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        "event_title":"GLNT: Finiteness of heights in isogeny classes of motives",
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        "combined_title":"GLNT: Finiteness of heights in isogeny classes of motives: Alice Lin (Harvard)",
        "event_subtitle":"Alice Lin (Harvard)",
        "event_type":"Workshop \/ Seminar",
        "event_type_id":"21",
        "description":"Abstract: Using integral $p$-adic Hodge theory, Kato and Koshikawa define a generalization of the Faltings height of an abelian variety to motives defined over a number field. Assuming the adelic Mumford-Tate conjecture, we prove a finiteness property for heights in the isogeny class of a motive, where the isogenous motives are not required to be defined over the same number field. This expands on a result of Kisin and Mocz for the Faltings height in isogeny classes of abelian varieties.",
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                "group_name":"Group, Lie and Number Theory Seminar - Department of Mathematics",
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        "datetime_modified":"20260219T125308",
        "datetime_start":"20260223T160000",
        "datetime_end":"20260223T170000",
        "has_end_time":1,
        "date_start":"2026-02-23",
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        "time_zone":"America\/Detroit",
        "event_title":"Mixed Ehrhart theory and Alexandrov\u2013Fenchel-type inequalities",
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        "combined_title":"Mixed Ehrhart theory and Alexandrov\u2013Fenchel-type inequalities: Joel Hakavuori",
        "event_subtitle":"Joel Hakavuori",
        "event_type":"Workshop \/ Seminar",
        "event_type_id":"21",
        "description":"Ehrhart theory studies the polynomial function that counts lattice points in integer dilates of a lattice polytope. This talk will focus on a natural mixed extension: counting lattice points in Minkowski sums of several scaled lattice polytopes. This produces a multivariate polynomial whose coefficients in the binomial basis are known as discrete mixed volumes, which generalize the classical mixed volumes in the case of lattice polytopes. Mixed volumes famously satisfy the Alexandrov\u2013Fenchel inequalities, which has been used to prove various log-concavity results in combinatorics. A natural question is whether analogous inequalities hold for the discrete mixed volumes. I will present an asymptotic Alexandrov\u2013Fenchel\u2013type inequality valid for general families of lattice polytopes, and an exact inequality in the case of coordinate simplices, where the proof relies on an exceptional version of the Hirzebruch\u2013Riemann\u2013Roch theorem on the permutohedral variety due to Berget\u2013Eur\u2013Spink\u2013Tseng. We will also see that such inequalities fail in general.",
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                "group_name":"Student Combinatorics Seminar - Department of Mathematics",
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