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    "151180-21911039":
    {
        "datetime_modified":"20260901T081333",
        "datetime_start":"20260909T160000",
        "datetime_end":"20260909T170000",
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        "date_start":"2026-09-09",
        "date_end":"2026-09-09",
        "time_start":"16:00:00",
        "time_end":"17:00:00",
        "time_zone":"America\/Detroit",
        "event_title":"Probability and Analysis Seminar: A Riemann-Hilbert approach to Dyson Brownian motion and Gaussian multiplicative chaos",
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        "combined_title":"Probability and Analysis Seminar: A Riemann-Hilbert approach to Dyson Brownian motion and Gaussian multiplicative chaos: Nathan Hayford (Umich)",
        "event_subtitle":"Nathan Hayford (Umich)",
        "event_type":"Workshop \/ Seminar",
        "event_type_id":"21",
        "description":"Abstract: The connection between random matrices and Gaussian multiplicative chaos (GMC) has been studied intensively since the work of Fyodorov and Keating (2014). There has been recent interest in the appearance of GMC in dynamical ensembles of random matrices and their eigenvalues, such as the Dyson Brownian motion (Keles 2025). We propose a Riemann-Hilbert approach to this problem. I will explain how our approach allows one to probe the \u201cmicroscopic scale\u201d (a scale which is inaccessible via loop equations), where the appearance of Painlev\u00e9 transcendents is anticipated. This is joint work with Ahmad Barhoumi.",
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        "tags":["Mathematics"],
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    {
        "datetime_modified":"20260803T153429",
        "datetime_start":"20260909T160000",
        "datetime_end":"20260909T170000",
        "has_end_time":1,
        "date_start":"2026-09-09",
        "date_end":"2026-09-09",
        "time_start":"16:00:00",
        "time_end":"17:00:00",
        "time_zone":"America\/Detroit",
        "event_title":"Stability, Approximation, and Robustness of Optimal Policies in POMDPs",
        "occurrence_title":"",
        "combined_title":"Stability, Approximation, and Robustness of Optimal Policies in POMDPs: Yunus Emre Demirci, UM",
        "event_subtitle":"Yunus Emre Demirci, UM",
        "event_type":"Workshop \/ Seminar",
        "event_type_id":"21",
        "description":"In this talk, I will focus on the stability, approximation, and robustness of optimal policies in partially observable Markov decision processes (POMDPs) under discounted and average cost criteria.\n\nI will begin with filter kernel perturbation under model change. I will establish how small perturbations in the transition or observation kernels lead to explicit, nonasymptotic bounds on both the filter kernel and the performance of the induced policies. A primary result demonstrates that an optimal policy computed under an incorrect model remains near optimal for the true model, with quantitatively bounded errors.\n\nBuilding on these stability concepts, I will then talk about the average cost setting and describe conditions under which the nonlinear filter exhibits a contraction property. Under these conditions, the vanishing discounted approach yields a solution to the average cost optimality equation, guaranteeing the existence of a stationary optimal policy. Furthermore, this provides explicit bounds that quantify the influence of initial prior distribution errors and model errors on long run performance.\n\nFinally, I will present results on implementable approximations. I will introduce refined error bounds for finite window controllers and conclude by discussing how Q learning can be utilized through either finite window or the quantization of the belief process to obtain near optimal policies for both discounted and average cost criteria.",
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        "room":"1360",
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        "tags":["Mathematics"],
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        "sponsors":[
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                "group_name":"Financial\/Actuarial Mathematics Seminar - Department of Mathematics",
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