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    "143314-21892894":
    {
        "datetime_modified":"20260119T121312",
        "datetime_start":"20260126T160000",
        "datetime_end":"20260126T170000",
        "has_end_time":1,
        "date_start":"2026-01-26",
        "date_end":"2026-01-26",
        "time_start":"16:00:00",
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        "time_zone":"America\/Detroit",
        "event_title":"GLNT: Ring of Modular forms on certain unitary Shimura Varieties",
        "occurrence_title":"",
        "combined_title":"GLNT: Ring of Modular forms on certain unitary Shimura Varieties: Yuxin Lin (Caltech)",
        "event_subtitle":"Yuxin Lin (Caltech)",
        "event_type":"Workshop \/ Seminar",
        "event_type_id":"21",
        "description":"The modular forms on the quotient $\\mathrm{SL}_2(\\mathbb{Z})\\backslash \\mathcal{H}$ can be viewed as $\\mathrm{SL}_2(\\mathbb{Z})$-invariant holomorphic differentials on $\\mathcal{H}$. Interpreting $\\mathrm{SL}_2(\\mathbb{Z})\\backslash \\mathcal{H}$ as the moduli space of elliptic curves, these forms can equivalently be described as global sections of the Hodge line bundle. A natural question is whether this perspective extends beyond $\\mathrm{SL}_2(\\mathbb{Z})$.\r\n\r\nIn this talk, I will introduce modular forms on certain Shimura varieties and illustrate the definitions through a sequence of examples: Hilbert modular surfaces, unitary Shimura curves, and finally a unitary Shimura surface arising from a special family of cyclic covers of $\\mathbb{P}^1$. I will explain how the geometry of this family makes the Hodge line bundle computable, and how level structure on the Shimura variety can be interpreted concretely in this setting.",
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        "tags":["Mathematics"],
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                "group_name":"Group, Lie and Number Theory Seminar - Department of Mathematics",
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    {
        "datetime_modified":"20260120T231803",
        "datetime_start":"20260126T160000",
        "datetime_end":"20260126T170000",
        "has_end_time":1,
        "date_start":"2026-01-26",
        "date_end":"2026-01-26",
        "time_start":"16:00:00",
        "time_end":"17:00:00",
        "time_zone":"America\/Detroit",
        "event_title":"Painlev\u00e9 Universality class for the maximal amplitude solution of the Focusing Nonlinear Schr\u00f6dinger Equation with randomness",
        "occurrence_title":"",
        "combined_title":"Painlev\u00e9 Universality class for the maximal amplitude solution of the Focusing Nonlinear Schr\u00f6dinger Equation with randomness: Aikaterini Gkogkou (Tulane University)",
        "event_subtitle":"Aikaterini Gkogkou (Tulane University)",
        "event_type":"Livestream \/ Virtual",
        "event_type_id":"24",
        "description":"In this work, we establish universality results for the $N$-soliton solution of the focusing NLS equation at maximal amplitude. Specifically, we choose the associated normalization constants so that the solution achieves its maximal peak, which, in the large-$N$ limit, satisfies a Painlev\u00e9-type equation independently of the distribution of the (random) discrete eigenvalues. We identify two distinct universality classes, determined by the structure of the discrete eigenvalues: the \\textit{Painlev\u00e9--III} and \\textit{Painlev\u00e9--V} rogue-wave solutions. In the Painlev\u00e9--III case, the eigenvalues take the form $\\lambda_j = v_j + i \\mu_j$, while for Painlev\u00e9--V they satisfy $\\lambda_j = -\\zeta \\, j + v_j + i \\mu_j$, with $0 < \\zeta < 1$. In both cases, $v_j$ and $\\mu_j$ are sub-exponential random variables. Universality can then be summarized as follows: regardless of the specific realizations of the amplitudes and velocities, provided they are sub-exponential random variables and the normalization constants are chosen to maximize the \\(N\\)-soliton solution, the resulting maximal peak always corresponds to either a Painlev\u00e9--III or Painlev\u00e9--V rogue-wave profile in the large-$N$ limit.",
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        "building_name":"Off Campus Location",
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        "tags":["Mathematics","Seminar","Virtual"],
        "website":"https:\/\/sites.google.com\/umich.edu\/isrmt-seminar\/home?authuser=0",
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                "group_name":"Integrable Systems and Random Matrix Theory Seminar - Department of Mathematics",
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