka<\/td>\n<td>Universit\u00e4t Z\u00fcrich<\/td>\n<td>Feb 08, 2026<\/td>\n<td>Feb 12, 2026<\/td>\n<\/tr>\n<tr>\n<td>Joachim<\/td>\n<td>Kerner<\/td>\n<td>University of Hagen<\/td>\n<td>Feb 08, 2026<\/td>\n<td>Feb 12, 2026<\/td>\n<\/tr>\n<tr>\n<td>Alfred<\/td>\n<td>Kirsch<\/td>\n<td>Technische Universit\u00e4t M\u00fcnchen (TUM)<\/td>\n<td>Feb 08, 2026<\/td>\n<td>Feb 12, 2026<\/td>\n<\/tr>\n<tr>\n<td>Siming<\/td>\n<td>Li<\/td>\n<td>Dalian University<\/td>\n<td>Feb 04, 2026<\/td>\n<td>Jul 31, 2026<\/td>\n<\/tr>\n<tr>\n<td>Jo\u00e3o<\/td>\n<td>Lopes Dias<\/td>\n<td>ISEG - Universidade de Lisboa<\/td>\n<td>Apr 15, 2026<\/td>\n<td>Apr 18, 2026<\/td>\n<\/tr>\n<tr>\n<td>Jessica Elisa<\/td>\n<td>Massetti<\/td>\n<td>Universit\u00e0 degli Studi di Roma Tor Vergata<\/td>\n<td>Feb 24, 2026<\/td>\n<td>Feb 27, 2026<\/td>\n<\/tr>\n<tr>\n<td>Vieri<\/td>\n<td>Mastropietro<\/td>\n<td>Sapienza Universit\u00e0 di Roma<\/td>\n<td>Feb 08, 2026<\/td>\n<td>Feb 12, 2026<\/td>\n<\/tr>\n<tr>\n<td>Ngoc Nhi<\/td>\n<td>Nguyen<\/td>\n<td>Universit\u00e9 de Lille<\/td>\n<td>Feb 08, 2026<\/td>\n<td>Feb 12, 2026<\/td>\n<\/tr>\n<tr>\n<td>Enrico<\/td>\n<td>Ortu<\/td>\n<td>Politecnico di Torino<\/td>\n<td>Feb 08, 2026<\/td>\n<td>Feb 12, 2026<\/td>\n<\/tr>\n<tr>\n<td>Lorenzo<\/td>\n<td>Pettinari<\/td>\n<td>Universit\u00e0 degli Studi di Trento<\/td>\n<td>Feb 08, 2026<\/td>\n<td>Feb 12, 2026<\/td>\n<\/tr>\n<tr>\n<td>Francesca<\/td>\n<td>Pieroni<\/td>\n<td>Sapienza Universit\u00e0 di Roma<\/td>\n<td>Feb 08, 2026<\/td>\n<td>Feb 12, 2026<\/td>\n<\/tr>\n<tr>\n<td>Marcello<\/td>\n<td>Porta<\/td>\n<td>SISSA, Trieste<\/td>\n<td>Feb 08, 2026<\/td>\n<td>Feb 12, 2026<\/td>\n<\/tr>\n<tr>\n<td>Simone<\/td>\n<td>Rademacher<\/td>\n<td>Ludwig-Maximilians Universit\u00e4t M\u00fcnchen<\/td>\n<td>Feb 08, 2026<\/td>\n<td>Feb 11, 2026<\/td>\n<\/tr>\n<tr>\n<td>Jonathan<\/td>\n<td>Rau<\/td>\n<td>Karlsruher Institut f\u00fcr Technologie (KIT)<\/td>\n<td>Feb 08, 2026<\/td>\n<td>Feb 12, 2026<\/td>\n<\/tr>\n<tr>\n<td>Jos\u00e9 Pedro<\/td>\n<td>Romana Gaiv\u00e3o<\/td>\n<td>ISEG - Universidade de Lisboa<\/td>\n<td>Apr 08, 2026<\/td>\n<td>Apr 18, 2026<\/td>\n<\/tr>\n<tr>\n<td>Thaddeus<\/td>\n<td>Roussign\u00e9<\/td>\n<td>Universit\u00e9 Paris Dauphine<\/td>\n<td>Feb 08, 2026<\/td>\n<td>Feb 12, 2026<\/td>\n<\/tr>\n<tr>\n<td>Andrew James<\/td>\n<td>Rout<\/td>\n<td>Politecnico di Milano<\/td>\n<td>Feb 08, 2026<\/td>\n<td>Feb 12, 2026<\/td>\n<\/tr>\n<tr>\n<td>Blazej<\/td>\n<td>Ruba<\/td>\n<td>University of Warsaw<\/td>\n<td>Feb 08, 2026<\/td>\n<td>Feb 12, 2026<\/td>\n<\/tr>\n<tr>\n<td>Benjamin<\/td>\n<td>Schlein<\/td>\n<td>Universit\u00e4t Z\u00fcrich<\/td>\n<td>Feb 09, 2026<\/td>\n<td>Feb 12, 2026<\/td>\n<\/tr>\n<tr>\n<td>Severin<\/td>\n<td>Schraven<\/td>\n<td>Technische Universit\u00e4t M\u00fcnchen (TUM)<\/td>\n<td>Feb 08, 2026<\/td>\n<td>Feb 12, 2026<\/td>\n<\/tr>\n<tr>\n<td>Marvin R.<\/td>\n<td>Schulz<\/td>\n<td>University of Copenhagen<\/td>\n<td>Feb 08, 2026<\/td>\n<td>Feb 12, 2026<\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-5854\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">2025<\/h6><div id=\"ac-5854\" class=\"c-accordion__content\"><!-- QUERY_STRING [https:\/\/manage.dm.unipi.it\/api\/v0\/visit?_sort=person&startDate__lte_or_null=2025-12-31&endDate__gte_or_null=2025-01-01&SSD=MAT%2F07] -->\n<!-- 200 OK -->\n<table class=\"peopletable\">\n<thead><tr>\n<th>First Name<\/th>\n<th class=\"enable-sort\">Last Name<\/th>\n<th> Affiliation<\/th>\n<th> From<\/th>\n<th> To<\/th>\n<\/tr><\/thead><tbody>\n<tr>\n<td>Jon<\/td>\n<td>Aaronson<\/td>\n<td>Tel Aviv University<\/td>\n<td>Sep 30, 2025<\/td>\n<td>Oct 03, 2025<\/td>\n<\/tr>\n<tr>\n<td>Elisa Maria<\/td>\n<td>Alessi<\/td>\n<td>IMATI-CNR, Milano<\/td>\n<td>Nov 11, 2025<\/td>\n<td>Nov 13, 2025<\/td>\n<\/tr>\n<tr>\n<td>Simon<\/td>\n<td>Becker<\/td>\n<td>ETH Z\u00fcrich<\/td>\n<td>Jun 02, 2025<\/td>\n<td>Jun 04, 2025<\/td>\n<\/tr>\n<tr>\n<td>Yann<\/td>\n<td>Chaubet<\/td>\n<td>Universit\u00e9 de Nantes<\/td>\n<td>May 14, 2025<\/td>\n<td>May 16, 2025<\/td>\n<\/tr>\n<tr>\n<td>Haritha<\/td>\n<td>Cheriyath<\/td>\n<td>Center for Mathematical Modeling<\/td>\n<td>Sep 10, 2025<\/td>\n<td>Sep 22, 2025<\/td>\n<\/tr>\n<tr>\n<td>Kasun<\/td>\n<td>Fernando<\/td>\n<td>Brunel University of London<\/td>\n<td>Jun 08, 2025<\/td>\n<td>Jun 21, 2025<\/td>\n<\/tr>\n<tr>\n<td>Robert<\/td>\n<td>Jedicke<\/td>\n<td>University of Hawaii<\/td>\n<td>Nov 11, 2025<\/td>\n<td>Nov 15, 2025<\/td>\n<\/tr>\n<tr>\n<td>Joachim<\/td>\n<td>Kerner<\/td>\n<td>University of Hagen<\/td>\n<td>Mar 17, 2025<\/td>\n<td>Mar 21, 2025<\/td>\n<\/tr>\n<tr>\n<td>Damya<\/td>\n<td>Souami<\/td>\n<td>IMCCE -- Observatoire de Paris<\/td>\n<td>Jun 09, 2025<\/td>\n<td>Jun 12, 2025<\/td>\n<\/tr>\n<tr>\n<td>Giovanni<\/td>\n<td>Valsecchi<\/td>\n<td>Istituto Nazionale di Astrofisica, Osservatorio Astrofisico di Torino<\/td>\n<td>May 28, 2025<\/td>\n<td>May 28, 2025<\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-5851\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">2024<\/h6><div id=\"ac-5851\" class=\"c-accordion__content\"><!-- QUERY_STRING [https:\/\/manage.dm.unipi.it\/api\/v0\/visit?_sort=person&startDate__lte_or_null=2024-12-31&endDate__gte_or_null=2024-01-01&SSD=MAT%2F07] -->\n<!-- 200 OK -->\n<table class=\"peopletable\">\n<thead><tr>\n<th>First Name<\/th>\n<th class=\"enable-sort\">Last Name<\/th>\n<th> Affiliation<\/th>\n<th> From<\/th>\n<th> To<\/th>\n<\/tr><\/thead><tbody>\n<tr>\n<td>Mauro<\/td>\n<td>Artigiani<\/td>\n<td>Universidad del Rosario<\/td>\n<td>Jun 10, 2024<\/td>\n<td>Jun 21, 2024<\/td>\n<\/tr>\n<tr>\n<td>Niels<\/td>\n<td>Benedikter<\/td>\n<td>Universit\u00e0 degli Studi di Milano (La Statale)<\/td>\n<td>Dec 08, 2024<\/td>\n<td>Dec 11, 2024<\/td>\n<\/tr>\n<tr>\n<td>Anna Miriam<\/td>\n<td>Benini<\/td>\n<td>Universit\u00e0 di Parma<\/td>\n<td>Jan 16, 2024<\/td>\n<td>Jan 17, 2024<\/td>\n<\/tr>\n<tr>\n<td>Antonio<\/td>\n<td>Capella<\/td>\n<td>Universidad Nacional Aut\u00f3noma de M\u00e9xico<\/td>\n<td>Sep 30, 2024<\/td>\n<td>Oct 04, 2024<\/td>\n<\/tr>\n<tr>\n<td>Lorenzo<\/td>\n<td>Carletti<\/td>\n<td>Universit\u00e0 di Bologna<\/td>\n<td>Jul 22, 2024<\/td>\n<td>Jul 24, 2024<\/td>\n<\/tr>\n<tr>\n<td>Xiangyuan<\/td>\n<td>Li<\/td>\n<td>Universit\u00e4t Z\u00fcrich<\/td>\n<td>Nov 19, 2024<\/td>\n<td>Nov 22, 2024<\/td>\n<\/tr>\n<tr>\n<td>Stefano<\/td>\n<td>Mar\u00f2<\/td>\n<td>Universidad de Oviedo<\/td>\n<td>Jun 10, 2024<\/td>\n<td>Jun 14, 2024<\/td>\n<\/tr>\n<tr>\n<td>Domenico<\/td>\n<td>Monaco<\/td>\n<td>Sapienza Universit\u00e0 di Roma<\/td>\n<td>Dec 08, 2024<\/td>\n<td>Dec 11, 2024<\/td>\n<\/tr>\n<tr>\n<td>Umberto<\/td>\n<td>Morellini<\/td>\n<td>Universit\u00e9 Paris Dauphine<\/td>\n<td>Jun 24, 2024<\/td>\n<td>Jun 28, 2024<\/td>\n<\/tr>\n<tr>\n<td>Ngoc Nhi<\/td>\n<td>Nguyen<\/td>\n<td>Universit\u00e0 degli Studi di Milano (La Statale)<\/td>\n<td>Dec 08, 2024<\/td>\n<td>Dec 11, 2024<\/td>\n<\/tr>\n<tr>\n<td>Jos\u00e9 Pedro<\/td>\n<td>Romana Gaiv\u00e3o<\/td>\n<td>ISEG - Universidade de Lisboa<\/td>\n<td>Jun 29, 2024<\/td>\n<td>Jul 04, 2024<\/td>\n<\/tr>\n<tr>\n<td>Melaine<\/td>\n<td>Saillenfest<\/td>\n<td>IMCCE -- Observatoire de Paris<\/td>\n<td>Nov 16, 2024<\/td>\n<td>Nov 23, 2024<\/td>\n<\/tr>\n<tr>\n<td>Theresa<\/td>\n<td>Simon<\/td>\n<td>Universit\u00e4t M\u00fcnster<\/td>\n<td>Feb 22, 2024<\/td>\n<td>Feb 27, 2024<\/td>\n<\/tr>\n<tr>\n<td>Cinzia<\/td>\n<td>Soresina<\/td>\n<td>Universit\u00e0 degli Studi di Trento<\/td>\n<td>Feb 21, 2024<\/td>\n<td>Feb 23, 2024<\/td>\n<\/tr>\n<tr>\n<td>David<\/td>\n<td>Vokroulicky<\/td>\n<td>Charles University - Univerzita Karlova<\/td>\n<td>Jun 18, 2024<\/td>\n<td>Jun 27, 2024<\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-5852\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">2023<\/h6><div id=\"ac-5852\" class=\"c-accordion__content\"><!-- QUERY_STRING [https:\/\/manage.dm.unipi.it\/api\/v0\/visit?_sort=person&startDate__lte_or_null=2023-12-31&endDate__gte_or_null=2023-01-01&SSD=MAT%2F07] -->\n<!-- 200 OK -->\n<table class=\"peopletable\">\n<thead><tr>\n<th>First Name<\/th>\n<th class=\"enable-sort\">Last Name<\/th>\n<th> Affiliation<\/th>\n<th> From<\/th>\n<th> To<\/th>\n<\/tr><\/thead><tbody>\n<tr>\n<td>Mauro<\/td>\n<td>Artigiani<\/td>\n<td>Universidad del Rosario<\/td>\n<td>Oct 16, 2023<\/td>\n<td>Oct 18, 2023<\/td>\n<\/tr>\n<tr>\n<td>Adriano<\/td>\n<td>Barra<\/td>\n<td>Universit\u00e0 del Salento<\/td>\n<td>May 31, 2023<\/td>\n<td>Jun 01, 2023<\/td>\n<\/tr>\n<tr>\n<td>Tien-Cuong<\/td>\n<td>Dinh<\/td>\n<td>National University of Singapore<\/td>\n<td>Oct 23, 2023<\/td>\n<td>Oct 23, 2023<\/td>\n<\/tr>\n<tr>\n<td>Giovanni<\/td>\n<td>Panti<\/td>\n<td>Universit\u00e0 degli Studi di Udine<\/td>\n<td>Feb 14, 2023<\/td>\n<td>Feb 17, 2023<\/td>\n<\/tr>\n<tr>\n<td>Davide<\/td>\n<td>Ravotti<\/td>\n<td>Universit\u00e4t Wien<\/td>\n<td>Feb 13, 2023<\/td>\n<td>Feb 18, 2023<\/td>\n<\/tr>\n<tr>\n<td>Davide<\/td>\n<td>Ravotti<\/td>\n<td>Universit\u00e4t Wien<\/td>\n<td>Sep 03, 2023<\/td>\n<td>Sep 09, 2023<\/td>\n<\/tr>\n<tr>\n<td>Ana<\/td>\n<td>Sanches Rivero<\/td>\n<td>Universidad de Sevilla<\/td>\n<td>Sep 15, 2023<\/td>\n<td>Dec 14, 2023<\/td>\n<\/tr>\n<tr>\n<td>Theresa<\/td>\n<td>Simon<\/td>\n<td>Universit\u00e4t M\u00fcnster<\/td>\n<td>Mar 27, 2023<\/td>\n<td>Apr 02, 2023<\/td>\n<\/tr>\n<tr>\n<td>Matteo<\/td>\n<td>Tanzi<\/td>\n<td>CNRS, Sorbonne Universit\u00e9<\/td>\n<td>Jan 25, 2023<\/td>\n<td>Jan 28, 2023<\/td>\n<\/tr>\n<tr>\n<td>Matteo<\/td>\n<td>Tanzi<\/td>\n<td>Laboratoire de Probabilit\u00e9s, Statistique et Mod\u00e9lisation<\/td>\n<td>Dec 19, 2023<\/td>\n<td>Dec 21, 2023<\/td>\n<\/tr>\n<tr>\n<td>Paulo<\/td>\n<td>Varandas<\/td>\n<td>Universidade Federal da Bahia<\/td>\n<td>Oct 04, 2023<\/td>\n<td>Oct 12, 2023<\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h6 id=\"at-5853\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">2022<\/h6><div id=\"ac-5853\" class=\"c-accordion__content\"><!-- QUERY_STRING [https:\/\/manage.dm.unipi.it\/api\/v0\/visit?_sort=person&startDate__lte_or_null=2022-12-31&endDate__gte_or_null=2022-01-01&SSD=MAT%2F07] -->\n<!-- 200 OK -->\n<table class=\"peopletable\">\n<thead><tr>\n<th>First Name<\/th>\n<th class=\"enable-sort\">Last Name<\/th>\n<th> Affiliation<\/th>\n<th> From<\/th>\n<th> To<\/th>\n<\/tr><\/thead><tbody>\n<tr>\n<td>Claudio<\/td>\n<td>Bombardelli<\/td>\n<td>Universidad Polit\u00e9cnica de Madrid<\/td>\n<td>Jul 24, 2022<\/td>\n<td>Aug 17, 2022<\/td>\n<\/tr>\n<tr>\n<td>Giovanni<\/td>\n<td>Canestrari<\/td>\n<td>Universit\u00e0 degli Studi di Roma Tor Vergata<\/td>\n<td>Nov 09, 2022<\/td>\n<td>Nov 09, 2022<\/td>\n<\/tr>\n<tr>\n<td>Alessandro<\/td>\n<td>Della Corte<\/td>\n<td>Universit\u00e0 di Camerino<\/td>\n<td>Nov 30, 2022<\/td>\n<td>Nov 30, 2022<\/td>\n<\/tr>\n<tr>\n<td>Mikael<\/td>\n<td>Granvik<\/td>\n<td>University of Helsinki<\/td>\n<td>Nov 07, 2022<\/td>\n<td>Nov 11, 2022<\/td>\n<\/tr>\n<tr>\n<td>Robert<\/td>\n<td>Jedicke<\/td>\n<td>University of Hawaii<\/td>\n<td>Oct 31, 2022<\/td>\n<td>Nov 04, 2022<\/td>\n<\/tr>\n<tr>\n<td>Alexey<\/td>\n<td>Korepanov<\/td>\n<td>Laboratoire de Probabilit\u00e9s, Statistique et Mod\u00e9lisation<\/td>\n<td>Dec 12, 2022<\/td>\n<td>Dec 17, 2022<\/td>\n<\/tr>\n<tr>\n<td>Philipp<\/td>\n<td>Kunde<\/td>\n<td>Universit\u00e4t Hamburg<\/td>\n<td>Dec 12, 2022<\/td>\n<td>Dec 17, 2022<\/td>\n<\/tr>\n<tr>\n<td>Carlangelo<\/td>\n<td>Liverani<\/td>\n<td>Universit\u00e0 degli Studi di Roma Tor Vergata<\/td>\n<td>Dec 12, 2022<\/td>\n<td>Dec 17, 2022<\/td>\n<\/tr>\n<tr>\n<td>Jo\u00e3o<\/td>\n<td>Lopes Dias<\/td>\n<td>ISEG - Universidade de Lisboa<\/td>\n<td>Oct 08, 2022<\/td>\n<td>Oct 19, 2022<\/td>\n<\/tr>\n<tr>\n<td>Jo\u00e3o<\/td>\n<td>Lopes Dias<\/td>\n<td>ISEG - Universidade de Lisboa<\/td>\n<td>Oct 27, 2022<\/td>\n<td>Oct 28, 2022<\/td>\n<\/tr>\n<tr>\n<td>Jos\u00e9 Pedro<\/td>\n<td>Romana Gaiv\u00e3o<\/td>\n<td>ISEG - Universidade de Lisboa<\/td>\n<td>Oct 27, 2022<\/td>\n<td>Oct 28, 2022<\/td>\n<\/tr>\n<tr>\n<td>Melaine<\/td>\n<td>Saillenfest<\/td>\n<td>IMCCE -- Observatoire de Paris<\/td>\n<td>Dec 01, 2022<\/td>\n<td>Dec 03, 2022<\/td>\n<\/tr>\n<tr>\n<td>Tanja<\/td>\n<td>Schindler<\/td>\n<td>Universit\u00e4t Wien<\/td>\n<td>May 27, 2022<\/td>\n<td>Jul 02, 2022<\/td>\n<\/tr>\n<tr>\n<td>Paolo<\/td>\n<td>Tortora<\/td>\n<td>Universit\u00e0 di Bologna<\/td>\n<td>Nov 07, 2022<\/td>\n<td>Nov 11, 2022<\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>The research areas of the Mathematical Physics group are: More specific research topics investigated by this group are described below.&hellip;<\/p>\n<p><a class=\"btn btn-dark btn-sm unipi-read-more-link\" href=\"https:\/\/www.dm.unipi.it\/research\/areas\/mathematical-physics\/\">Read More&#8230;<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":3211,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-58","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Mathematical Physics - Research<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link 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