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SUMMARY:Benjamin Nill (Otto-von-Guericke-Universität Magdeburg)
DTSTART:20221124T151500Z
DTEND:20221124T170000Z
DTSTAMP:20260422T070136Z
UID:CJCS/91
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CJCS/91/">An
  update on Gorenstein polytopes : reducibility and local $h*$-polynomials<
 /a>\nby Benjamin Nill (Otto-von-Guericke-Universität Magdeburg) as part o
 f Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nReflexive poly
 topes and more generally Gorenstein polytopes are the key objects in the B
 atyrev-Borisov mirror-symmetry construction of Calabi-Yau manifolds in Gor
 enstein toric Fano varieties. Moreover\, they are beautiful combinatorial 
 objects that appear prominently in the Ehrhart theory of lattice polytopes
 . In this talk I plan to present two recent combinatorial results regardin
 g Gorenstein polytopes. First I will discuss a conjecture of Batyrev-Juny 
 on Gorenstein polytopes of small Ehrhart degree corresponding to Gorenstei
 n toric Fano varieties that have highly divisible anticanonical divisors. 
 And second I will explain a characterization when Gorenstein polytopes are
  "thin"\, namely when their l*-polynomial vanishes. This polynomial is an 
 Ehrhart-theoretic invariant that had been independently studied by Gelfand
 -Kapranov-Zelevinsky\, Stanley\, Karu\, Borisov-Mavlyutov and Katz-Stapled
 on among others. I will highlight how underlying both results is a natural
  notion of reducibility for Gorenstein polytopes. This is partly joint wor
 k with Christopher Borger\, Andreas Kretschmer\, and Jan Schepers.\n
LOCATION:https://researchseminars.org/talk/CJCS/91/
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