Full Professor and FIM Director, ETH Zurich

Email: alessio.figalli AT math.ethz.ch

Home-page: https://people.math.ethz.ch/~afigalli/

Available papers (184):

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• A. Figalli - X. Ros-Oton - J. Serra (J. Amer. Math. Soc)
  The singular set in the Stefan problem (2024)
• K. Böröczky - A. Figalli - J. P. G. Ramos (Ann. Inst. H. Poincaré Anal. Non Linéaire)
  A quantitative stability result for the Prékopa-Leindler inequality for arbitrary measurable functions (2024)
• M. Bonforte - A. Figalli (Nonlinear Anal.)
  The Cauchy-Dirichlet Problem for the Fast Diffusion Equation on Bounded Domains (2024)
• A. Figalli - Y. R. Y. Zhang (Comm. Pure Appl. Math.)
  Uniform boundedness for finite Morse index solutions to supercritical semilinear elliptic equations (2024)
• E. Borgonovo - A. Figalli - E. Plischke - G. Savaré (Accepted Paper: Management Science)
  Global sensitivity analysis via optimal transport (2024)
• L. Chizat - M. Colombo - X. Fernández-Real - A. Figalli (Accepted Paper: Comm. Pure Appl. Math.)
  Infinite-width limit of deep linear neural networks (2024)
• A. Figalli - A. Guerra - S. Kim - H. Shahgholian (Accepted Paper: J. Eur. Math. Soc. (JEMS))
  Constraint maps with free boundaries: the Bernoulli case (2024)
• A. Figalli - A. Guerra - S. Kim - H. Shahgholian (Submitted Paper)
  Constraint maps: singularities vs free boundaries (2024)
• M. Datres - G. P. Leonardi - A. Figalli - D. Sutter (Accepted Paper: NeurIPS)
  A Two-Scale Complexity Measure for Deep Learning Models (2024)
• G. Carlier - A. Figalli - F. Santambrogio (Accepted Paper: Ann. Inst. H. Poincaré Anal. Non Linéaire)
  On optimal transport maps between 1/d-concave densities (2024)
• S. Eberle - A. Figalli - G. S. Weiss (Accepted Paper: Ann. of Math.)
  Complete classification of global solutions to the obstacle problem (2024)
• A. Figalli - J. P. G. Ramos (Accepted Paper)
  Improved stability versions of the Prékopa–Leindler inequality (2024)
• A. Figalli - A. Guerra - S. Kim - H. Shahgholian (Lecture Notes: Preprint)
  Constraint Maps and Free Boundaries (2024)
• A. Figalli - K. Sunghan - H. Shahgholian (Arch. Ration. Mech. Anal.)
  Constraint maps with free boundaries: the obstacle case (2024)
• A. Figalli - Y. Jhaveri (Adv. Nonlinear Stud.)
  Regularity properties of monotone measure-preserving maps (2023)
• A. Figalli - C. Kehle (Discrete Contin. Dyn. Syst.)
  On the prescribed negative Gauss curvature problem for graphs (2023)
• A. Figalli - Y. R. Y. Zhang (Submitted Paper)
  Strong stability of convexity with respect to the perimeter (2023)
• A. Figalli (Lecture Notes: Preprint)
  An introduction to optimal transport and Wasserstein gradient flows (2023)
• J. Dolbeault - M. J. Esteban - A. Figalli - F. Rupert - M. Loss (Lecture Notes: Proceedings of ICIAM 2023)
  A short review on improvements and stability for some interpolation inequalities (2023)
• A. Figalli - S. Kim - H. Shahgholian (Nonlinear Anal.)
  Lipschitz Regularity in Vectorial Linear Transmission Problems (2022)
• A. Figalli - Y. R. Y. Zhang (Duke Math. J.)
  Sharp gradient stability for the Sobolev inequality (2022)
• G. Bordigoni - A. Figalli - A. Ledford - P. Ustinov (Appl. Math. Finance)
  Strategic execution trajectories (2022)
• A. Figalli - A. Belotto da Silva - A. Parusiński - L. Rifford (Invent. Math.)
  Strong Sard Conjecture and regularity of singular minimizing geodesics for analytic sub-Riemannian structures in dimension 3 (2022)
• Y. R. Y. Zhang - A. Figalli (Comm. Pure Appl. Math.)
  Strong stability for the Wulff inequality with a crystalline norm (2022)
• A. Figalli - X. Fernández-Real (Lecture Notes: Published, Springer, Cham)
  The Continuous Formulation of Shallow Neural Networks as Wasserstein-Type Gradient Flows (2022)
• A. Abbas - D. Sutter - C. Zoufal - A. Lucchi - A. Figalli - S. Woerner (Nat. Comput. Sci.)
  The power of quantum neural networks (2021)
• A. Figalli - D. Jerison (Ann. Sci. Éc. Norm. Supér.)
  A sharp Freiman type estimate for semisums in two and three dimensional Euclidean spaces (2021)
• M. Bonforte - A. Figalli (Comm. Pure Appl. Math.)
  Sharp Extinction Rates for Fast Diffusion Equations on Generic Bounded Domains (2021)
• L. Caffarelli - F. Cagnetti - A. Figalli (Arch. Ration. Mech. Anal.)
  Optimal regularity and structure of the free boundary for minimizers in cohesive zone models (2020)
• X. Fernández-Real - A. Figalli (Math. Eng.)
  On the obstacle problem for the 1D wave equation (2020)
• A. Figalli - J. Serra (Invent. Math.)
  On stable solutions for boundary reactions: a De Giorgi-type result in dimension 4+1 (2020)
• A. Figalli - F. Glaudo (Arch. Ration. Mech. Anal.)
  On the sharp stability of critical points of the Sobolev inequality (2020)
• G. Ciraolo - A. Figalli - A. Roncoroni (Geom. Funct. Anal.)
  Symmetry results for critical anisotropic $p$-Laplacian equations in convex cones (2020)
• X. Cabré - A. Figalli - X. Ros-Oton - J. Serra (Acta Math.)
  Stable solutions to semilinear elliptic equations are smooth up to dimension 9 (2020)
• X. Ros-Oton - J. Serra - A. Figalli (Publ. Math. Inst. Hautes Études Sci.)
  Generic regularity of free boundaries for the obstacle problem (2020)
• A. Figalli - R. Neumayer (J. Eur. Math. Soc. (JEMS))
  Gradient stability for the Sobolev inequality: the case $p\geq 2$ (2019)
• A. Figalli - M. J. Kang (Anal. PDE)
  A rigorous derivation from the kinetic Cucker-Smale model to the pressureless Euler system with nonlocal alignment (2019)
• A. Figalli - J. Serra (Invent. Math.)
  On the fine structure of the free boundary for the classical obstacle problem (2019)
• J. E. M. Braga - A. Figalli - D. Moreira (Comm. Math. Phys.)
  Optimal regularity for the convex envelope and semiconvex functions related to supersolutions of fully nonlinear elliptic equations (2019)
• D. Cordero-Erausquin - A. Figalli (Discrete Contin. Dyn. Syst.)
  Regularity of monotone transport maps between unbounded domains (2019)
• A. Figalli (Lecture Notes)
  On the Monge-Ampère equation (2018)
• A. Figalli - J. Palmer - A. Pelayo (Ann. Scuola Norm. Sup. Pisa Cl. Sci.)
  Symplectic G-capacities and integrable systems (2018)
• G. Ciraolo - A. Figalli - F. Maggi - M. Novaga (J. Reine Angew. Math.)
  Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature (2018)
• G. Ciraolo - A. Figalli - F. Maggi (Int. Math. Res. Not. IMRN)
  A quantitative analysis of metrics on $\mathbb R^n$ with almost constant positive scalar curvature, with applications to fast diffusion flows (2018)
• B. Barrios - A. Figalli - X. Ros-Oton (Amer. J. Math.)
  Global regularity for the free boundary in the obstacle problem for the fractional Laplacian (2018)
• B. Barrios - A. Figalli - X. Ros-Oton (Comm. Pure Appl. Math.)
  Free boundary regularity in the parabolic fractional obstacle problem (2018)
• A. Figalli - M. J. Kang - J. Morales (Arch. Ration. Mech. Anal.)
  Global well-posedness of the spatially homogeneous Kolmogorov-Vicsek model as a gradient flow (2018)
• A. Figalli - C. Mooney (Arch. Ration. Mech. Anal.)
  An obstacle problem for conical deformations of thin elastic sheets (2018)
• M. Bonforte - A. Figalli - J. L. Vazquez (Anal. PDE)
  Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains (2018)
• A. Figalli - F. Maggi - C. Mooney (Camb. J. Math.)
  The sharp quantitative Euclidean concentration inequality (2018)
• A. Figalli (Nonlinear Anal.)
  On the Continuity of Center-Outward Distribution and Quantile Functions (2018)
• M. Bonforte - A. Figalli - J. L. Vazquez (Calc. Var. Partial Differential Equations)
  Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations (2018)
• A. Figalli (Lecture Notes: Journées équations aux dérivées partielles)
  Free boundary regularity in obstacle problems (2018)
• A. Figalli (Proceedings: Proceedings ICM 2018)
  Regularity of interfaces in phase transitions via obstacle problems (2018)
• E. Baer - A. Figalli (Discrete Contin. Dyn. Syst.)
  Characterization of isoperimetric sets inside almost-convex cones (2017)
• A. Figalli - D. Jerison (Chin. Ann. Math.)
  Quantitative stability of the Brunn-Minkowski inequality for sets of equal volume (2017)
• G. De Philippis - A. Figalli (Nonlinear Anal.)
  Rigidity and stability of Caffarelli's log-concave perturbation theorem (2017)
• S. Chen - A. Figalli (J. Funct. Anal.)
  Partial $W^{2,p}$ regularity for optimal transport maps (2017)
• A. Figalli - D. Jerison (Adv. Math.)
  Quantitative stability for the Brunn-Minkowski inequality (2017)
• A. Figalli - E. Valdinoci (J. Reine Angew. Math.)
  Regularity and Bernstein-type results for nonlocal minimal surfaces (2017)
• M. Colombo - A. Figalli - Y. Jhaveri (Ann. Sc. Norm. Super. Pisa Cl. Sci.)
  Lipschitz changes of variables between perturbations of log-concave measures (2017)
• A. Figalli - B. Krummel - X. Ros-Oton (J. Differential Equations)
  On the regularity of the free boundary in the p-Laplacian obstacle problem (2017)
• A. Figalli (J. Diff. Geom.)
  Regularity of codimension-1 minimizing currents under minimal assumptions on the integrand (2017)
• M. Bonforte - A. Figalli - X. Ros-Oton (Comm. Pure Appl. Math.)
  Infinite speed of propagation and regularity of solutions to the fractional porous medium equation in general domains (2017)
• J. A. Carrillo - A. Figalli - F. S. Patacchini (Ann. Inst. H. Poincaré Anal. Non Linéaire)
  Geometry of minimizers for the interaction energy with mildly repulsive potentials (2017)
• L. Ambrosio - M. Colombo - A. Figalli (Duke Math. J.)
  On the Lagrangian structure of transport equations: the Vlasov-Poisson system (2017)
• A. Figalli (Lecture Notes: Boll. Unione Mat. Ital.)
  A transportation approach to universality in random matrix theory (2016)
• M. Cozzi - A. Figalli (Lecture Notes: CIME Lecture Notes)
  Regularity theory for local and nonlocal minimal surfaces: an overview (2016)
• L. Ambrosio - H. Brezis - J. Bourgain - A. Figalli (Comm. Pure Appl. Math.)
  $BMO$-type norms related to the perimeter of sets (2016)
• A. Figalli - Y. Jhaveri - C. Mooney (J. Funct. Anal.)
  Nonlinear bounds in Hölder spaces for the Monge-Ampère equation (2016)
• S. Chen - A. Figalli (J. Math. Pures Appl.)
  Stability results on the smoothness of optimal transport maps with general costs (2016)
• A. Figalli - A. Pelayo (Adv. Geom.)
  On the density function on moduli spaces of toric 4-manifolds (2016)
• A. Figalli - D. Gomes - D. Marcon (Calc. Var. Partial Differential Equations)
  Weak KAM Theory for a Weakly Coupled System of Hamilton-Jacobi Equations (2016)
• A. Figalli - A. Guionnet (Acta Math.)
  Universality in several-matrix models via approximate transport maps (2016)
• A. Figalli - H. Shahgholian (Accepted Paper: Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.)
  An overview of unconstrained free boundary problems (2015)
• A. Figalli (Lecture notes: CIME Lecture Notes)
  Global existence for the semigeostrophic equations via Sobolev estimates for Monge-Ampère (2015)
• G. De Philippis - A. Figalli (Trans. Amer. Math. Soc.)
  Optimal regularity of the convex envelope (2015)
• A. Figalli - H. Shahgholian (Ann. Mat. Pura Appl.)
  A general class of free boundary problems for fully nonlinear parabolic equations (2015)
• A. Figalli - D. Jerison (J. Eur. Math. Soc. (JEMS))
  Quantitative stability for sumsets in $R^n$ (2015)
• G. Contreras - A. Figalli - L. Rifford (Invent. Math.)
  Generic hyperbolicity of Aubry sets on surfaces (2015)
• G. De Philippis - A. Figalli (Publ. Math. Inst. Hautes Études Sci.)
  Partial Regularity for optimal transport maps (2015)
• A. Figalli - L. Rifford (Comm. Pure Appl. Math.)
  Closing Aubry sets I (2015)
• A. Figalli - L. Rifford (Comm. Pure Appl. Math.)
  Closing Aubry sets II (2015)
• A. Figalli - N. Fusco - F. Maggi - V. Millot - M. Morini (Comm. Math. Phys.)
  Isoperimetry and stability properties of balls with respect to nonlocal energies (2015)
• A. Figalli - T. Gallouët - L. Rifford (SIAM J. Math. Anal.)
  On the convexity of injectivity domains on nonfocal manifolds (2015)
• S. Chen - A. Figalli (Adv. Math.)
  Boundary $\varepsilon$-regularity in optimal transportation (2015)
• G. De Philippis - A. Figalli (Differential Integral Equations)
  A note on the dimension of the singular set in free interface problems (2015)
• F. Bekermam - A. Figalli - A. Guionnet (Comm. Math. Phys.)
  Transport maps for $\beta$-matrix models and Universality (2015)
• L. Ambrosio - M. Colombo - A. Figalli (Arch. Ration. Mech. Anal.)
  Existence and uniqueness of maximal regular flows for non-smooth vector fields (2015)
• A. Figalli (Proceedings ICM 2014)
  Quantitative stability results for the Brunn-Minkowski inequality (2014)
• A. Figalli (Accepted Paper: Colloquium De Giorgi 2013-2014)
  Stability results for the Brunn-Minkowski inequality (2014)
• G. De Philippis - A. Figalli (Springer INdAM series)
  Partial regularity results in optimal transportation (2014)
• G. De Philippis - A. Figalli (Accepted Paper: Bull. Amer. Math. Soc.)
  The Monge-Ampère equation and its link to optimal transportation (2014)
• A. Figalli (J. Math. Sci. (N.Y.))
  Sobolev regularity for the Monge-Ampère equation, with application to the semigeostrophic equations (2014)
• A. Figalli - F. Maggi - A. Pratelli (Ann. Inst. Henri Poincaré Probab. Stat.)
  A Geometric Approach to Correlation Inequalities in the Plane (2014)
• B. Barrios - A. Figalli - E. Valdinoci (Ann. Scuola Norm. Sup. Pisa Cl. Sci.)
  Bootstrap regularity for integro-differential operators and its application to nonlocal minimal surfaces (2014)
• L. Ambrosio - M. Colombo - G. De Philippis - A. Figalli (Discrete Contin. Dyn. Syst.)
  A global existence result for the semigeostrophic equations in three dimensional convex domains (2014)
• A. Figalli - C. Klein - P. Markovich - C. Sparber (Comm. Pure Appl. Math.)
  WKB analysis of Bohmian dynamics (2014)
• M. Colombo - A. Figalli (J. Math. Pures Appl.)
  Regularity results for very degenerate elliptic equations (2014)
• A. Figalli - D. Jerison (J. Funct. Anal.)
  How to recognize convexity of a set from its marginals (2014)
• M. Colombo - A. Figalli (Discrete Contin. Dyn. Syst.)
  An excess-decay result for a class of degenerate elliptic equations (2014)
• G. De Philippis - A. Figalli (Arch. Ration. Mech. Anal.)
  Higher integrability for minimizers of the Mumford-Shah functional (2014)
• A. Figalli - H. Shahgholian (Arch. Ration. Mech. Anal.)
  A general class of free boundary problems for fully nonlinear elliptic equations (2014)
• S. Dipierro - A. Figalli - E. Valdinoci (Comm. Partial Differential Equations)
  Strongly nonlocal dislocation dynamics in crystals (2014)
• A. Figalli - Y. H. Kim - R. J. McCann (J. Eur. Math. Soc. (JEMS))
  Regularity of optimal transport maps on multiple products of spheres (2013)
• L. Caffarelli - A. Figalli (J. Reine Angew. Math.)
  Regularity of solutions to the parabolic fractional obstacle problem (2013)
• G. De Philippis - A. Figalli (Invent. Math.)
  $W^{2,1}$ regularity for solutions of the Monge-Ampère equation (2013)
• A. Figalli - F. Maggi - A. Pratelli (Adv. Math.)
  Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation (2013)
• A. Figalli - E. Indrei (J. Geom. Anal.)
  A sharp stability result for the relative isoperimetric inequality inside convex cones (2013)
• E. Carlen - A. Figalli (Duke Math. J.)
  Stability for a GNS inequality and the Log-HLS inequality, with application to the critical mass Keller-Segel equation (2013)
• A. Figalli - F. Maggi (Calc. Var. Partial Differential Equations)
  On the isoperimetric problem for radial log-convex densities (2013)
• S. Dipierro - A. Figalli - G. Palatucci - E. Valdinoci (Discrete Contin. Dyn. Syst.)
  Asymptotics of the $s$-perimeter as $s \searrow 0$ (2013)
• G. De Philippis - A. Figalli - O. Savin (Math. Ann.)
  A note on interior $W^{2,1+\varepsilon}$ estimates for the Monge-Ampere equation (2013)
• G. De Philippis - A. Figalli (Anal. PDE)
  Second order stability for the Monge-Ampere equation and strong Sobolev convergence of optimal transport maps (2013)
• L. Ambrosio - A. Figalli - E. Runa (Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl.)
  On sets of finite perimeter in Wiener spaces: reduced boundary and convergence to halfspaces (2013)
• A. Figalli - Y. H. Kim - R. J. McCann (Arch. Ration. Mech. Anal.)
  Hölder continuity and injectivity of optimal maps (2013)
• G. De Philippis - A. Figalli (SIAM J. Math. Anal.)
  Sobolev regularity for Monge-Ampère type equations (2013)
• A. Figalli - Y. H. Kim - R. J. McCann (Methods Appl. Anal.)
  On supporting hyperplanes to convex bodies (2013)
• A. Figalli (Congress of Mathematics)
  Stability in geometric and functional inequalities (2013)
• A. Figalli - L. Rifford (Lecture Notes: Contemp. Math.)
  Aubry sets, Hamilton-Jacobi equations, and the Mañé Conjecture (2013)
• S. Daneri - A. Figalli (Lecture Notes: AIMS Ser. Appl. Math.)
  Variational models for the incompressible Euler equations (2013)
• A. Figalli - L. Rifford - C. Villani (Amer. J. Math.)
  Nearly round spheres look convex (2012)
• A. Figalli - Y. Ge (Adv. Calc. Var.)
  Isoperimetric-type inequalities on constant curvature manifolds (2012)
• L. Ambrosio - M. Colombo - G. De Philippis - A. Figalli (Comm. Partial Differential Equations)
  Existence of Eulerian solutions to the semigeostrophic equations in physical space: the 2-dimensional periodic case (2012)
• C. Bjorland - L. Caffarelli - A. Figalli (Comm. Pure Appl. Math.)
  Non-Local Tug-of-War and the Infinity Fractional Laplacian (2012)
• J. A. Carrillo - M. Di Francesco - A. Figalli - T. Laurent - D. Slepčev (Nonlinear Anal.)
  Confinement in nonlocal interaction equations (2012)
• A. Figalli - M. Ligabò - T. Paul (Indiana Univ. Math. J.)
  Semiclassical limit for mixed states with singular and rough potentials (2012)
• M. Bonforte - A. Figalli (J. Differential Equations)
  Total Variation Flow and Sign Fast Diffusion in one dimension (2012)
• C. Bjorland - L. Caffarelli - A. Figalli (Adv. Math.)
  Non-Local Gradient Dependent Operators (2012)
• A. Figalli - N. Gigli (ESAIM Control Optim. Calc. Var.)
  Local semiconvexity of Kantorovich potentials on non-compact manifolds (2011)
• A. Figalli - V. Mandorino (Discrete Contin. Dyn. Syst.)
  Fine properties of minimizers of mechanical Lagrangians with Sobolev potentials (2011)
• A. Figalli - F. Maggi (Arch. Ration. Mech. Anal.)
  On the shape of liquid drops and crystals in the small mass regime (2011)
• L. Ambrosio - A. Figalli (Ann. Fac. Sci. Toulouse Math.)
  Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces (2011)
• A. Figalli - W. Gangbo - T. Yolcu (Ann. Scuola Norm. Sup. Pisa Cl. Sci.)
  A variational method for a class of parabolic PDEs (2011)
• J. A. Carrillo - M. Di Francesco - A. Figalli - T. Laurent - D. Slepčev (Duke Math. J.)
  Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations (2011)
• A. Figalli - Y. H. Kim - R. J. McCann (J. Econom. Theory)
  When is multidimensional screening a convex program? (2011)
• A. Figalli - L. Rifford - C. Villani (Differential Geom. Appl.)
  Tangent cut loci on surfaces (2011)
• A. Figalli - L. Rifford - C. Villani (Tohoku Math. J.)
  Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds (2011)
• A. Luigi - A. Figalli - G. Friesecke - J. Giannoulis - T. Paul (Comm. Pure Appl. Math.)
  Semiclassical limit of quantum dynamics with rough potentials and well posedness of transport equations with measure initial data (2011)
• A. Figalli (Contemp. Math.)
  Quantitative isoperimetric inequalities, with applications to the stability of liquid drops and crystals (2011)
• L. Ambrosio - L. Ambrosio - G. Crippa - G. Crippa - A. Figalli - A. Figalli - L. V. Spinolo - L. V. Spinolo (IMA Vol. Math. Appl.)
  Existence and uniqueness results for the continuity equation and applications to the chromatography system (2011)
• L. Ambrosio - L. Ambrosio - G. Crippa - G. Crippa - A. Figalli - A. Figalli - L. V. Spinolo - L. V. Spinolo (IMA Vol. Math. Appl.)
  Existence and uniqueness results for the continuity equation and applications to the chromatography system (2011)
• A. Figalli - F. Maggi - A. Pratelli (Invent. Math.)
  A mass transportation approach to quantitative isoperimetric inequalities (2010)
• A. Fathi - A. Figalli (Israel J. Math.)
  Optimal transportation on non-compact manifolds (2010)
• A. Figalli - L. Rifford (Geom. Funct. Anal.)
  Mass Transportation on Sub-Riemannian Manifolds (2010)
• A. Figalli (Math. Ann.)
  On flows of $H^{3/2}$-vector fields on the circle (2010)
• A. Figalli (Arch. Ration. Mech. Anal.)
  The optimal partial transport problem (2010)
• A. Figalli (Comm. Partial Differential Equations)
  Regularity properties of optimal maps between nonconvex domains in the plane (2010)
• A. Figalli - N. Gigli (J. Math. Pures Appl.)
  A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions (2010)
• A. Figalli - L. Rifford - C. Villani (Calc. Var. Partial Differential Equations)
  On the Ma-Trudinger-Wang curvature on surfaces (2010)
• L. Ambrosio - A. Figalli (C. R. Math. Acad. Sci. Paris)
  Almost everywhere well-posedness of continuity equations with measure initial data (2010)
• A. Figalli - Y. H. Kim (Discrete Contin. Dyn. Syst. Series A)
  Partial regularity of Brenier solutions of the Monge-Ampère equation (2010)
• A. Figalli (Lecture Notes: Bull. Amer. Math. Soc.)
  Optimal transport. Old and new. [book review] (2010)
• A. Figalli (Lecture Notes: Astérisque)
  Regularity of optimal transport maps (after Ma-Trudinger-Wang and Loeper) (2010)
• L. Ambrosio - G. Crippa - A. Figalli - L. V. Spinolo (SIAM J. Math. Anal.)
  Some new well-posedness results for continuity and transport equations, and applications to the chromatography system (2009)
• L. Ambrosio - A. Figalli (Lecture notes)
  Lecture notes on variational models for incompressible Euler equations (2009)
• A. Figalli (Mémoire HDR)
  Optimal transport, Euler equations, Mather and DiPerna-Lions theories (2009)
• A. Figalli - F. Maggi - A. Pratelli (Ann. Inst. H. Poincaré Anal. Non Linéaire)
  A refined Brunn-Minkowski inequality for convex sets (2009)
• M. Bernot - A. Figalli - F. Santambrogio (J. Math. Pures Appl.)
  Generalized solutions for the Euler equations in one and two dimensions (2009)
• L. Ambrosio - A. Figalli (Arch. Rat. Mech. Anal.)
  Geodesics in the space of measure-preserving maps and plans (2009)
• A. Figalli (ESAIM Control Optim. Calc. Var.)
  A geometric lower bound on Grad's number (2009)
• A. Fathi - A. Figalli - L. Rifford (Comm. Pure Appl. Math.)
  On the Hausdorff Dimension of the Mather Quotient (2009)
• L. Ambrosio - A. Figalli (J. Funct. Anal.)
  On flows associated to Sobolev vector fields in Wiener spaces: an approach a' la DiPerna-Lions (2009)
• A. Figalli - F. Maggi - A. Pratelli (Proc. Amer. Math. Soc.)
  A note on Cheeger sets (2009)
• A. Figalli - G. Loeper (Calc. Var. Partial Differential Equations)
  $C^1$ regularity of solutions of the Monge-Ampère equation for optimal transport in dimension two (2009)
• A. Figalli (Rend. Circ. Mat. Palermo)
  A note on the regularity of the free boundaries in the optimal partial transport problem (2009)
• A. Figalli - L. Rifford (Comm. Pure Appl. Math.)
  Continuity of optimal transport maps and convexity of injectivity domains on small deformations of S^2 (2009)
• L. Desvillettes - A. Figalli (Lecture Notes: Gazette SMF)
  Cédric Villani reçoit un prix de la Société Mathématique Européenne (2009)
• A. Figalli - C. Villani (Lecture Notes)
  Optimal Transport and Curvature (2008)
• L. Ambrosio - A. Figalli (Calc. Var. Partial Differential Equations)
  On the regularity of the pressure field of Brenier's weak solutions to incompressible Euler equations (2008)
• A. Figalli (J. Funct. Anal.)
  Existence and uniqueness of martingale solutions for SDEs with rough or degenerate coefficients (2008)
• A. Figalli (Proc. Amer. Math. Soc.)
  A simple proof of the Morse-Sard Theorem in Sobolev Spaces (2008)
• A. Figalli - N. Juillet (J. Funct. Anal.)
  Absolute continuity of Wasserstein geodesics in the Heisenberg group (2008)
• A. Figalli - C. Villani (Methods Appl. Anal.)
  An approximation lemma about the cut locus, with applications in optimal transport theory (2008)
• A. Figalli - R. Philipowski (ALEA Lat. Am. J. Probab. Math. Stat.)
  Convergence to the viscous porous medium equation and propagation of chaos (2008)
• M. Bernot - A. Figalli (ESAIM: COCV)
  Synchronized traffic plans and stability of optima (2008)
• A. Abbondandolo - A. Figalli (J. Fixed Point Theory Appl.)
  Invariant measures of Hamiltonian systems with prescribed asymptotic Maslov index (2008)
• A. Figalli (Ph.D. Thesis)
  Optimal transportation and action-minimizing measures (2007)
• A. Figalli (Rend. Sem. Mat. Univ. Padova)
  The Monge problem on non-compact manifolds (2007)
• A. Figalli - C. Villani (Mathematische Zeitschrift)
  Strong displacement convexity on Riemannian manifolds (2007)
• A. Figalli (SIAM Journal on Mathematical Analysis)
  Existence, uniqueness and regularity of optimal transport maps (2007)
• A. Abbondandolo - A. Figalli (J. Differential Equations)
  High action orbits for Tonelli Lagrangians and superlinear Hamiltonians on compact configuration spaces (2007)
• A. Figalli (Degree Thesis (5th year))
  Trasporto ottimale su varietà non compatte (2006)
• A. Figalli (Degree Thesis (3rd year))
  Il problema di Bernstein e una congettura di De Giorgi (2004)

Seminars:

• 17 dec 2013: Stability results for the semisum of sets in R^n

Speaker:

• 24 jun 2024 - 28 jun 2024: Vito Volterra Meeting in Calculus of Variations 2024
• 12 jun 2023 - 16 jun 2023: Calculus of Variations and Geometric Measure Theory
• 6 apr 2022 - 8 apr 2022: Probability, Analysis and Dynamics '22
• 5 sep 2021 - 10 sep 2021: New Trends in Nonlinear Diffusion: a Bridge between PDEs, Analysis and Geometry (Online)
• 10 jun 2021 - 10 jun 2021: James (Jim) Perry Browne Sussex Mathematics Colloquium, 10 June 2021, 3:00-4:00 (UK time zone, via Zoom)
• 17 jan 2019 - 19 jan 2019: Workshop "Variational problems, PDEs and applications"
• 3 sep 2018 - 6 sep 2018: Meeting on Applied Mathematics and Calculus of Variations
• 3 jul 2017 - 6 jul 2017: Recent Advances in PDEs and the Calculus of Variations
• 24 apr 2017 - 26 apr 2017: Transport problems in Zurich
• 19 sep 2016 - 23 sep 2016: A Mathematical Tribute to Ennio De Giorgi
• 14 dec 2015 - 18 dec 2015: Trilateral Meeting on Nonlinear Partial Differential Equations and Applications
• 30 jun 2014 - 5 jul 2014: Existence and Regularity for Nonlinear Sytems of Partial Differential Equations
• 16 jun 2014 - 20 jun 2014: 12th workshop on interactions between dynamical systems and partial differential equations (JISD2014)
• 10 jun 2014 - 14 jun 2014: Recent advances in non-local and non-linear analysis: theory and applications
• 9 jun 2014 - 14 jun 2014: 1° Corso Intensivo di Calcolo delle Variazioni
• 2 jun 2014 - 7 jun 2014: Partial Differential Equations and Geometric Measure Theory
• 15 jul 2013 - 2 aug 2013: School and Workshop on "Geometric Measure Theory and Optimal Transport"
• 5 nov 2012 - 9 nov 2012: ERC Workshop on Optimal Transportation and Applications
• 13 jun 2011 - 17 jun 2011: Colab Summer School on ''Aubry-Mather Theory and Optimal Transport"
• 5 jun 2011 - 10 jun 2011: ERC-Summer School on "Calculus of Variations, Continuum Mechanics and Geometric Inequalities"
• 15 jun 2009 - 27 jun 2009: Optimal transportation: Theory and applications

Organizer:

• 6 mar 2024 - 7 mar 2024: Particle Systems in Dynamics, Optimization, and Learning
• 24 jan 2023 - 25 jan 2023: Workshop on Interpolation of Measures
• 18 may 2015 - 29 may 2015: Calculus of Variations and Nonlinear Partial Differential Equations