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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)",
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        "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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    {
        "datetime_modified":"20260223T020145",
        "datetime_start":"20260225T160000",
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        "event_title":"Student AIM Seminar: A Beginner\u2019s introduction to optimal control theory",
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        "combined_title":"Student AIM Seminar: A Beginner\u2019s introduction to optimal control theory: Renato Pinto Reveggino",
        "event_subtitle":"Renato Pinto Reveggino",
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        "description":"In this talk I describe the basic deterministic control problem and how to solve it using the method of the adjoint function. The method is motivated through examination of the problem\u2019s structure and properties its solutions would exhibit. Hopefully by the end of this talk you\u2019ll know what an adjoint function is, be able to solve basic optimal control problems, and have an idea of when solutions exist.",
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