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
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
Collaborators and Ph.D. students at other institutions
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
Collaborators
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
Collaborators
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
Collaborators
PDEs, ODEs, and dynamical systems
Members
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
Collaborators
davide.faranda@lsce.ipsl.fr
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
Collaborators
Hyperbolic Equations, dispersive equations, and Kirchhoff equations
Members
Collaborators
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
Collaborators
People
Faculty
Affiliate Members
Name | Surname | Personal Card | |
---|---|---|---|
Paolo | Acquistapace | paolo.acquistapace@unipi.it | |
Francesco | Bartaloni | francesco.bartaloni1@gmail.com | |
Hugo | Beirao da Veiga | bveiga@dma.unipi.it | |
Vieri | Benci | vieri.benci@gmail.com | |
Ferruccio | Colombini | ferruccio.colombini@unipi.it | |
Placido | Longo | placido.longo@unipi.it | |
Ilaria | Lucardesi | ||
Adele | Manes | adele.manes@unipi.it | |
Antonio | Marino | marino@dm.unipi.it | |
Anna Maria | Micheletti | a.micheletti@dma.unipi.it | |
Sergio | Spagnolo | spagnolo@dm.unipi.it | |
Antonio | Tarsia | tarsia@dm.unipi.it |
Former Members
there is no data
Postdoctoral Fellows
Name | Surname | Personal Card | |
---|---|---|---|
Luca | Benatti | luca.benatti@dm.unipi.it | |
Giulia | Bevilacqua | giulia.bevilacqua@dm.unipi.it | |
Carlo | Gasparetto | carlo.gasparetto@dm.unipi.it | |
Masayuki | Hayashi | masayuki.hayashi@dm.unipi.it | |
Roberto | Ognibene | roberto.ognibene12@gmail.com | |
Rossano | Sannipoli | rossano.sannipoli94@gmail.com | |
Giorgio | Tortone | giorgio.tortone@dm.unipi.it |
Ph.D. Students at the University of Pisa
Name | Surname | Personal Card | |
---|---|---|---|
Daniele | Barbera | daniele.barbera@phd.unipi.it | |
Jeremy | Mirmina | jeremy.mirmina@phd.unipi.it | |
Mario | Rastrelli | mario.rastrelli@phd.unipi.it | |
Luciano | Sciaraffia Rubio | luciano.sciaraffia@phd.unipi.it |
Ph.D. Students at other institutions
Name | Surname | Affiliation |
---|---|---|
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) |
---|---|---|---|---|
2023 | Konstantinos | Bessas | Nonlocal Models in Calculus of Variations | Matteo Novaga |
2023 | Luca | Briani Medeiros Dos Santo | Shape optimization problems with competing terms | Giuseppe Buttazzo |
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 Claude Bernard Lyon 1 | 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 Cité | 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
Current
-
NO^3 - Nodal Optimization, NOnlinear elliptic equations, NOnlocal geometric problems, with a focus on regularity (Prin 2022)
Principal Investigator: Nicola Soave
Coordinator of the Research Unit: Bozhidar Velichkov
Project period: Sep 28, 2023 – Sep 27, 2025
-
Classical equations of compressible fluids mechanics: existence and properties of non-classical solutions (Prin 2022)
Principal Investigator: Stefano Spirito
Coordinator of the Research Unit: Elisabetta Chiodaroli
Project period: Sep 28, 2023 – Sep 27, 2025
-
Geometric Measure Theory: Structure of Singular Measures, Regularity Theory and Applications in the Calculus of Variations (Prin 2022)
Principal Investigator: Andrea Marchese
Coordinator of the Research Unit: Giovanni Alberti
Project period: Sep 28, 2023 – Sep 27, 2025
-
Geometric Evolution Problems and Shape Optimization (GEPSO) (Prin 2022)
Principal Investigator: Nicola Fusco
Coordinator of the Research Unit: Matteo Novaga
Project period: Sep 28, 2023 – Sep 27, 2025
-
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
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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
Past
-
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
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Mathematical Logic: models, sets, computability (Prin 2017)
Principal Investigator: Alessandro Berarducci
Project period: Aug 01, 2019 – Aug 19, 2023
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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
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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
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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
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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
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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
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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 |
---|---|---|
Sören | Bartels | Albert-Ludwigs-Universität Freiburg |
Claudia | Bucur | Università degli Studi di Milano (La Statale) |
Eleonora | Cinti | Università di Bologna |
Vito | Crismale | Sapienza Università di Roma |
Simone | Di Marino | Università di Genova |
Michele | Stecconi | University of Luxembourg |
Marta | Strani | Università Ca' Foscari |
Kenta | Tomioka | Waseda University |
Current
First Name | Last Name | Affiliation | Building | Floor | Office |
---|---|---|---|---|---|
Alex Niklas | Kaltenbach | Albert-Ludwigs-Universität Freiburg | ex DMA | Second floor | 4 |
Li | Wei | Huazhong University of Science and Technology | Building A | Ground floor | 130 |
Grouped by year
2023
First Name | Last Name | Affiliation | From | To |
---|---|---|---|---|
Elisa | Affili | Università di Bologna | Mar 27, 2023 | Mar 29, 2023 |
Sören | Bartels | Albert-Ludwigs-Universität Freiburg | Oct 11, 2023 | Oct 25, 2023 |
Francesca | Bianchi | Università di Parma | Mar 27, 2023 | Mar 29, 2023 |
Lorenzo | Brasco | Università degli Studi di Ferrara | May 04, 2023 | May 05, 2023 |
Claudia | Bucur | Università degli Studi di Milano (La Statale) | Oct 04, 2023 | Oct 06, 2023 |
Alan | Chang | Princeton University | Jan 21, 2023 | Jan 28, 2023 |
Alan | Chang | Princeton University | Jun 24, 2023 | Jul 15, 2023 |
Danila | Cherkashin | Bulgarian Academy of Sciences | Jul 09, 2023 | Jul 15, 2023 |
Rustum | Choksi | McGill University | May 01, 2023 | May 06, 2023 |
Eleonora | Cinti | Università di Bologna | Oct 04, 2023 | Oct 06, 2023 |
Gabriele | Cora | Università di Torino | Mar 27, 2023 | Mar 29, 2023 |
Vito | Crismale | Sapienza Università di Roma | Oct 04, 2023 | Oct 06, 2023 |
Luigi | De Masi | Università di Padova | Sep 24, 2023 | Sep 28, 2023 |
Simone | Di Marino | Università di Genova | Oct 04, 2023 | Oct 06, 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 |
Serena | Dipierro | The University of Western Australia | Aug 30, 2023 | Sep 08, 2023 |
Davide | Faranda | Laboratoire des Sciences du Climat et de l'Environnement (LSCE) | May 29, 2023 | May 31, 2023 |
Massimo | Fornasier | Technische Universität München (TUM) | May 01, 2023 | Jul 31, 2023 |
Kazumasa | Fujiwara | Nagoya University | Jan 08, 2023 | Jan 22, 2023 |
Seongmin | Jeon | KTH Royal Institute of Technology | 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 |
Lorenzo | Mazzieri | Università di Trento | Sep 04, 2023 | Sep 08, 2023 |
Dario | Mazzoleni | Università degli Studi di Pavia | Apr 03, 2023 | Apr 05, 2023 |
Tohru | Ozawa | Waseda University | Mar 09, 2023 | Mar 11, 2023 |
Fabrice | Planchon | Sorbonne Université | Jun 18, 2023 | Jun 20, 2023 |
Marco | Pozzetta | Università degli Studi di Napoli Federico II | Feb 06, 2023 | Feb 11, 2023 |
Marco | Pozzetta | Università degli Studi di Napoli Federico II | Sep 20, 2023 | Sep 22, 2023 |
Alfio | Quarteroni | Politecnico di Milano | Sep 06, 2023 | Sep 07, 2023 |
Filip | Rindler | University of Warwick | Apr 20, 2023 | Apr 22, 2023 |
Eduardo | Saenz De Cabezon | Universidad de La Rioja | Sep 07, 2023 | Sep 09, 2023 |
Giovanni | Siclari | Università degli Studi 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 | Massachusetts Institute of Technology (MIT) | Sep 07, 2023 | Sep 14, 2023 |
Michele | Stecconi | University of Luxembourg | Nov 20, 2023 | Nov 24, 2023 |
Marta | Strani | Università Ca' Foscari | Oct 04, 2023 | Oct 06, 2023 |
Yukihide | Tadano | Tokyo Institute of Technology | Jul 03, 2023 | Jul 08, 2023 |
Koichi | Taniguchi | Tohoku University | May 09, 2023 | May 28, 2023 |
Mirko | Tarulli Di Giallonardo | American University in Bulgaria | May 20, 2023 | Jul 20, 2023 |
Yana | Teplitskaya | Leiden University | Jul 09, 2023 | Jul 15, 2023 |
Kenta | Tomioka | Waseda University | Apr 11, 2023 | Jul 01, 2023 |
Kenta | Tomioka | Waseda University | Sep 30, 2023 | Mar 30, 2024 |
Damià | Torres | Universitat Autònoma de Barcelona | Feb 16, 2023 | Mar 18, 2023 |
Damià | Torres | Universitat Autònoma de Barcelona | Jun 19, 2023 | Jun 24, 2023 |
Enrico | Valdinoci | The University of Western Australia | Aug 30, 2023 | Sep 08, 2023 |
Renato Adolfo | Velozo Ruiz | Sorbonne Université | Jul 20, 2023 | Jul 20, 2023 |
George | Venkov | Technical University of Sofia | May 22, 2023 | May 28, 2023 |
Stefano | Vita | Università di Torino | Mar 27, 2023 | Mar 29, 2023 |
Li | Wei | Huazhong University of Science and Technology | Jan 16, 2023 | Jan 31, 2024 |
Jorg | Wolf | Chung-Ang University | Feb 20, 2023 | Feb 23, 2023 |
Anna Chiara | Zagati | Università degli Studi di Ferrara | Jun 12, 2023 | Jun 16, 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 |
Juan | Casado-Diaz | Universidad de Sevilla | Nov 28, 2022 | Dec 02, 2022 |
Francesca | Corni | Università di Bologna | Dec 05, 2022 | Dec 09, 2022 |
Sergio | Cruz Blazquez | Università degli Studi della Campania "Luigi Vanvitelli" | Nov 29, 2022 | Nov 29, 2022 |
Cristiana | De Filippis | Università di Parma | Apr 10, 2022 | Apr 13, 2022 |
Alessandra | De Luca | Università degli Studi di Milano-Bicocca | Nov 08, 2022 | Nov 08, 2022 |
Luigi | De Masi | SISSA, Trieste | Nov 08, 2022 | Nov 08, 2022 |
Max | Engelstein | University of Minnesota | Sep 22, 2022 | Sep 25, 2022 |
Davide | Faranda | Laboratoire des Sciences du Climat et de l'Environnement (LSCE) | Oct 16, 2022 | Oct 22, 2022 |
Filippo | Gaia | Eidgenössische Technische Hochschule (ETH) Zürich | Nov 08, 2022 | Nov 08, 2022 |
Carlo | Gasparetto | SISSA, Trieste | Nov 07, 2022 | Nov 18, 2022 |
Carlo | Gasparetto | SISSA, Trieste | Dec 04, 2022 | Dec 08, 2022 |
Alain | Haraux | CNRS | Nov 21, 2022 | Nov 26, 2022 |
Tom | Ilmanen | Eidgenössische Technische Hochschule (ETH) Zürich | Nov 13, 2022 | Nov 23, 2022 |
Danela Oana | Ivanovici | Sorbonne Université | Sep 12, 2022 | Sep 16, 2022 |
Roger | Lewandowski | 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 degli Studi di Pavia | Apr 03, 2022 | Apr 08, 2022 |
Riccardo | Molle | Università degli Studi di Roma Tor Vergata | Nov 15, 2022 | Nov 15, 2022 |
Riccardo | Montalto | Università degli Studi di Milano (La Statale) | Sep 29, 2022 | Oct 02, 2022 |
Riccardo | Montalto | Università degli Studi di Milano (La Statale) | Oct 20, 2022 | Oct 25, 2022 |
Mickael | Nahon | Université de Savoie Mont Blanc | 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 | Westfälische Wilhelms-Universität Münster | Sep 14, 2022 | Sep 15, 2022 |
Gaetano | Siciliano | Instituto de Matemática e Estatística (IME/USP) - 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 V.A. Steklov Institute of Mathematics of the Russian Academy of Sciences | Oct 01, 2022 | Dec 31, 2022 |
Salvatore | Stuvard | Università degli Studi di Milano (La 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 | Eidgenössische Technische Hochschule (ETH) Zürich | Oct 25, 2021 | Oct 28, 2021 |
Ekaterina | Mukoseeva | University of Helsinki | Sep 10, 2021 | Sep 24, 2021 |
Mickael | Nahon | Université de Savoie Mont Blanc | Jul 04, 2021 | Jul 10, 2021 |
Luca | Spolaor | University of California San Diego | Dec 05, 2021 | Dec 09, 2021 |