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        "event_title":"Learning MFG via MFAC Flow",
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        "combined_title":"Learning MFG via MFAC Flow: Ruimeng Hu, UCSB",
        "event_subtitle":"Ruimeng Hu, UCSB",
        "event_type":"Workshop \/ Seminar",
        "event_type_id":"21",
        "description":"We introduce the Mean-Field Actor-Critic (MFAC) flow, a continuous-time learning dynamics for solving mean-field games (MFGs), drawing on ideas from reinforcement learning, generative modeling, and optimal transport. The MFAC framework jointly evolves the actor, critic, and distribution through gradient-based updates, with the distribution governed by a novel Optimal Transport Geodesic Picard (OTGP) flow. The OTGP flow drives the distribution toward equilibrium along Wasserstein-2 geodesics. We rigorously analyze the MFAC flow using Lyapunov functionals and establish global exponential convergence under suitable time scales. The analysis highlights the coupled structure of the algorithm and offers practical guidelines for choosing learning rates. Numerical results further support the theory and demonstrate the effectiveness of the proposed approach. This is joint work with Mo Zhou (UCLA) and Haosheng Zhou (UCSB).",
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        "datetime_modified":"20260211T135224",
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        "event_title":"Probability and Analysis Seminar: Finite time singularities in the Landau equation with very hard potentials",
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        "combined_title":"Probability and Analysis Seminar: Finite time singularities in the Landau equation with very hard potentials: Jiajie Chen (University of Chicago)",
        "event_subtitle":"Jiajie Chen (University of Chicago)",
        "event_type":"Workshop \/ Seminar",
        "event_type_id":"21",
        "description":"The Landau equation, introduced by Lev Landau in 1936, is one of the central equations in kinetic theory. We consider the Landau equation with very hard potentials $\\gamma \\in (\\sqrt{3},2]$, which is known to admit global smooth solutions for homogeneous data. Inspired by hydrodynamic limits from kinetic equations to fluid equations, we construct smooth, strictly positive initial data that develop a finite-time singularity by lifting imploding singularities from the compressible Euler equations. In self\u2011similar variables, the solution becomes asymptotically hydrodynamic\u2014the distribution function converges to a local Maxwellian, while the hydrodynamic fields develop an asymptotically self\u2011similar implosion whose profile coincides with a smooth imploding profile of the compressible Euler equations.  To our knowledge, this provides the first example of a collisional kinetic model which is globally well-posed in the homogeneous setting, but admits finite time singularities for inhomogeneous data.\n \nThis is joint work with Jacob Bedrossian (UCLA), Maria Gualdani (UT Austin), Sehyun Ji (UChicago), Vlad Vicol (NYU), and Jincheng Yang (JHU).",
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