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    "149752-21907056":
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        "date_end":"2026-09-25",
        "time_start":"15:00:00",
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        "time_zone":"America\/Detroit",
        "event_title":"A tale of two polynomials: positivity in wonderful varieties and matroids",
        "occurrence_title":"",
        "combined_title":"A tale of two polynomials: positivity in wonderful varieties and matroids: Shiyue Li (University of Michigan)",
        "event_subtitle":"Shiyue Li (University of Michigan)",
        "event_type":"Workshop \/ Seminar",
        "event_type_id":"21",
        "description":"I will share a story of two polynomials, the Poincar\u00e8 polynomial of Chow rings of toric varieties of matroids, and the h-polynomials of nested set complexes of matroids. The story is set in a rich network of positivity properties coming from geometry and combinatorics of matroids, with connections to moduli spaces of rational stable curves. The main theorems are matroidal analogues of Gal\u2019s conjecture, and real-rootedness of some of these polynomials. (Joint works with Basile Coron, and Luis Ferroni)",
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                "group_name":"Combinatorics Seminar - Department of Mathematics",
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    {
        "datetime_modified":"20260920T131857",
        "datetime_start":"20260925T150000",
        "datetime_end":"20260925T160000",
        "has_end_time":1,
        "date_start":"2026-09-25",
        "date_end":"2026-09-25",
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        "time_zone":"America\/Detroit",
        "event_title":"AIM Seminar:  Discrete structure, continuous dynamics: graph-theoretic approaches and singular parametric limits in biochemical reaction networks",
        "occurrence_title":"",
        "combined_title":"AIM Seminar:  Discrete structure, continuous dynamics: graph-theoretic approaches and singular parametric limits in biochemical reaction networks: Sabina Haque (Mathematics, University of Michigan)",
        "event_subtitle":"Sabina Haque (Mathematics, University of Michigan)",
        "event_type":"Lecture \/ Discussion",
        "event_type_id":"13",
        "description":"Abstract: A biochemical reaction network is based on a discrete object: a directed graph whose edges are labeled with reaction rates. At the same time, it is governed by continuous dynamics, typically expressed as a nonlinear system of polynomial ODEs. These two descriptions encode the same system but have fundamentally different mathematical structures. This mathematical tension raises the question: how does the discrete structure of a biochemical network govern its continuous dynamics? In this talk, I will explore this question through several examples at the intersection of graph theory, dynamical systems, and applied algebraic geometry. In particular, I will focus on singular limits in which reaction-rate parameters tend to infinity. These limits motivate a graph operation that resembles an edge contraction, and I will examine their effects on graph invariants expressed as rational functions of the model parameters. I will then extend this construction to structural identifiability and discuss how model reduction alters the geometry of parameter space. Finally, I will turn to a stochastic interpretation of this graph-theoretic framework and describe how asymmetry in the spectral decomposition of a finite-state continuous-time Markov process gives rise to a signature of departure from thermodynamic equilibrium, with unexpectedly nonmonotone behavior even on the simplest networks. I will conclude with a discussion of broader future directions focused on understanding how network operations may affect qualitative dynamical properties of the system. Together, these examples illustrate how biologically inspired networks generate subtle structural questions and new mathematics at the interface of discrete and continuous systems.\n\nContact:  Zhiyan Ding",
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        "tags":["Applied Mathematics","Mathematics"],
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                "group_name":"Applied Interdisciplinary Mathematics (AIM) Seminar - Department of Mathematics",
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