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    "145740-21897757":
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        "datetime_modified":"20260219T125308",
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        "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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        "tags":["Mathematics"],
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        "date_start":"2026-02-23",
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        "time_zone":"America\/Detroit",
        "event_title":"Partnership for Public Service - Information Session on Summer 2026 Internship",
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        "combined_title":"Partnership for Public Service - Information Session on Summer 2026 Internship",
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        "event_type":"Careers \/ Jobs",
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        "description":"The Partnership for Public Service is a nonpartisan, nonprofit organization dedicated to building a more effective federal government and a stronger democracy by improving how government works, attracting talent, and fostering leadership for public service.PPS has hired U-M students over the last few years, and they will be hosting an info session on their internship program about their summer 2026 internship! Please attend this info session if you would like to know more about the internship and application process.\u00a0This event's information is shown in Handshake as well as on the Happening @ Michigan calendar so thatit will be seen by a larger number of U-M Students. You can only registerto attend this event within Handshake. If you'd like to indicate that you'll be attending this event and see more details, please go to this webpage:\u00a0https:\/\/umich.joinhandshake.com\/events\/1907151\/share_preview\u00a0We want to ensure full and equitable participationin our events. If an accessibility accommodation would promote your full participation in this event, please indicate your accommodation requirements via the link below, preferably at least 14 days prior to the program to ensure sufficient time for arranging your requested accommodation(s) orexploring suitable alternatives. If you have any questions regarding access to our programs, please don't hesitate to reach out to Cierra Sutherland at\u00a0cierrasu@umich.edu. Accessibility accommodation form:\u00a0https:\/\/forms.gle\/FmFn35ZLxJ8kvPfSA\u00a0\u00a0#UCC\u00a0",
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