I am an analyst. My research interests are around calculus of variations; nonlinear PDEs; optimal mass transport; mean field games; optimal control. Using optimal transport as main tool I study mainly models arising in mean field games; macroscopic crowd motions; degenerate diffusion equations; particle systems; machine learning; fluid mechanics; etc. Recently I have been working on infinite dimensional Hamiltonian dynamics in the framework of the Wasserstein space and on master equations in the theory of MFG. I am also interested in some aspects of metric/differential geometry; stochastic analysis and probability; geometric measure theory. In general, I am curious about almost all phenomena that can be formulated by means of PDEs.

My research is currently partially supported by the EPSRC New Investigator Award EP/X020320/1, Mean Field Games and Master Equations.

I am present on google scholar.

Preprints

• Long Time Behavior and Stabilization for Displacement Monotone Mean Field Games (with M. Cirant), [arXiv:2412.14903] [cvgmt].
• Improved convergence rates for the Hele-Shaw limit in the presence of confining potentials (with N. David, F. Santambrogio), [arXiv:2405.07227] [cvgmt].
• Convergence analysis of controlled particle systems arising in deep learning: from finite to infinite sample size (with H. Liao, C. Mou, C. Zhou), [arXiv:2404.05185] [cvgmt].
• Kinetic-type Mean Field Games with Non-separable Local Hamiltonians (with D. Ambrose, M. Griffin-Pickering), [arXiv:2403.12829] [cvgmt].
• Hidden monotonicity and canonical transformations for mean field games and master equations (with M. Bansil), [arXiv:2403.05426] [cvgmt].
• On classical solutions and canonical transformations for Hamilton-Jacobi-Bellman equations (with M. Bansil), [arXiv:2403.05412] [cvgmt].
• On nonexpansiveness of metric projection operators on Wasserstein spaces (with A. Adve), [arXiv:2009.01370] [cvgmt].

Published or accepted papers

• Global Well-Posedness of Displacement Monotone Degenerate Mean Field Games Master Equations (with M. Bansil, C. Mou), to appear in SIAM J. Control Optim.,[arXiv:2308.16167] [cvgmt].
• On Some Mean Field Games and Master Equations through the lens of conservation laws (with J. Graber), Math. Ann., 390 (2024), no. 3, 4497-4533. [arXiv:2208.10360] [cvgmt].
• Mean Field Games systems under displacement monotonicity (with C. Mou), SIAM J. Math. Anal., 56 (2024), no. 1, 529-553. [arXiv:2109.06687] [cvgmt].
• On monotonicity conditions for Mean Field Games (with J. Graber), J. Funct. Anal., 285 (2023), Issue 9, 110095. [arXiv:2210.02281] [cvgmt].
• Well-posedness of mean field games master equations involving non-separable local Hamiltonians (with D.M. Ambrose), Trans. Amer. Math. Soc., 376 (2023), no. 4, 2481-2523. [arXiv:2105.03926] [cvgmt].
• Mean Field Games Master Equations with Non-separable Hamiltonians and Displacement Monotonicity (with W. Gangbo, C. Mou, J. Zhang), Ann. Probab., 50 (2022), No. 6, pp. 2178-2217. [arXiv:2101.12362] [cvgmt].
• A variational approach to first order kinetic mean field games with local couplings (with M. Griffin-Pickering), Comm. Partial Differential Equations, 47 (2022), Issue 10, pp. 1945-2022. [arXiv:2112.03141] [cvgmt].
• Global well-posedness of Master equations for deterministic displacement convex potential mean field games (with W. Gangbo), Comm. Pure Appl. Math., 75 (2022), Issue 12, pp. 2685-2801. [arXiv:2004.01660] [cvgmt].
• Degenerate nonlinear parabolic equations with discontinuous diffusion coefficients (with D. Kwon), J. Lond. Math. Soc., 104(2), (2021), pp. 688-746. [arXiv:1907.11319] [cvgmt].
• Weak solutions to the Muskat problem with surface tension via optimal transport (with M. Jacobs and I. Kim), Arch. Ration. Mech. Anal., 239 (2021), 389-430. [arXiv:1905.05370].
• The planning problem in Mean Field Games as regularized mass transport (with J. Graber, F. Silva and D. Tonon), Calc. Var. Partial Differential Equations, 58 (2019), no. 3, Art. 115, 28 pp. [arXiv:1811.02706].
• On nonlinear cross-diffusion systems: an optimal transport approach (with I. Kim), Calc. Var. Partial Differential Equations, 57 (2018), no. 3, Art. 79, 40 pp. [cvgmt] [arXiv]
• Sobolev regularity for first order Mean Field Games (with J. Graber), Ann. Inst. H. Poincaré Anal. Non Linéaire, Vol. 35 (2018), Issue 6, 1557-1576. [cvgmt] [arXiv]
• On the variational formulation of some stationary second order mean field game systems , (with F.J. Siva), SIAM J. on Math. Anal., 50-1 (2018), 1255-1277. [cvgmt] [arXiv]
• First order Mean Field Games with density constraints: Pressure equals Price, (with P. Cardaliaguet and F. Santambrogio), SIAM J. Control Optim., Vol. 54 (2016), Issue 5, 2672-2709. [cvgmt] [arXiv]
• Uniqueness issues for evolution equations with density constraints, (with S. Di Marino), Math. Models Methods Appl. Sci., Vol. 26 (2016), No. 9, 1761-1783. [cvgmt] [arXiv]
• Advection-diffusion equations with density constraints, (with F. Santambrogio), Analysis & PDE, Vol. 9 (2016), No. 3, 615-644. [cvgmt] [arXiv]
• BV estimates in optimal transportation and applications, (with G. De Philippis, F. Santambrogio and B. Velichkov), Arch. Ration. Mech. Anal., Vol. 219 (2016), Issue 2, pp. 829-860. [cvgmt] [arXiv]
• A variational approach for second order mean field games with density constraints: the stationary case, (with F.J. Silva), J. Math. Pures Appl., Vol. 104 (2015), Issue 6, pp. 1135-1159, [cvgmt] [arXiv]

Undergraduate papers

• On the solutions of linear ordinary differential equations and Bessel-type special functions on the Levi-Civita field (with K. Shamseddine), J. Contemp. Math Anal., Vol. 50 (2015), Issue 2, pp. 53-62. [preprint]
• Ulam-Hyers stability of elliptic partial differential equations in Sobolev spaces (with Sz. András), Appl. Math. Comp., Vol. 229 (2014), pp. 131-138. [preprint]
• Ulam-Hyers stability of dynamical equations on time scales via Picard operators (with Sz. András), Appl. Math. Comp., Vol. 219 (2013), Issue 9, pp. 4853-4864. [preprint]
• Wendroff type inequalities on time scales via Picard operators (with Sz. András), Math. Ineq. Appl., Vol. 16 (2013), No. 1, pp. 159-174. [preprint]
• Remarks on some Wendroff type inequalities (with Sz. András), J. Math. Ineq., Vol. 5 (2011), No. 3, pp. 401-411. [preprint]

Collaborators

Anshul Adve (Princeton, USA); David M. Ambrose (Philadelphia, USA); Szilárd András (Cluj-Napoca, Romania); Mohit Bansil (New York, USA); Pierre Cardaliaguet (Paris, France); Marco Cirant (Padova, Italy); Noemi David (Lyon, France); Guido De Philippis (New York, USA); Simone Di Marino (Genova, Italy); Wilfrid Gangbo (Los Angeles, USA); Jameson Graber (Waco, TX, USA); Megan Griffin-Pickering (Zürich, Switzerland); Matt Jacobs (Santa Barbara, CA, USA); Inwon Kim (Los Angeles, USA); Dohyun Kwon (Seoul, Republic of Korea); Huafu Liao (Dalian, Liaoning, China); Chenchen Mou (Hong Kong); Filippo Santambrogio (Lyon, France); Khodr Shamseddine (Winnipeg, Canada); Francisco J. Silva (Limoges, France); Daniela Tonon (Padova, Italy); Bozhidar Velichkov (Pisa, Italy); Jianfeng Zhang (Los Angeles, USA); Chao Zhou (Singapore).

Recent invited talks (conferences/workshops)

• BIRS workshop 24w5198 Optimal Transport and Dynamics, Casa Matemática Oaxaca (CMO), Oaxaca, Mexico, August 2024.
• 2nd Joint Meeting AMS-UMI, Special Session A1 Mean Field Games and Related Topics, Palermo, Italy, July 2024.
• North-East and Midlands Stochastic Analysis Seminars, Durham University, UK, July 2024.
• BIRS workshop 24w5277 New Trends and Challenges in Stochastic Differential Games, UBC Okanagan, Kelowna, Canada, June 2024.
• INdAM-RISM congress Mean-Field models in optimal control, Riemann International School of Mathematics, Varese, Italy, June 2024.
• Workshop on Analysis of PDEs in Mathematical Physics, University of Bath, UK, June 2024.
• Workshop on Numerical Methods for Mean Field Games and related PDE, UCL, London, UK, July 2023.
• KAUST Research Conference on Advances in nonlinear elliptic and parabolic PDEs, AlUla, Al Madinah, Kingdom of Saudi Arabia, May 2023.
• Distributed Solutions to Complex Societal Problems - Reunion Workshop, IMSI, University of Chicago, February 2023 (virtual).
• 19th International Symposium on Dynamic Games and Applications, mini-symposium on "Mean Field Games", Porto, Portugal, July 2022.
• SIAM 2022 Conference on Analysis of Partial Differential Equations, mini-symposium on "Population Dynamics: Individual-Based and Continuum Models", TU Berlin, Germany, March 2022 (virtual).
• Mathematical Advances in Mean Field Games; part of the program "Distributed Solutions to Complex Societal Problems", IMSI, University of Chicago, December 2021 (virtual).
• 8th International Conference on Mathematics and Informatics, Sapientia University, Targu-Mures, Romania, September 2021 (virtual).
• Workshop on Geometric and Applied Analysis, Hausdorff Center for Mathematics, University of Bonn, July 2021 (virtual).
• Mean Field Games and related fields, AIMS South Africa, March 2021 (virtual).
• Geometric and functional inequalities and recent topics in nonlinear PDEs, Purdue University, IN, USA, March 2021 (virtual).
• Workshop on Mean Field Games and Applications (within the long program 'High Dimensional Hamilton-Jacobi PDEs'), IPAM, UCLA, CA, USA, May 2020 (virtual).
• SIAM Conference on Analysis of PDE, mini-symposium on "Mean-field models for large interacting agent systems", La Quinta, CA, USA, December 2019.
• Dynamics, Equations and Application, AGH UST, Kraków, Poland, September 2019.
• People in Optimal Transport and Applications, Cortona, Italy, June 2019.
• CMS Winter Meeting, Special Session on Nonlocal Interaction Models: From Collective Behavior to Pattern Formation, Vancouver, BC, Canada, December 2018.
• 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Special Session on Mean Field Games, Taipei, Taiwan, July 2018.
• SIAM Conference on Analysis of PDE, Special Session on Mean Field Games, Baltimore, MD, December 2017.
• AMS Sectional Meeting, Special Session Particle Methods & Nonlocal PDEs, UC Riverside, CA, November 2017.
• Optimal Control and PDE, conference in the thematic semester on Nonlinear Partial Differential Equations for Future Applications, Tohoku University, Sendai, Japan, July 2017.
• AMS Sectional Meeting, special session on Analysis of Variational Problems and Nonlinear Partial Differential Equations, Indiana University, Bloomington, IN, April 2017.
• 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications, special session on mean field games, Orlando, FL, July 2016.
• KIAS CMC conference on Analysis, Geometry, and Optimal Transport, KIAS, Seoul, Korea, June 2016.

Recent seminar and colloquium talks

• SITE Research Center Seminar, NYU Abu Dhabi, United Arab Emirates, January 2024.
• ELISA Seminar, Université Côte d'Azur, Nice, France, October 2023.
• Research Seminar, Department of Decision Sciences, Bocconi University, Milan, Italy, May 2023.
• SITE Research Center Seminar, NYU Abu Dhabi, United Arab Emirates, April 2023 (virtual).
• Imperial-UCL Numerics Seminar, UCL, London, UK, October 2022.
• Bachelier seminar, Institute Henri Poincaré, Paris, France, June 2022.
• Optimal transport and Mean Field Games seminar, UCLA, CA, USA, October 2021 (virtual).
• PDE and Applied Mathematics seminar, UC Riverside, CA, USA, October 2021 (virtual).
• OSSUR-PDEs seminar, Gran Sasso Science Institute (GSSI), L'Aquila, Italy, June 2021 (virtual).
• Seminari di equazioni differenziali e applicazioni, University of Padova, Italy, April 2021 (virtual).
• Applied Mathematics Seminar, Baylor University, Waco, TX, February 2021 (virtual).
• Two seminar talks within the long program 'High Dimensional Hamilton-Jacobi PDEs', IPAM, UCLA, CA, USA, April 2020 (virtual).
• Pro Scientia Siculorum Lecture, Babes-Bolyai University, Romania, March 2020.
• Colloquium, Queen's University, Belfast, Northern Ireland, UK, February 2020.
• Pure Maths Colloquium, Durham University, Durham, UK, February 2020.
• Analysis Seminar, Heriot-Watt University, Edinburgh, UK, January 2020.
• Analysis and/of PDE, Durham University, Durham, UK, October 2019.
• Applied PDEs Seminar, Imperial College, London, UK, October 2019.
• PDE seminar, UC Riverside, CA, May 2019.
• Mathematics Colloquium, Loyola University, Chicago, IL, March 2019.
• Mathematics Colloquium, Durham University, Durham, UK, March 2019.
• Mathematics Colloquium, West Virginia University, Morgantown, WV, January 2019.
• Mathematics Colloquium, North Carolina State University, Rayleigh, NC, January 2019.
• Diff. Geom, Math. Phys., PDE Seminar, University of British Columbia, Vancouver, BC, Canada, December 2018.
• PDE and Applied Mathematics Seminar, Drexel University, Philadelphia, PA, October 2018.
• Analysis Seminar, University of Pennsylvania, Philadelphia, PA, October 2018.
• Analysis and PDE Seminar, Caltech, Pasadena, CA, June 2018.
• Mathematics Colloquium, Baylor University, Waco, TX, April 2018.
• Applied Mathematics Seminar, McGill University, Montreal, Canada, September 2017.
• Informal Analysis Seminar, Tohoku University, Sendai, Japan, August 2017.
• Joint Informal Geometric Analysis and PDE-Applied Math seminar, University of Maryland, College Park, MD, USA, March 2017.
• Analysis and PDE seminar, USC, Los Angeles, CA, USA, March 2017.
• Nonlinear PDE seminar, UC Irvine, CA, USA, November 2016.
• Analysis and PDE seminar, UCLA, Los Angeles, CA, USA, April 2016.

Theses

• Density Constraints in Optimal Transport, PDEs and Mean Field Games, PhD thesis, Université Paris-Sud, Orsay, France. Defended on September 10th 2015.
• Mean Field Games with Density Constraints, MSc thesis, École Polytechnique, Palaiseau, France, 2012.
• From Integral Inequalities to Ulam-Hyers Stability via Picard Operators, MSc thesis, Babes-Bolyai University, Cluj-Napoca, Romania, 2012.
• Differential Equations and Bessel type Special Functions on the Levi-Civita Field, BSc thesis (in Hungarian), Babes-Bolyai University, Cluj-Napoca, Romania, 2010.