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DTSTAMP:20260221T113512
DTSTART;TZID=America/Detroit:20260223T160000
DTEND;TZID=America/Detroit:20260223T170000
SUMMARY:Workshop / Seminar:GLNT: Finiteness of heights in isogeny classes of motives
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.
UID:143317-21892897@events.umich.edu
URL:https://events.umich.edu/event/143317
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 4096
CONTACT:
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DTSTAMP:20260219T125308
DTSTART;TZID=America/Detroit:20260223T160000
DTEND;TZID=America/Detroit:20260223T170000
SUMMARY:Workshop / Seminar:Mixed Ehrhart theory and Alexandrov–Fenchel-type inequalities
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–Fenchel 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–Fenchel–type 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–Riemann–Roch theorem on the permutohedral variety due to Berget–Eur–Spink–Tseng. We will also see that such inequalities fail in general.
UID:145740-21897757@events.umich.edu
URL:https://events.umich.edu/event/145740
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 3866
CONTACT:
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