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        "event_title":"2026 SIAM Student Mini-Symposium in Applied Mathematics",
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        "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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        "event_title":"DE Seminar: Mathematical Analysis of Many-Body Quantum Simulation with Coulomb Potentials",
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        "combined_title":"DE Seminar: Mathematical Analysis of Many-Body Quantum Simulation with Coulomb Potentials: Di Fang (Duke)",
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        "description":"Efficient simulation of many-body quantum dynamics is central to advances in physics, chemistry, and quantum computing. A fundamental question is whether the simulation cost can scale polynomially with system size in the presence of realistic interactions. In this talk, we focus on many-body quantum systems with Coulomb interactions, which play a central role in electronic and molecular dynamics. We prove that first-order Trotterization for such unbounded Hamiltonians admits a polynomial dependence on the number of particles in the continuum limit, with a convergence rate of order $1\/4$\u2014in contrast to prior Trotter analyses for bounded operators, which diverge in this limit. The result holds for all initial wavefunctions in the domain of the Hamiltonian. This $1\/4$-order rate is optimal, as previous work shows that it can be saturated by the ground state of the hydrogen atom. Moreover, higher-order Trotter formulas do not improve the worst-case scaling. We also discuss additional regularity conditions on the initial state under which the original Trotter convergence rate can be recovered. Finally, we discuss our recent development on the spatial error and algorithm complexities.",
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        "event_title":"Algebraic Geometry Seminar: TBA",
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        "combined_title":"Algebraic Geometry Seminar: TBA: Siddharth Mathur (University of Georgia)",
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        "event_title":"Optimal Contract, Delegated Investment, and Information Acquisition",
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        "combined_title":"Optimal Contract, Delegated Investment, and Information Acquisition: Yuyang Zhang, UM",
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        "description":"We study a model of delegated investment within a noisy rational expectations equilibrium framework. Portfolio managers can acquire costly private information about asset payoffs but incur portfolio management costs, and are compensated by investors to make investment decisions on their behalf. We show that the optimal contract features a benchmark component that mitigates the agency frictions arising from portfolio management costs. The precision of managers' private information is determined endogenously in market equilibrium, with private and public information acting as substitutes. As portfolio management costs increase, both the performance-based and benchmark components of the optimal contract become more sensitive to investment outcomes, while fewer private signals are incorporated into prices, reducing market informational efficiency. We further show that when a social planner places sufficient weight on the welfare of direct investors and liquidity providers, the socially optimal equilibrium achieves greater price informational efficiency than the decentralized equilibrium. The talk will focus on the interaction between optimal contracting, information acquisition, and market efficiency, together with the economic intuition underlying these results.",
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        "combined_title":"Foundation models and agentic AI for discovery in fluid mechanics: Ricardo Vinuesa (Aerospace Engineering, University of Michigan)",
        "event_subtitle":"Ricardo Vinuesa (Aerospace Engineering, University of Michigan)",
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        "description":"Abstract:  In this seminar we discuss a unified framework that combines explainable deep learning, deep reinforcement learning (DRL) and foundation models to advance both understanding and control of turbulence, with direct implications for accelerated design and discovery. First, we will show how explainable deep learning techniques can be used to identify the flow features that are truly responsible for key turbulent processes in wall-bounded flows. By systematically interrogating trained neural networks, we uncover the most influential coherent structures driving momentum transport and drag. Our results reveal that classically studied structures (while important) provide only a partial and sometimes misleading perspective, motivating a more data-driven and physics-aware view of turbulence organization. Building on these insights, we will demonstrate how deep reinforcement learning can be used to actively control turbulent flows by targeting the dynamically relevant structures identified through explainability. This approach achieves over 30% drag reduction in canonical wall-bounded turbulence and extends naturally to more complex configurations, including turbulent wings, highlighting the scalability of learning-based control strategies. Finally, we will introduce a foundation-model-based framework for accelerated design, optimization and scientific discovery. By learning compact, interpretable latent representations of high-dimensional flow physics, these models (combined with agentic-AI systems) enable rapid exploration of design spaces, causal reasoning and closed-loop optimization, bridging the gap between expensive simulations, control and engineering decision making. Together, these results illustrate how explainable and agentic AI are becoming essential for turbulence physics, flow control and next-generation engineering design.\n\n\nContact:  Silas Alben",
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        "event_title":"Topology seminar: TBA",
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        "event_title":"Algebraic Geometry Seminar -- TBA",
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        "combined_title":"Algebraic Geometry Seminar -- TBA: Caleb Ji, University of Michigan",
        "event_subtitle":"Caleb Ji, University of Michigan",
        "event_type":"Workshop \/ Seminar",
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        "datetime_modified":"20260727T104702",
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        "time_start":"16:00:00",
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        "time_zone":"America\/Detroit",
        "event_title":"Buying Time: Optimal Service Purchase and Retirement Timing in Defined Benefit Plans",
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        "combined_title":"Buying Time: Optimal Service Purchase and Retirement Timing in Defined Benefit Plans: Kristen Moore, UM",
        "event_subtitle":"Kristen Moore, UM",
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        "description":"We study retirement timing decisions in a defined benefit (DB) pension plan with a service-purchase\noption. An employee who would otherwise retire at a fixed time T may elect to purchase L additional\nyears of service and retire early. Earlier retirement provides additional leisure but requires an upfront\npayment and typically results in a reduced post-retirement income stream. We model this trade-off in\na continuous-time retirement framework by allowing the employee to choose L to maximize the value\nof wealth and leisure at retirement in both deterministic and life-contingent settings. Our model\ncaptures a common feature of public pension systems: early retirement is often accompanied by both\nan upfront cost and a permanent reduction in benefits. We show that this structure yields tractable\nand intuitive results in several benchmark cases, including settings without mortality risk and settings\nwith mortality risk under simplifying assumptions. In more general cases, we characterize optimal\nbehavior through comparative statics and numerical examples. A key insight is that the interaction\nbetween the finite-horizon value of leisure and the lifetime cost embedded in pension pricing can\ngenerate a range of behaviors, including monotone strategies and interior optima. While many results\nalign with economic intuition, others require more careful interpretation. We also extend the model to\nallow for dynamic decision-making via a multi-period service-purchase option, solved by backward\ninduction. The results provide insight into optimal retirement timing and the role of plan design in\nshaping participant behavior. This is joint work with David Kausch and Virginia Young.",
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        "time_end":"17:20:00",
        "time_zone":"America\/Detroit",
        "event_title":"RTG SEMINAR GEOMETRY, TOPOLOGY, DYNAMICS: Global Rigidity of Codimenson 1 Actions",
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        "combined_title":"RTG SEMINAR GEOMETRY, TOPOLOGY, DYNAMICS: Global Rigidity of Codimenson 1 Actions: Camilo Arosemena",
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        "time_zone":"America\/Detroit",
        "event_title":"GEOMETRY SEMINAR: TBA",
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