A. Figalli: Il problema di Bernstein e una congettura di De Giorgi (Degree Thesis (3rd year)) p. 69, 2004 A. Figalli: Trasporto ottimale su varietà non compatte (Degree Thesis (5th year)) p. 99, 2006 A. Figalli: Optimal transportation and action-minimizing measures (Ph.D. Thesis) p. 251, 2007 A. Figalli: The Monge problem on non-compact manifolds Rend. Sem. Mat. Univ. Padova 2007 A. Figalli: Existence, uniqueness and regularity of optimal transport maps SIAM Journal on Mathematical Analysis 2007 A. Abbondandolo, A. Figalli: High action orbits for Tonelli Lagrangians and superlinear Hamiltonians on compact configuration spaces J. Differential Equations 2007 A. Figalli, C. Villani: Strong displacement convexity on Riemannian manifolds Mathematische Zeitschrift 2007 A. Figalli, C. Villani: Optimal Transport and Curvature (Lecture Notes) 2008 L. Ambrosio, A. Figalli: On the regularity of the pressure field of Brenier's weak solutions to incompressible Euler equations Calc. Var. Partial Differential Equations 2008 A. Figalli: Existence and uniqueness of martingale solutions for SDEs with rough or degenerate coefficients J. Funct. Anal. 2008 A. Figalli: A simple proof of the Morse-Sard Theorem in Sobolev Spaces Proc. Amer. Math. Soc. 2008 A. Figalli, N. Juillet: Absolute continuity of Wasserstein geodesics in the Heisenberg group J. Funct. Anal. 2008 A. Figalli, C. Villani: An approximation lemma about the cut locus, with applications in optimal transport theory Methods Appl. Anal. 2008 M. Bernot, A. Figalli: Synchronized traffic plans and stability of optima ESAIM: COCV 2008 A. Figalli, R. Philipowski: Convergence to the viscous porous medium equation and propagation of chaos ALEA Lat. Am. J. Probab. Math. Stat. 2008 A. Abbondandolo, A. Figalli: Invariant measures of Hamiltonian systems with prescribed asymptotic Maslov index J. Fixed Point Theory Appl. 2008 L. Ambrosio, G. Crippa, A. Figalli, L. V. Spinolo: Some new well-posedness results for continuity and transport equations, and applications to the chromatography system SIAM J. Math. Anal. Vol. 41, N. 5, p. 1890-1920, 2009 L. Ambrosio, A. Figalli: Lecture notes on variational models for incompressible Euler equations (Lecture notes) 2009 A. Figalli: Optimal transport, Euler equations, Mather and DiPerna-Lions theories (Mémoire HDR) p. 53, 2009 A. Figalli, F. Maggi, A. Pratelli: A refined Brunn-Minkowski inequality for convex sets Ann. Inst. H. Poincaré Anal. Non Linéaire 2009 M. Bernot, A. Figalli, F. Santambrogio: Generalized solutions for the Euler equations in one and two dimensions J. Math. Pures Appl. 2009 L. Ambrosio, A. Figalli: Geodesics in the space of measure-preserving maps and plans Arch. Rat. Mech. Anal. 2009 A. Figalli: A geometric lower bound on Grad's number ESAIM Control Optim. Calc. Var. 2009 A. Fathi, A. Figalli, L. Rifford: On the Hausdorff Dimension of the Mather Quotient Comm. Pure Appl. Math. 2009 L. Ambrosio, A. Figalli: On flows associated to Sobolev vector fields in Wiener spaces: an approach a' la DiPerna-Lions J. Funct. Anal. 2009 A. Figalli, F. Maggi, A. Pratelli: A note on Cheeger sets Proc. Amer. Math. Soc. 2009 A. Figalli: A note on the regularity of the free boundaries in the optimal partial transport problem Rend. Circ. Mat. Palermo 2009 A. Figalli, G. Loeper: $C^1$ regularity of solutions of the Monge-Ampère equation for optimal transport in dimension two Calc. Var. Partial Differential Equations 2009 A. Figalli, L. Rifford: Continuity of optimal transport maps and convexity of injectivity domains on small deformations of S^2 Comm. Pure Appl. Math. 2009 L. Desvillettes, A. Figalli: Cédric Villani reçoit un prix de la Société Mathématique Européenne Gazette SMF (Lecture Notes) 2009 A. Figalli, F. Maggi, A. Pratelli: A mass transportation approach to quantitative isoperimetric inequalities Invent. Math. 2010 A. Fathi, A. Figalli: Optimal transportation on non-compact manifolds Israel J. Math. 2010 A. Figalli, L. Rifford: Mass Transportation on Sub-Riemannian Manifolds Geom. Funct. Anal. 2010 A. Figalli: On flows of $H^{3/2}$-vector fields on the circle Math. Ann. 2010 A. Figalli: The optimal partial transport problem Arch. Ration. Mech. Anal. 2010 A. Figalli: Regularity properties of optimal maps between nonconvex domains in the plane Comm. Partial Differential Equations 2010 A. Figalli, N. Gigli: A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions J. Math. Pures Appl. 2010 A. Figalli, L. Rifford, C. Villani: On the Ma-Trudinger-Wang curvature on surfaces Calc. Var. Partial Differential Equations 2010 L. Ambrosio, A. Figalli: Almost everywhere well-posedness of continuity equations with measure initial data C. R. Math. Acad. Sci. Paris 2010 A. Figalli, Y. H. Kim: Partial regularity of Brenier solutions of the Monge-Ampère equation Discrete Contin. Dyn. Syst. Series A 2010 A. Figalli: Optimal transport. Old and new. [book review] Bull. Amer. Math. Soc. (Lecture Notes) 2010 A. Figalli: Regularity of optimal transport maps (after Ma-Trudinger-Wang and Loeper) Astérisque (Lecture Notes) 2010 A. Figalli, N. Gigli: Local semiconvexity of Kantorovich potentials on non-compact manifolds ESAIM Control Optim. Calc. Var. 2011 A. Figalli, V. Mandorino: Fine properties of minimizers of mechanical Lagrangians with Sobolev potentials Discrete Contin. Dyn. Syst. 2011 A. Figalli, W. Gangbo, T. Yolcu: A variational method for a class of parabolic PDEs Ann. Scuola Norm. Sup. Pisa Cl. Sci. 2011 J. A. Carrillo, M. Di Francesco, A. Figalli, T. Laurent, D. Slepev: Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations Duke Math. J. 2011 A. Figalli, F. Maggi: On the shape of liquid drops and crystals in the small mass regime Arch. Ration. Mech. Anal. 2011 L. Ambrosio, A. Figalli: Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces Ann. Fac. Sci. Toulouse Math. 2011 A. Figalli, Y. H. Kim, R. J. McCann: When is multidimensional screening a convex program? J. Econom. Theory 2011 A. Figalli, L. Rifford, C. Villani: Tangent cut loci on surfaces Differential Geom. Appl. 2011 A. Figalli, L. Rifford, C. Villani: Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds Tohoku Math. J. 2011 A. Figalli, G. Friesecke, J. Giannoulis, A. Luigi, T. Paul: Semiclassical limit of quantum dynamics with rough potentials and well posedness of transport equations with measure initial data Comm. Pure Appl. Math. 2011 A. Figalli: Quantitative isoperimetric inequalities, with applications to the stability of liquid drops and crystals Contemp. Math. 2011 L. Ambrosio, L. Ambrosio, G. Crippa, G. Crippa, A. Figalli, A. Figalli, L. V. Spinolo, L. V. Spinolo: Existence and uniqueness results for the continuity equation and applications to the chromatography system IMA Vol. Math. Appl. 2011 L. Ambrosio, L. Ambrosio, G. Crippa, G. Crippa, A. Figalli, A. Figalli, L. V. Spinolo, L. V. Spinolo: Existence and uniqueness results for the continuity equation and applications to the chromatography system IMA Vol. Math. Appl. 2011 A. Figalli, L. Rifford, C. Villani: Nearly round spheres look convex Amer. J. Math. 2012 C. Bjorland, L. Caffarelli, A. Figalli: Non-Local Tug-of-War and the Infinity Fractional Laplacian Comm. Pure Appl. Math. 2012 A. Figalli, Y. Ge: Isoperimetric-type inequalities on constant curvature manifolds Adv. Calc. Var. 2012 J. A. Carrillo, M. Di Francesco, A. Figalli, T. Laurent, D. Slepev: Confinement in nonlocal interaction equations Nonlinear Anal. 2012 A. Figalli, M. Ligabò, T. Paul: Semiclassical limit for mixed states with singular and rough potentials Indiana Univ. Math. J. 2012 L. Ambrosio, M. Colombo, G. De Philippis, A. Figalli: Existence of Eulerian solutions to the semigeostrophic equations in physical space: the 2-dimensional periodic case Comm. Partial Differential Equations 2012 M. Bonforte, A. Figalli: Total Variation Flow and Sign Fast Diffusion in one dimension J. Differential Equations 2012 C. Bjorland, L. Caffarelli, A. Figalli: Non-Local Gradient Dependent Operators Adv. Math. 2012 L. Caffarelli, A. Figalli: Regularity of solutions to the parabolic fractional obstacle problem J. Reine Angew. Math. 2013 G. De Philippis, A. Figalli: $W^{2,1}$ regularity for solutions of the Monge-Ampère equation Invent. Math. 2013 A. Figalli, F. Maggi, A. Pratelli: Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation Adv. Math. 2013 A. Figalli, Y. H. Kim, R. J. McCann: Regularity of optimal transport maps on multiple products of spheres J. Eur. Math. Soc. (JEMS) 2013 A. Figalli, E. Indrei: A sharp stability result for the relative isoperimetric inequality inside convex cones J. Geom. Anal. 2013 E. Carlen, A. Figalli: Stability for a GNS inequality and the Log-HLS inequality, with application to the critical mass Keller-Segel equation Duke Math. J. 2013 A. Figalli, F. Maggi: On the isoperimetric problem for radial log-convex densities Calc. Var. Partial Differential Equations 2013 S. Dipierro, A. Figalli, G. Palatucci, E. Valdinoci: Asymptotics of the $s$-perimeter as $s \searrow 0$ Discrete Contin. Dyn. Syst. Vol. 33, N. 7, p. 2777-2790, 2013 G. De Philippis, A. Figalli, O. Savin: A note on interior $W^{2,1+\varepsilon}$ estimates for the Monge-Ampere equation Math. Ann. 2013 G. De Philippis, A. Figalli: Second order stability for the Monge-Ampere equation and strong Sobolev convergence of optimal transport maps Anal. PDE 2013 L. Ambrosio, A. Figalli, E. Runa: On sets of finite perimeter in Wiener spaces: reduced boundary and convergence to halfspaces Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 2013 G. De Philippis, A. Figalli: Sobolev regularity for Monge-Ampère type equations SIAM J. Math. Anal. 2013 A. Figalli, Y. H. Kim, R. J. McCann: Hölder continuity and injectivity of optimal maps Arch. Ration. Mech. Anal. 2013 A. Figalli, Y. H. Kim, R. J. McCann: On supporting hyperplanes to convex bodies Methods Appl. Anal. 2013 A. Figalli: Stability in geometric and functional inequalities Congress of Mathematics 2013 A. Figalli, L. Rifford: Aubry sets, Hamilton-Jacobi equations, and the Mañé Conjecture Contemp. Math. (Lecture Notes) 2013 S. Daneri, A. Figalli: Variational models for the incompressible Euler equations AIMS Ser. Appl. Math. (Lecture Notes) 2013 A. Figalli: Quantitative stability results for the Brunn-Minkowski inequality (Proceedings ICM 2014) 2014 A. Figalli: Stability results for the Brunn-Minkowski inequality Colloquium De Giorgi 2013-2014 (Accepted Paper) 2014 G. De Philippis, A. Figalli: Partial regularity results in optimal transportation (Springer INdAM series) 2014 G. De Philippis, A. Figalli: The Monge-Ampère equation and its link to optimal transportation Bull. Amer. Math. Soc. (Accepted Paper) http://arxiv.org/abs/1310.6167 2014 A. Figalli: Sobolev regularity for the Monge-Ampère equation, with application to the semigeostrophic equations J. Math. Sci. (N.Y.) 2014 A. Figalli, F. Maggi, A. Pratelli: A Geometric Approach to Correlation Inequalities in the Plane Ann. Inst. Henri Poincaré Probab. Stat. 2014 B. Barrios, A. Figalli, E. Valdinoci: Bootstrap regularity for integro-differential operators and its application to nonlocal minimal surfaces Ann. Scuola Norm. Sup. Pisa Cl. Sci. 2014 L. Ambrosio, M. Colombo, G. De Philippis, A. Figalli: A global existence result for the semigeostrophic equations in three dimensional convex domains Discrete Contin. Dyn. Syst. 2014 A. Figalli, C. Klein, P. Markovich, C. Sparber: WKB analysis of Bohmian dynamics Comm. Pure Appl. Math. 2014 M. Colombo, A. Figalli: Regularity results for very degenerate elliptic equations J. Math. Pures Appl. 2014 A. Figalli, D. Jerison: How to recognize convexity of a set from its marginals J. Funct. Anal. 2014 M. Colombo, A. Figalli: An excess-decay result for a class of degenerate elliptic equations Discrete Contin. Dyn. Syst. 2014 G. De Philippis, A. Figalli: Higher integrability for minimizers of the Mumford-Shah functional Arch. Ration. Mech. Anal. 2014 A. Figalli, H. Shahgholian: A general class of free boundary problems for fully nonlinear elliptic equations Arch. Ration. Mech. Anal. 2014 S. Dipierro, A. Figalli, E. Valdinoci: Strongly nonlocal dislocation dynamics in crystals Comm. Partial Differential Equations 2014 A. Figalli, H. Shahgholian: An overview of unconstrained free boundary problems Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. (Accepted Paper) 2015 A. Figalli: Global existence for the semigeostrophic equations via Sobolev estimates for Monge-Ampère CIME Lecture Notes (Lecture notes) 2015 G. De Philippis, A. Figalli: Optimal regularity of the convex envelope Trans. Amer. Math. Soc. 2015 A. Figalli, H. Shahgholian: A general class of free boundary problems for fully nonlinear parabolic equations Ann. Mat. Pura Appl. 2015 A. Figalli, L. Rifford: Closing Aubry sets I Comm. Pure Appl. Math. 2015 A. Figalli, L. Rifford: Closing Aubry sets II Comm. Pure Appl. Math. 2015 A. Figalli, D. Jerison: Quantitative stability for sumsets in $R^n$ J. Eur. Math. Soc. (JEMS) 2015 G. Contreras, A. Figalli, L. Rifford: Generic hyperbolicity of Aubry sets on surfaces Invent. Math. 2015 A. Figalli, N. Fusco, F. Maggi, V. Millot, M. Morini: Isoperimetry and stability properties of balls with respect to nonlocal energies Comm. Math. Phys. 2015 G. De Philippis, A. Figalli: Partial Regularity for optimal transport maps Publ. Math. Inst. Hautes Études Sci. 2015 A. Figalli, T. Gallouët, L. Rifford: On the convexity of injectivity domains on nonfocal manifolds SIAM J. Math. Anal. 2015 S. Chen, A. Figalli: Boundary $\varepsilon$-regularity in optimal transportation Adv. Math. 2015 G. De Philippis, A. Figalli: A note on the dimension of the singular set in free interface problems Differential Integral Equations 2015 F. Bekermam, A. Figalli, A. Guionnet: Transport maps for $\beta$-matrix models and Universality Comm. Math. Phys. 2015 L. Ambrosio, M. Colombo, A. Figalli: Existence and uniqueness of maximal regular flows for non-smooth vector fields Arch. Ration. Mech. Anal. 2015 A. Figalli: A transportation approach to universality in random matrix theory Boll. Unione Mat. Ital. (Lecture Notes) 2016 M. Cozzi, A. Figalli: Regularity theory for local and nonlocal minimal surfaces: an overview CIME Lecture Notes (Lecture Notes) 2016 L. Ambrosio, J. Bourgain, H. Brezis, A. Figalli: $BMO$-type norms related to the perimeter of sets Comm. Pure Appl. Math. 2016 A. Figalli, A. Pelayo: On the density function on moduli spaces of toric 4-manifolds Adv. Geom. 2016 A. Figalli, Y. Jhaveri, C. Mooney: Nonlinear bounds in Hölder spaces for the Monge-Ampère equation J. Funct. Anal. 2016 S. Chen, A. Figalli: Stability results on the smoothness of optimal transport maps with general costs J. Math. Pures Appl. 2016 A. Figalli, D. Gomes, D. Marcon: Weak KAM Theory for a Weakly Coupled System of Hamilton-Jacobi Equations Calc. Var. Partial Differential Equations 2016 A. Figalli, A. Guionnet: Universality in several-matrix models via approximate transport maps Acta Math. 2016 E. Baer, A. Figalli: Characterization of isoperimetric sets inside almost-convex cones Discrete Contin. Dyn. Syst. 2017 A. Figalli, D. Jerison: Quantitative stability of the Brunn-Minkowski inequality for sets of equal volume Chin. Ann. Math. 2017 G. De Philippis, A. Figalli: Rigidity and stability of Caffarelli's log-concave perturbation theorem Nonlinear Anal. 2017 S. Chen, A. Figalli: Partial $W^{2,p}$ regularity for optimal transport maps J. Funct. Anal. 2017 A. Figalli, B. Krummel, X. Ros-Oton: On the regularity of the free boundary in the p-Laplacian obstacle problem J. Differential Equations 2017 A. Figalli, D. Jerison: Quantitative stability for the Brunn-Minkowski inequality Adv. Math. 2017 A. Figalli: Regularity of codimension-1 minimizing currents under minimal assumptions on the integrand J. Diff. Geom. 2017 M. Bonforte, A. Figalli, X. Ros-Oton: Infinite speed of propagation and regularity of solutions to the fractional porous medium equation in general domains Comm. Pure Appl. Math. 2017 A. Figalli, E. Valdinoci: Regularity and Bernstein-type results for nonlocal minimal surfaces J. Reine Angew. Math. 2017 M. Colombo, A. Figalli, Y. Jhaveri: Lipschitz changes of variables between perturbations of log-concave measures Ann. Sc. Norm. Super. Pisa Cl. Sci. 2017 J. A. Carrillo, A. Figalli, F. S. Patacchini: Geometry of minimizers for the interaction energy with mildly repulsive potentials Ann. Inst. H. Poincaré Anal. Non Linéaire 2017 L. Ambrosio, M. Colombo, A. Figalli: On the Lagrangian structure of transport equations: the Vlasov-Poisson system Duke Math. J. 2017 A. Figalli: On the Monge-Ampère equation (Lecture Notes) 2018 A. Figalli, J. Palmer, A. Pelayo: Symplectic G-capacities and integrable systems Ann. Scuola Norm. Sup. Pisa Cl. Sci. 2018 G. Ciraolo, A. Figalli, F. Maggi, M. Novaga: Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature J. Reine Angew. Math. Vol. 741, p. 275-294, 2018 G. Ciraolo, A. Figalli, F. Maggi: A quantitative analysis of metrics on $\mathbb R^n$ with almost constant positive scalar curvature, with applications to fast diffusion flows Int. Math. Res. Not. IMRN p. 31, 2018 B. Barrios, A. Figalli, X. Ros-Oton: Global regularity for the free boundary in the obstacle problem for the fractional Laplacian Amer. J. Math. 2018 B. Barrios, A. Figalli, X. Ros-Oton: Free boundary regularity in the parabolic fractional obstacle problem Comm. Pure Appl. Math. 2018 A. Figalli, M. J. Kang, J. Morales: Global well-posedness of the spatially homogeneous Kolmogorov-Vicsek model as a gradient flow Arch. Ration. Mech. Anal. 2018 A. Figalli, C. Mooney: An obstacle problem for conical deformations of thin elastic sheets Arch. Ration. Mech. Anal. 2018 A. Figalli: On the Continuity of Center-Outward Distribution and Quantile Functions Nonlinear Anal. 2018 M. Bonforte, A. Figalli, J. L. Vazquez: Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains Anal. PDE 2018 A. Figalli, F. Maggi, C. Mooney: The sharp quantitative Euclidean concentration inequality Camb. J. Math. 2018 M. Bonforte, A. Figalli, J. L. Vazquez: Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations Calc. Var. Partial Differential Equations 2018 A. Figalli: Free boundary regularity in obstacle problems Journées équations aux dérivées partielles (Lecture Notes) 2018 A. Figalli: Regularity of interfaces in phase transitions via obstacle problems Proceedings ICM 2018 (Proceedings) 2018 A. Figalli, R. Neumayer: Gradient stability for the Sobolev inequality: the case $p\geq 2$ J. Eur. Math. Soc. (JEMS) 2019 D. Cordero-Erausquin, A. Figalli: Regularity of monotone transport maps between unbounded domains Discrete Contin. Dyn. Syst. 2019 A. Figalli, M. J. Kang: A rigorous derivation from the kinetic Cucker-Smale model to the pressureless Euler system with nonlocal alignment Anal. PDE 2019 A. Figalli, J. Serra: On the fine structure of the free boundary for the classical obstacle problem Invent. Math. 2019 J. E. M. Braga, A. Figalli, D. Moreira: Optimal regularity for the convex envelope and semiconvex functions related to supersolutions of fully nonlinear elliptic equations Comm. Math. Phys. 2019 L. Caffarelli, F. Cagnetti, A. Figalli: Optimal regularity and structure of the free boundary for minimizers in cohesive zone models Arch. Ration. Mech. Anal. 2020 X. Fernández-Real, A. Figalli: On the obstacle problem for the 1D wave equation Math. Eng. 2020 A. Figalli, J. Serra: On stable solutions for boundary reactions: a De Giorgi-type result in dimension 4+1 Invent. Math. 2020 A. Figalli, F. Glaudo: On the sharp stability of critical points of the Sobolev inequality Arch. Ration. Mech. Anal. 2020 G. Ciraolo, A. Figalli, A. Roncoroni: Symmetry results for critical anisotropic $p$-Laplacian equations in convex cones Geom. Funct. Anal. 2020 X. Cabré, A. Figalli, X. Ros-Oton, J. Serra: Stable solutions to semilinear elliptic equations are smooth up to dimension 9 Acta Math. 2020 A. Figalli, X. Ros-Oton, J. Serra: Generic regularity of free boundaries for the obstacle problem Publ. Math. Inst. Hautes Études Sci. 2020 A. Abbas, A. Figalli, A. Lucchi, D. Sutter, S. Woerner, C. Zoufal: The power of quantum neural networks Nat. Comput. Sci. 2021 A. Figalli, D. Jerison: A sharp Freiman type estimate for semisums in two and three dimensional Euclidean spaces Ann. Sci. Éc. Norm. Supér. 2021 M. Bonforte, A. Figalli: Sharp Extinction Rates for Fast Diffusion Equations on Generic Bounded Domains Comm. Pure Appl. Math. 2021 A. Figalli, S. Kim, H. Shahgholian: Lipschitz Regularity in Vectorial Linear Transmission Problems Nonlinear Anal. 2022 A. Figalli, Y. R. Y. Zhang: Sharp gradient stability for the Sobolev inequality Duke Math. J. 2022 G. Bordigoni, A. Figalli, A. Ledford, P. Ustinov: Strategic execution trajectories Appl. Math. Finance 2022 A. Belotto da Silva, A. Figalli, A. Parusiski, L. Rifford: Strong Sard Conjecture and regularity of singular minimizing geodesics for analytic sub-Riemannian structures in dimension 3 Invent. Math. 2022 X. Fernández-Real, A. Figalli: The Continuous Formulation of Shallow Neural Networks as Wasserstein-Type Gradient Flows Published, Springer, Cham (Lecture Notes) 2022 A. Figalli, Y. R. Y. Zhang: Strong stability for the Wulff inequality with a crystalline norm Comm. Pure Appl. Math. 2022 A. Figalli, Y. Jhaveri: Regularity properties of monotone measure-preserving maps Adv. Nonlinear Stud. 2023 A. Figalli, C. Kehle: On the prescribed negative Gauss curvature problem for graphs Discrete Contin. Dyn. Syst. 2023 A. Figalli: An introduction to optimal transport and Wasserstein gradient flows Preprint (Lecture Notes) 2023 J. Dolbeault, M. J. Esteban, A. Figalli, M. Loss, F. Rupert: A short review on improvements and stability for some interpolation inequalities Proceedings of ICIAM 2023 (Lecture Notes) 2023 A. Figalli, Y. R. Y. Zhang: Strong stability of convexity with respect to the perimeter (Submitted Paper) http://arxiv.org/abs/2307.01633 2023 K. Böröczky, A. Figalli, J. P. G. Ramos : A quantitative stability result for the Prékopa-Leindler inequality for arbitrary measurable functions Ann. Inst. H. Poincaré Anal. Non Linéaire 2024 M. Bonforte, A. Figalli: The Cauchy-Dirichlet Problem for the Fast Diffusion Equation on Bounded Domains Nonlinear Anal. 2024 A. Figalli, Y. R. Y. Zhang: Uniform boundedness for finite Morse index solutions to supercritical semilinear elliptic equations Comm. Pure Appl. Math. 2024 A. Figalli, X. Ros-Oton, J. Serra: The singular set in the Stefan problem J. Amer. Math. Soc 2024 E. Borgonovo, A. Figalli, E. Plischke, G. Savaré: Global sensitivity analysis via optimal transport Management Science (Accepted Paper) 2024 M. Datres, A. Figalli, G. P. Leonardi, D. Sutter: A Two-Scale Complexity Measure for Deep Learning Models NeurIPS (Accepted Paper) http://arxiv.org/abs/2401.09184 2024 G. Carlier, A. Figalli, F. Santambrogio: On optimal transport maps between 1/d-concave densities Ann. Inst. H. Poincaré Anal. Non Linéaire (Accepted Paper) 2024 S. Eberle, A. Figalli, G. S. Weiss: Complete classification of global solutions to the obstacle problem Ann. of Math. (Accepted Paper) 2024 L. Chizat, M. Colombo, X. Fernández-Real, A. Figalli: Infinite-width limit of deep linear neural networks Comm. Pure Appl. Math. (Accepted Paper) 2024 A. Figalli, A. Guerra, S. Kim, H. Shahgholian: Constraint maps with free boundaries: the Bernoulli case J. Eur. Math. Soc. (JEMS) (Accepted Paper) 2024 A. Figalli, A. Guerra, S. Kim, H. Shahgholian: Constraint maps: singularities vs free boundaries (Submitted Paper) 2024 A. Figalli, J. P. G. Ramos: Improved stability versions of the PrékopaLeindler inequality (Accepted Paper) 2024 A. Figalli, H. Shahgholian, K. Sunghan: Constraint maps with free boundaries: the obstacle case Arch. Ration. Mech. Anal. 2024 A. Figalli, A. Guerra, S. Kim, H. Shahgholian: Constraint Maps and Free Boundaries to appear (Lecture Notes) 2025 A. Figalli, M. Tiba, P. Van Hintum: Sharp Quantitative Stability for the Prékopa-Leindler and Borell-Brascamp-Lieb Inequalities (Submitted Paper) 2025