Mathematical Analysis

The scientific activity of the Group “Mathematical Analysis” is focused on different subjects in the area of Calculus of Variations, Geometric Measure Theory, Fluid Dynamics, Dispersive equations, Nonlinear Analysis, Ergodic Theory, and Dynamical Systems.
Our research mainly contributes to Pure Mathematics but provides also several applications in the natural and applied sciences, e.g., Physics, Biology, and Mechanics.
The group works in close collaboration with members of the Faculty of Sciences of Scuola Normale Superiore and  Centro di Ricerca Matematica Ennio De Giorgi.

The group runs a Seminar Series: further information may be found here.

Research Topics

Calculus of variations and geometric measure theory

The research of a large portion of the group “Mathematical Analysis” is focused on the Calculus of Variations and Geometric Measure Theory. The list of research directions includes shape and spectral optimization, free boundary problems, isoperimetric problems and related stability estimates, local and non-local geometric flows, the structure of measures and differentiability, analysis and geometric measure theory in non-Euclidean settings.
A relevant part of the research in this area is devoted to the application of Calculus of Variations and Geometric Measure Theory to problems in Mathematical Physics, Continuum Mechanics, and other areas of Mathematics.

This group has strong connections with Scuola Normale Superiore and Centro De Giorgi.
The repository CVGMT collects preprints in this area, as well as information about seminars and conferences.

Members
Giovanni Alberti
giovanni.alberti@unipi.it
Konstantinos Bessas
konstantinos.bessas@phd.unipi.it
Luca Briani Medeiros Dos Santo
luca.briani@phd.unipi.it
Giuseppe Buttazzo
giuseppe.buttazzo@unipi.it
Maria Stella Gelli
maria.stella.gelli@unipi.it
Massimo Gobbino
massimo.gobbino@unipi.it
Valentino Magnani
valentino.magnani@unipi.it
Cyrill Muratov
cyrill.muratov@unipi.it
Matteo Novaga
matteo.novaga@unipi.it
Roberto Ognibene
roberto.ognibene12@gmail.com
Emanuele Paolini
emanuele.paolini@unipi.it
Alessandra Pluda
alessandra.pluda@unipi.it
Aldo Pratelli
aldo.pratelli@unipi.it
Luciano Sciaraffia Rubio
luciano.sciaraffia@phd.unipi.it
Giorgio Tortone
giorgio.tortone@dm.unipi.it
Vincenzo Maria Tortorelli
vincenzo.tortorelli@unipi.it
Dario Trevisan
dario.trevisan@unipi.it
Bozhidar Velichkov
bozhidar.velichkov@unipi.it

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.

Free boundary problems

The free boundary problems are PDE problems (often elliptic or parabolic) in which the domain of the solution is not a priori prescribed but is part of the variables of the problem. The boundary conditions are overdetermined and might involve the trace of the function, its gradient (or just the normal derivative), and the curvature of the boundary. Solutions to free boundary problems are obtained for instance from the minimization of variational functionals that take into account both the state function (the solution of the PDE) and its domain of definition. Well-known examples of free boundary problems are the one-phase and the two-phase Bernoulli problems, the obstacle problem, the thin-obstacle problem, the optimal partitions problems, Mumford-Shah, free transmission problems, and their parabolic counterparts, for instance, the Stefan problem.

The focus is on the free boundary regularity theory, which is the study of the fine local structure of the free boundary and relates to the analysis of the interplay between the geometry of the domain and the behavior of the state function (the solution of the PDE). Of particular interest are theorems that guarantee (under some geometric conditions) that the boundary is a smooth manifold (the so-called epsilon-regularity theorems) and the analysis of the free boundaries around singularities. The methods include blow-up analysis, monotonicity formulas, density estimates, estimates on the dimension of the singular set, viscosity solutions, analysis of the stable cones, improvement-of-flatness methods, epiperimetric inequalities.

The free boundary problems are strongly related to problems in Geometric Analysis as the regularity of area-minimizing surfaces and currents; in Elliptic PDEs, for instance to the analysis of the nodal sets to the solutions of PDEs or the behavior at the boundary of the solutions (Boundary Harnack inequalities); and also to some Shape Optimization problems.

Members
Giulia Bevilacqua
giulia.bevilacqua@dm.unipi.it
Lorenzo Ferreri
lorenzo.ferreri@sns.it
Roberto Ognibene
roberto.ognibene12@gmail.com
Giorgio Tortone
giorgio.tortone@dm.unipi.it
Bozhidar Velichkov
bozhidar.velichkov@unipi.it
Collaborators
Guido De Philippis
Carlo Gasparetto
Dario Mazzoleni
dario.mazzoleni@unipv.it
Luca Spolaor
lspolaor@ucsd.edu
Susanna Terracini
Geometric flows

The idea of deforming a geometric object by means of a parabolic PDEs to simplify it (e.g. to reduce its topological complexity or to make it more symmetric) goes back to Eells and Sampson who introduced the first geometric evolution equation: the harmonic map flow. Since 1964, geometric flows have been applied to a variety of topological, analytical, and physical problems, giving in some cases very fruitful results.

Among other geometric equations, we mention the mean curvature flow. This flow can be regarded as the gradient flow of the area functional: an n-dimensional time-dependent surface evolves with normal velocity its mean curvature, at any point and time. In place of the area functional, one may consider generalized perimeters, such as the fractional perimeter, and the corresponding gradient flows. Concerning the study of these flows, we are interested in the long-time existence of (weak and strong) solutions and in the classification of possible singularities. Besides the urge to introduce a non-local version of mean curvature flow, one wants also to extend it to the more singular geometric objects.

Motived by the study of grain boundaries, Brakke introduces the first weak versions of the flow and in the years a plethora of weak definitions (level set approach, minimizing movements, thresholding scheme, canonical Brakke flow) has been developed, but the one-dimensional version of this problem is also studied in the framework of classical PDEs. In such a situation the flow is called network flow.

We are interested in several aspects of evolution: well-posedness, long-time behavior, analysis of singularities, flow past singularities, and stability. Our main goal is to exploit the known results to a higher dimension.

Members
Matteo Novaga
matteo.novaga@unipi.it
Alessandra Pluda
alessandra.pluda@unipi.it
Collaborators
Annalisa Cesaroni
Antonin Chambolle
Carlo Mantegazza
Rafe Mazzeo
Massimiliano Morini
Marcello Ponsiglione
Marco Pozzetta
marco.pozzetta@gmail.com
Mariel Saez
Geometric measure theory

The development of Geometric Measure Theory (GMT) began about one hundred years ago, with the first intrinsic notions of dimension for general sets, which could be possibly non-integer, and the corresponding intrinsic notions of measure, where “intrinsic” means that it does not rely on parametrizations.
In the second half of the last century, one of the driving problems was the existence of d-dimensional surfaces with minimal area and prescribed boundary (Plateau problem), which led to the development of several “weak” notions of surface, such as finite perimeter set (Caccioppoli, De Giorgi), integral currents (Federer and Fleming), and varifolds (Almgren).

In the past fifty years these notions played a fundamental role in the treatment of many problems of geometric nature besides minimal surfaces, from the asymptotic behavior of singular perturbations problems in continuum mechanics and physics (e.g, scalar and vector models of Ginzburg-Landau type) to the notions of weak solutions of geometric evolution problems (e.g., the mean curvature flow).

At the same time, many attempts have been made to extend these theories to various non-Euclidean settings (sub-Riemannian manifolds and metric spaces with bounds on curvature). These attempts have led to several fundamental questions that have not yet been fully answered–indeed in many cases our understanding is still quite limited.

The Italian mathematical community in Calculus of Variations and Geometric Measure Theory, whose origins can be traced back to the work of Ennio De Giorgi here in Pisa, gave essential contributions to the developments mentioned above. Among the topics currently studied in our department, we mention the following:

• GMT in sub-Riemannian manifolds: area formulas, contact sets, currents;
• Minimal partitions;
• Gauss-Green formulas, sets of finite perimeter and rectifiability in stratified Lie groups;
• Weak solutions to geometric evolution problems;
• Structure of measures and differentiability of Lipschitz functions.
Members
Giovanni Alberti
giovanni.alberti@unipi.it
Valentino Magnani
valentino.magnani@unipi.it
Matteo Novaga
matteo.novaga@unipi.it
Emanuele Paolini
emanuele.paolini@unipi.it
Vincenzo Maria Tortorelli
vincenzo.tortorelli@unipi.it
Collaborators
Marianna Csornyei
csornyei@math.uchicago.edu
Andrea Marchese
andrea.marchese@unitn.it
Annalisa Massacesi
annalisa.massaccesi@unipd.it
Andrea Merlo
andrea.merlo@u-psud.fr
David Preiss
d.preiss@warwick.ac.uk
Eugene Stepanov
stepanov.eugene@gmail.com
Shape optimization

The field of shape optimization had very strong growth in the last decades, mainly due to the several applications in engineering, but also for the mathematical interest related to several problems in spectral geometry. The goal is to find a domain $\Omega$ that minimizes a given cost functional, that may involve geometrical quantities as perimeter or measure, as well as other quantities related to PDEs like for instance the related energies or eigenvalues. Showing the existence of optimal shapes, and their regularity is often a very challenging issue that needs the development of new and deep tools.

Members
Luca Briani Medeiros Dos Santo
luca.briani@phd.unipi.it
Giuseppe Buttazzo
giuseppe.buttazzo@unipi.it
Aldo Pratelli
aldo.pratelli@unipi.it
Collaborators
Guy Bouchitté
Lorenzo Brasco
Thierry Champion
Luigi De Pascale
Faustino Maestre
fmaestre@us.es
Francesca Agnese Prinari
Michiel van den Berg
PDEs, ODEs, and dynamical systems
Members
Jacopo Bellazzini
jacopo.bellazzini@unipi.it
Luigi Carlo Berselli
luigi.carlo.berselli@unipi.it
Carlo Carminati
carlo.carminati@unipi.it
Elisabetta Chiodaroli
elisabetta.chiodaroli@unipi.it
Luigi Forcella
luigi.forcella@unipi.it
Stefano Galatolo
stefano.galatolo@unipi.it
Marco Gipo Ghimenti
marco.ghimenti@unipi.it
Marina Ghisi
marina.ghisi@unipi.it
Massimo Gobbino
massimo.gobbino@unipi.it
Carlo Romano Grisanti
carlo.romano.grisanti@unipi.it
Francesco Grotto
francesco.grotto@unipi.it
Pietro Majer
pietro.majer@unipi.it
Claudio Saccon
claudio.saccon@unipi.it
Nicola Visciglia
nicola.visciglia@unipi.it

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.

Dynamical systems and ergodic theory

Our research focuses on the statistical properties of deterministic and random dynamical systems.

These studies have a wide range of applications, from a number of theoretical and geometrical questions to the understanding of the behavior of models of real-world phenomena like the dynamics of fluids, the evolution of climate and its extreme events, the dynamics of extended systems in a mean-field coupling and other complex systems. The methods used in this research are often related to probability, functional analysis, transport, and geometric measure theory.

Our research also focused on reliable computational tools for the study of the statistical properties of dynamics, computer-aided proofs, and their relation to theoretical computer science.

Members
Carlo Carminati
carlo.carminati@unipi.it
Roberto Castorrini
roberto.castorrini@gmail.com
Stefano Galatolo
stefano.galatolo@unipi.it
Paolo Giulietti
paolo.giulietti@unipi.it
Collaborators
Wael Bahsoun
Angelo Di Garbo
Franco Flandoli
franco.flandoli@gmail.com
Gary Froyland
Michael Ghil
Dong Han Kim
Maurizio Monge
Isaia Nisoli
Maria José Pacifico
Federico Giovanni Poloni
federico.poloni@unipi.it
Yuzuru Sato
Matteo Tanzi
Sandro Vaienti
Fluid dynamics equations

Our research focuses on the pure and applied aspects of mathematical fluid dynamics of Newtonian and non-Newtonian fluids.

The research interests span from the most theoretical questions of existence, uniqueness, and regularity of weak solutions towards applications to the numerical analysis of such flows (with finite element/differences methods) and to the study of turbulent flows, with applications to geophysical problems. The methods we use stem from those of classical analysis of PDEs in Sobolev spaces, but for the problems we consider we are using also: convex integration, analysis in Orlicz, weighted spaces, and approximate methods like reduced-order ones. More specifically for the Equations of classical fluid mechanics: incompressible Euler and Navier-Stokes equations. Existence, uniqueness, properties, and regularity of weak and suitable solutions.

Concerning non-Newtonian fluids, we are interested in the existence, regularity, numerical approximation, and long-time behavior of classes of p-fluids or electrorheological ones.

For the turbulent flows, we study the mathematical properties and the mathematical modeling of such methods, having in mind the application to the study of boundary layers and air-sea interaction, together with other multi-phase problems arising in the study of volcanic eruptions.

Members
Luigi Carlo Berselli
luigi.carlo.berselli@unipi.it
Elisabetta Chiodaroli
elisabetta.chiodaroli@unipi.it
Carlo Romano Grisanti
carlo.romano.grisanti@unipi.it
Collaborators
Matteo Cerminara
Francesca Crispo
Camillo De Lellis
Eduard Feireisl
Ondrej Kreml
Paolo Maremonti
Michael Růžička
Stefano Spirito
Athanasios Tzavaras
Emil Wiedemann
Hyperbolic Equations, dispersive equations, and Kirchhoff equations
Members
Jacopo Bellazzini
jacopo.bellazzini@unipi.it
Luigi Forcella
luigi.forcella@unipi.it
Marina Ghisi
marina.ghisi@unipi.it
Nicola Visciglia
nicola.visciglia@unipi.it
Nicolas Burq
Tohru Ozawa
Fabrice Planchon
David Ruiz
Nikolay Tzvetkov
Dinh Van Duong
Nonlinear analysis

The nonlinear analysis group focuses on partial differential equations of elliptic and hyperbolic types in which the presence of the nonlinear term is crucial for the existence and qualitative properties of solutions.

The research interests span from nonlinear Schroedinger equations and Gross-Pitaevskij in a Euclidean setting to Yamabe problems on compact manifolds. The main topics of the research concerning elliptic equations are the existence and multiplicity of concentrated solutions, qualitative properties, blow-up analysis, and compactness of solutions. On the time-dependent side, we focus on the existence of solitons, stability and instability issues, and long-time dynamics for equations of physical interest. Another field of research is related to functional inequalities in presence of nonlocal terms: the existence of maximizers and the role of symmetry.

Members
Jacopo Bellazzini
jacopo.bellazzini@unipi.it
Marco Gipo Ghimenti
marco.ghimenti@unipi.it
Pietro Majer
pietro.majer@unipi.it
Anna Maria Micheletti
a.micheletti@dma.unipi.it
Collaborators
Mónica Clapp
Simone Dovetta
Louis Jeanjean
Enno Lenzmann
Vitaly Moroz
Angela Pistoia
David Ruiz
Jean Van Schaftingen
Pietro d'Avenia

People

Faculty
Name Surname Email Personal Card
Giovanni Alberti
Jacopo Bellazzini
Luigi Carlo Berselli
Giuseppe Buttazzo
Carlo Carminati
Elisabetta Chiodaroli
Luigi Forcella
Stefano Galatolo
Maria Stella Gelli
Marco Gipo Ghimenti
Marina Ghisi
Massimo Gobbino
Carlo Romano Grisanti
Francesco Grotto
Valentino Magnani
Pietro Majer
Matteo Novaga
Emanuele Paolini
Alessandra Pluda
Aldo Pratelli
Giuseppe Puglisi
Claudio Saccon
Vincenzo Maria Tortorelli
Bozhidar Velichkov
Nicola Visciglia
Affiliate Members
Name Surname Email Personal Card
Paolo Acquistapace
Francesco Bartaloni
Hugo Beirao da Veiga
Vieri Benci
Ferruccio Colombini
Placido Longo
Ilaria Lucardesi
Antonio Marino
Anna Maria Micheletti
Sergio Spagnolo
Antonio Tarsia
Postdoctoral Fellows
Name Surname Email Personal Card
Luca Benatti
Diego Berti
Giulia Bevilacqua
Masayuki Hayashi
Roberto Ognibene
Giorgio Tortone
Ph.D. Students at the University of Pisa
Name Surname Email Personal Card
Daniele Barbera
Konstantinos Bessas
Luca Briani Medeiros Dos Santo
Mario Rastrelli
Luciano Sciaraffia Rubio
Ph.D. Students at other institutions
Name Surname Affiliation Email
Davide Carazzato SNS, Pisa
Tommaso Cortopassi SNS, Pisa
Lorenzo Ferreri SNS, Pisa
François Legeais Université de Rennes
Joao Enrique Lirio Universidade Federal do Rio de Janeiro

Ph.D. Theses supervised by members of the group

awarded by the University of Pisa
Year Name Surname Title of the Thesis Supervisor(s)
2021 Luigi Marangio Rigorous computational methods for understanding the statistical behavior of random dynamical systems. Stefano Galatolo and Christophe Guyeux
2021 Obinna Kennedy Idu Higher order rectifiability criteria and a model for soap films Giovanni Alberti
2020 Marco Pozzetta Willmore-type energies of curves and surfaces Matteo Novaga
2019 Francesco Bartaloni Infinite horizon optimal control problems with non-compact control space. Existence results and dynamic programming Fausto Gozzi and Paolo Acquistapace
2019 Giacomo Del Nin Some asymptotic results on the global shape of planar clusters Giovanni Alberti
2019 Valerio Pagliari Asymptotic behaviour of rescaled nonlocal functionals and evolutions Matteo Novaga
2018 Harish Shrivastava Shape optimisation problems for integral functionals and regularity properties of optimal domain Giuseppe Buttazzo
2017 Anna Rita Giammetta Perturbed Hamiltonians in one dimension: analysis for linear and nonlinear Schrödinger problems Vladimir Simeonov Gueorguiev
2016 Augusto Gerolin Multi-marginal optimal transport and potential optimization problems for Schrodinger operators Giuseppe Buttazzo
2016 Alessandra Pluda Minimal and evolving networks Matteo Novaga and Carlo Mantegazza
2015 Marco Caroccia On the isoperimetric properties of planar N-clusters Giovanni Alberti and Francesco Maggi
2014 Serena Guarino Lo Bianco Some optimization problems in mass transport theory Giuseppe Buttazzo
2013 Andrea Marchese Two applications of the Theory of Currents Giovanni Alberti
2013 Matteo Scienza Differentiability properties and characterization of H-convex functions Valentino Magnani
2012 Nguyet Minh Mach Weak solution to rate-independent systems: Existence and Regularity Giovanni Alberti
2011 Al- hassem Nayam Shape optimization problems of higher codimension Giuseppe Buttazzo
2010 Jmmy Alfonso Mauro Some analytic questions in mathematical physic problems Vladimir Simeonov Gueorguiev and Paolo Maremonti
2010 Lorenzo Brasco Geodesics and PDE methods in transport models Giuseppe Buttazzo and Guillaume Carlier and Filippo Santambrogio
2008 Davide Catania Linear and nonlinear perturbed wave equations Vladimir Simeonov Gueorguiev
2006 Angel Ivanov Nonlinear evolution equations in mathematical physics Vladimir Simeonov Gueorguiev
2006 Mirko Tarulli Di Giallonardo Smoothing-Strichartz estimates for dispersive equations perturbed by a first-order differential operator Vladimir Simeonov Gueorguiev
2005 Luca Granieri Mass transportation problems and minimal measures Giuseppe Buttazzo
2004 Michele Gori Lower semicontinuity and relaxation for integral and supremal functionals Giuseppe Buttazzo and Paolo Marcellini
2004 Andrea Davini Finsler metrics in optimization problems and Hamilton-Jacobi equations Giuseppe Buttazzo
2004 Marco Gipo Ghimenti Geodesics in conical manifolds Vieri Benci
2003 Claudio Bonanno Applicazione dei metodi di teoria dell'informazione a sistemi dinamici Vieri Benci and Stefano Isola
2003 Giulia Menconi Nonlinear dynamics and information with applications to biological and physical systems Vieri Benci
2003 Francesca Agnese Prinari Calculus of variations for supremal functionals Giuseppe Buttazzo
2002 Stefano Galatolo Information, complexity and weak chaos in dynamical systems. Theory and measurement methods Vieri Benci
2001 Luigi De Pascale The Morse-Sard theorem in Sobolev spaces, optimal transport problems and applications Giovanni Alberti and Giuseppe Buttazzo
2001 Silvia Faggian First order Hamilton-Jacobi-Bellman equations in Hilbert spaces, boundary optimal control and applications to economics Fausto Gozzi and Paolo Acquistapace
2001 Dimitri Mugnai Reversed variational inequalities and asymptotically critical points Antonio Marino
2000 Ilaria Fragalà Tangential calculus and variational integrals with respect to a measure Giuseppe Buttazzo
2000 Luigi Carlo Berselli Some topics in fluid mechanics Hugo Beirao da Veiga and Alberto Valli
1999 Ariela Briani Hamilton-Jacobi-Bellman equations and Gamma-Convergence for optimal control problems Giuseppe Buttazzo and Paolo Acquistapace
1999 Alessandro Groli Jumping problems for semilinear and quasilinear variational inequalities Claudio Saccon and Antonio Marino
1998 Paola Trebeschi Esistenza di soluzioni in problemi di ottimizzazione di forma e ostacoli Giuseppe Buttazzo
1997 Marino Belloni Relaxation of variational problems with Lavrentiev Phenomenon Giuseppe Buttazzo
1997 Edgardo Molina Salazar Alcune applicazioni della teoria di Morse a varieta' di Lorentz Vieri Benci
1997 Giuseppina Vannella Alcune applicazioni della teoria di Morse a problemi di tipo ellittico Vieri Benci
1996 Cataldo Grammatico Unicità forte per operatori ellittici Ferruccio Colombini
1996 Angela Pistoia Un problema ellittico semilineare asintoticamente omogeneo e non simmetrico Antonio Marino
1994 Lorenzo Freddi Rilassamento e convergenza di problemi di controllo ottimo Giuseppe Buttazzo
1992 Antonio Masiello Metodi variazionali in geometria lorentziana Vieri Benci
1992 Nicola Orrù Problema di Cauchy per equazioni iperboliche lineari Ferruccio Colombini
1991 Francesco Serra Cassano Sergio Spagnolo
1988 Donato Passaseo Molteplicita di soluzioni per diseguaglianze variazionali Antonio Marino
awarded by another institution
Year Name Surname Title of the Thesis Institution Supervisor(s)
2022 Francesco Paolo Maiale Shape optimization problems and regularity of the free boundaries SNS, Pisa Giuseppe Buttazzo
2022 Kita Kosuke A study on the qualitative theory of solutions for some parabolic equations with nonlinear boundary conditions Waseda University Tohru Ozawa and Vladimir Simeonov Gueorguiev
2020 François Générau On a stable variational approximation of the cut locus, and a non-local isoperimetric problem Université Grenoble Alpes Bozhidar Velichkov and Édouard Oudet
2020 Andrea Merlo Geometry of 1-codimensional measures in Heisenberg groups SNS, Pisa Giovanni Alberti and Roberto Monti
2020 Dinh Duong Nguyen Some results on Turbulent models Université de Rennes Roger Lewandowski and Luigi Carlo Berselli
2020 Baptiste Trey Existence and regularity of optimal shapes for some spectral optimization problems Université Grenoble Alpes Bozhidar Velichkov and Emmanuel Russ
2018 Ricardo Bioni Liberalquino Computation of stationary densities of systems with additive noise Universidade Federal do Rio de Janeiro Maria José Pacifico
2018 Dayana Pagliardini Fractional minimal surfaces and Allen-Cahn equations SNS, Pisa Matteo Novaga and Andrea Malchiodi
2017 Luigi Forcella Asymptotic problems for some classes of dispersive PDEs SNS, Pisa Nicola Visciglia
2016 Matteo Cerminara Modeling dispersed gas–particle turbulence in volcanic ash plumes SNS, Pisa Luigi Carlo Berselli and Tomaso Esposti Ongaro
2016 François Dayrens Minimisations sous contraintes et flots du périmètre et de l’énergie de Willmore Université de Lyon Matteo Novaga and Simon Masnou
2016 Emanuela Radici Diffeomorphic approximation of planar elastic deformations Friedrich-Alexander-Universität Erlangen-Nürnberg Aldo Pratelli
2016 Andrea Tamagnini Planar Clusters Università degli Studi di Firenze Emanuele Paolini
2016 Florian Zeisler On the optimal transport problem with relativistic cost Friedrich-Alexander-Universität Erlangen-Nürnberg Aldo Pratelli
2015 Rafael Lucena Spectral gap for contracting fiber systems and applications Universidade Federal do Rio de Janeiro Stefano Galatolo and Maria José Pacifico
2014 Annalisa Massacesi Currents with coefficients in groups, applications, and other problems in Geometric Measure Theory SNS, Pisa Giovanni Alberti
2014 Dario Mazzoleni Existence and regularity results for solutions of spectral problems Friedrich-Alexander-Universität Erlangen-Nürnberg Aldo Pratelli
2013 Xin Yang Lu Geometric and regularity properties of solutions of some problems related to the average distance functional SNS, Pisa Giuseppe Buttazzo
2013 Berardo Ruffini Optimization problems for solution of elliptic equations and stability issues SNS, Pisa Giuseppe Buttazzo
2013 Bozhidar Velichkov Existence and regularity results for some shape optimization problems SNS, Pisa Giuseppe Buttazzo
2012 Stefano Spirito The artificial compressibility approximation and the inviscid limit for the incompressible Navier-Stokes equations Università degli Studi dell’Aquila Luigi Carlo Berselli and Pierangelo Marcati
2008 Cristóbal Rojas Randomness And Ergodic Theory: An Algorithmic Point of View École polytechnique Stefano Galatolo and Giuseppe Longo
2008 Mathieu Hoyrup Computability, Randomness and Ergodic Theory on Metric Spaces Université Paris Diderot Stefano Galatolo and Giuseppe Longo
2006 Alessio Brancolini Optimization problems for transportation networks SNS, Pisa Giuseppe Buttazzo
2006 Filippo Santambrogio Variational problems in transport theory with mass concentration SNS, Pisa Giuseppe Buttazzo
2005 Niccolò Desenzani Variational convergence of Ginzburg-Landau functionals with supercritical growth Università degli Studi di Milano (La Statale) Giovanni Alberti and Ilaria Fragalà
2005 Stefano Zappacosta Resolvent estimates and dispersive estimates for the wave equation with potential Università degli Studi dell'Aquila Vladimir Simeonov Gueorguiev
2004 Nicola Visciglia A priori estimates for the linear and semilinear perturbed wave equation SNS, Pisa Vladimir Simeonov Gueorguiev
1994 Loris Faina Some nonconvex variational problems in BV spaces SISSA, Trieste Giuseppe Buttazzo

Grants

• Variational approach to the regularity of the free boundaries (ERC-STG - Starting Grant)

Principal Investigator: Bozhidar Velichkov

Project period: Jun 01, 2020 – May 31, 2025

• Nonlinear evolution PDEs, fluid dynamics and transport equations: theoretical foundations and applications (Prin 2020)

Principal Investigator: Stefano Bianchini

Coordinator of the Research Unit: Luigi Carlo Berselli

Project period: Mar 22, 2022 – Mar 21, 2025

• Hamiltonian and dispersive PDEs (Prin 2020)

Principal Investigator: Massimiliano Berti

Coordinator of the Research Unit: Nicola Visciglia

Project period: Mar 22, 2022 – Mar 21, 2025

• Nonlinear dispersive equations and dynamics of fluids (Progetti di Ricerca di Ateneo (PRA) 2022-2023)

Principal Investigator: Jacopo Bellazzini

Project period: Oct 10, 2022 – Dec 31, 2024

• APRISE - Analysis and Probability in Science (Progetti di Ricerca di Ateneo (PRA) 2022-2023)

Principal Investigator: Marco Romito

Project period: Oct 10, 2022 – Dec 31, 2024

• GeoDom - Geometric evolution problems and PDEs on variable domains (Progetti di Ricerca di Ateneo (PRA) 2022-2023)

Principal Investigator: Bozhidar Velichkov

Project period: Oct 10, 2022 – Dec 31, 2024

• Variational methods for stationary and evolution problems with singularities and interfaces (Prin 2017)

Principal Investigator: Gianni Dal Maso

Coordinator of the Research Unit: Giovanni Alberti

Project period: Aug 01, 2019 – Aug 19, 2023

• Mathematical Logic: models, sets, computability (Prin 2017)

Principal Investigator: Alessandro Berarducci

Project period: Aug 01, 2019 – Aug 19, 2023

• Gradient flows, Optimal Transport and Metric Measure Structures (Prin 2017)

Principal Investigator: Luigi Ambrosio

Coordinator of the Research Unit: Giuseppe Buttazzo

Project period: Aug 01, 2019 – Feb 19, 2023

• Nuovi sviluppi per minimi dell'energia in problemi di ottimizzazione di forma (Progetti di Ricerca di Ateneo (PRA) 2020 - 2021)

Principal Investigator: Aldo Pratelli

Project period: Jul 07, 2020 – Dec 31, 2022

• Energia e regolarità: tecniche innovative per problemi classici di equazioni alle derivate parziali (Progetti di Ricerca di Ateneo (PRA) 2018 - 2020)

Principal Investigator: Elisabetta Chiodaroli

Project period: Jul 09, 2018 – Jul 08, 2020

• Analisi geometrica ed equazioni alle derivate parziali in ambiti singolari e non euclidei (Progetti di Ricerca di Ateneo (PRA) 2018 - 2020)

Principal Investigator: Valentino Magnani

Project period: Jul 09, 2018 – Jul 08, 2020

• Sistemi dinamici in analisi, geometria, logica e meccanica celeste (Progetti di Ricerca di Ateneo (PRA) 2017 - 2018)

Principal Investigator: Marco Abate

Project period: Apr 10, 2017 – Apr 09, 2019

• Problemi di ottimizzazione e di evoluzione in ambito variazionale (Progetti di Ricerca di Ateneo (PRA) 2017 - 2018)

Principal Investigator: Matteo Novaga

Project period: Apr 10, 2017 – Apr 09, 2019

Visitors

Prospective
First Name Last Name Affiliation
Elisa Affili Università di Bologna
Francesca Bianchi Università di Parma
Danila Cherkashin Bulgarian Academy of Sciences
Gabriele Cora Università di Torino
Antonia Diana Scuola Superiore Meridionale
Alex Niklas Kaltenbach Albert-Ludwigs-Universität Freiburg
Filip Rindler University of Warwick
Giovanni Siclari Università di Milano Bicocca
Luca Spolaor University of California San Diego
Gigliola Staffilani MIT
Koichi Taniguchi Tohoku University
Yana Teplitskaya Leiden University
Kenta Tomioka Waseda University
Kenta Tomioka Waseda University
Stefano Vita Università di Torino
Current
First Name Last Name Affiliation Building Floor Office
Stefano Spirito Università degli Studi dell'Aquila ex DMA 1 15
Li Wei Huazhong University Building A 0 130
Grouped by year
2023
First Name Last Name Affiliation From To
Elisa Affili Università di Bologna Mar 27, 2023 Mar 29, 2023
Francesca Bianchi Università di Parma Mar 27, 2023 Mar 29, 2023
Alan Chang Princeton University Jan 21, 2023 Jan 28, 2023
Danila Cherkashin Bulgarian Academy of Sciences Jul 09, 2023 Mar 15, 2023
Gabriele Cora Università di Torino Mar 27, 2023 Mar 29, 2023
Antonia Diana Scuola Superiore Meridionale Feb 13, 2023 Feb 17, 2023
Antonia Diana Scuola Superiore Meridionale Feb 27, 2023 Mar 10, 2023
Antonia Diana Scuola Superiore Meridionale Mar 27, 2023 Mar 31, 2023
Kazumasa Fujiwara Nagoya University Jan 08, 2023 Jan 22, 2023
Seongmin Jeon KTH Feb 25, 2023 Mar 04, 2023
Alex Niklas Kaltenbach Albert-Ludwigs-Universität Freiburg Jul 01, 2023 Mar 31, 2024
Kita Kosuke Waseda University Mar 06, 2023 Mar 13, 2023
Luca Lussardi Politecnico di Torino Mar 12, 2023 Mar 16, 2023
Tokio Matsuyama Chuo University Jan 08, 2023 Jan 22, 2023
Tohru Ozawa Waseda University Mar 09, 2023 Mar 11, 2023
Marco Pozzetta Università degli Studi di Napoli Federico II Feb 06, 2023 Feb 11, 2023
Filip Rindler University of Warwick Apr 20, 2023 Apr 22, 2023
Giovanni Siclari Università di Milano Bicocca Mar 27, 2023 Mar 29, 2023
Stefano Spirito Università degli Studi dell'Aquila Jan 22, 2023 Apr 30, 2023
Luca Spolaor University of California San Diego Apr 25, 2023 May 27, 2023
Gigliola Staffilani MIT Sep 07, 2023 Sep 14, 2023
Koichi Taniguchi Tohoku University May 09, 2023 May 23, 2023
Yana Teplitskaya Leiden University Jul 09, 2023 Mar 15, 2023
Kenta Tomioka Waseda University Apr 11, 2023 Jul 01, 2023
Kenta Tomioka Waseda University Sep 30, 2023 Mar 30, 2024
Stefano Vita Università di Torino Mar 27, 2023 Mar 29, 2023
Li Wei Huazhong University Jan 16, 2023 Jan 31, 2024
Jorg Wolf Chung-Ang University Feb 20, 2023 Feb 23, 2023
2022
First Name Last Name Affiliation From To
Giulia Bevilacqua Politecnico di Torino Feb 20, 2022 Feb 23, 2022
Federico Bonetto Georgia Institute of Technology Jun 13, 2022 Jun 17, 2022
Francesca Corni Università degli Studi di Bologna Dec 05, 2022 Dec 09, 2022
Sergio Cruz Blazquez Università degli Studi della Campania Nov 29, 2022 Nov 29, 2022
Cristiana De Filippis Università di Parma Apr 10, 2022 Apr 13, 2022
Alessandra De Luca Università di Milano Bicocca Nov 08, 2022 Nov 08, 2022
Luigi De Masi SISSA Nov 08, 2022 Nov 08, 2022
Max Engelstein University of Minnesota Sep 22, 2022 Sep 25, 2022
Davide Faranda LSCE laboratory, University of Paris-Saclay Oct 16, 2022 Oct 22, 2022
Filippo Gaia ETH Zürich Nov 08, 2022 Nov 08, 2022
Carlo Gasparetto SISSA Dec 04, 2022 Dec 08, 2022
Carlo Gasparetto SISSA Nov 07, 2022 Nov 18, 2022
Alain Haraux CNRS Nov 21, 2022 Nov 26, 2022
Tom Ilmanen ETH Zürich Nov 13, 2022 Nov 23, 2022
Danela Oana Ivanovici Sorbonne Université Sep 12, 2022 Sep 16, 2022
Roger Lewandowski IRMR, Université de Rennes Oct 17, 2022 Oct 20, 2022
Faustino Maestre Universidad de Sevilla Nov 28, 2022 Dec 02, 2022
Edoardo Mainini Università di Genova May 16, 2022 May 19, 2022
Carlo Mantegazza Università degli Studi di Napoli Federico II Jul 11, 2022 Jul 11, 2022
Annalisa Massacesi Università di Padova Sep 18, 2022 Sep 23, 2022
Idriss Mazari Université Paris-Dauphine Oct 16, 2022 Oct 21, 2022
Dario Mazzoleni Università di Pavia Apr 03, 2022 Apr 08, 2022
Riccardo Molle Università di Roma Tor Vergata Nov 15, 2022 Nov 15, 2022
Riccardo Montalto Università di Milano Statale Oct 20, 2022 Oct 25, 2022
Riccardo Montalto Università di Milano Statale Sep 29, 2022 Oct 02, 2022
Mickael Nahon Université de Savoie Jan 16, 2022 Jan 29, 2022
Francesca Oronzio Università degli Studi di Napoli Federico II Nov 08, 2022 Nov 08, 2022
Fabrice Planchon Sorbonne Université Sep 12, 2022 Sep 16, 2022
Raffaele Scandone Gran Sasso Science Institute Oct 09, 2022 Oct 16, 2022
Mario Bernhard Schulz University of Münster Sep 14, 2022 Sep 15, 2022
Gaetano Siciliano Instituto de Matemática e Estatística - Universidade de São Paulo Oct 09, 2022 Oct 11, 2022
Nicola Soave Politecnico di Milano Mar 08, 2022 Mar 10, 2022
Eugene Stepanov St. Petersburg Department of Steklov Mathematical Institute of the Russian Academy of Sciences Oct 01, 2022 Dec 31, 2022
Salvatore Stuvard Università di Milano Statale May 22, 2022 May 27, 2022
Yoshihiro Tonegawa Tokyo Institute of Technology Nov 14, 2022 Nov 25, 2022
Nikolay Tzvetkov CY Cergy Paris Université Sep 12, 2022 Sep 16, 2022
Gianmaria Verzini Politecnico di Milano Nov 30, 2022 Dec 02, 2022
Hui Yu National University of Singapore Oct 11, 2022 Oct 15, 2022
Anna Chiara Zagati Università degli Studi di Ferrara Nov 08, 2022 Nov 08, 2022
2021
First Name Last Name Affiliation From To
Alessandro Audrito ETH Zürich Oct 25, 2021 Oct 28, 2021
Ekaterina Mukoseeva University of Helsinki Sep 10, 2021 Sep 24, 2021
Mickael Nahon Université de Savoie Jul 04, 2021 Jul 10, 2021
Luca Spolaor University of California San Diego Dec 05, 2021 Dec 09, 2021