[Aalto AGC Seminar] Joel Hakavuori (Sorbonne University, IMJ-PRG) | Unimodality, Lefschetz theory, and F-purity | Mon 31.08. at 14:15

[Aalto Algebra, Geometry and Combinatorics Seminar]

We would like to invite you to the first talk of autumn in the Aalto AGC (Algebra, Geometry and Combinatorics) Seminar.

The talk is on
Mon 31.8. at 14:15-15:00
in
M3 (M234), Otakaari 1.

The speaker is
Joel Hakavuori (Sorbonne University, IMJ-PRG)
giving the talk
Unimodality, Lefschetz theory, and F-purity

Abstract: The g-conjecture for simplicial spheres and the Hibi-Ohsugi conjecture for IDP reflexive lattice polytopes are unimodality conjectures for face-number data and lattice-point enumerators, respectively. In both cases, these sequences occur as the Hilbert function of an associated Artinian Gorenstein algebra, and the desired unimodality follows from a Lefschetz property for that algebra. Recent proofs in characteristic 2 replace the positivity arguments familiar from the classical theory of simplicial polytopes by an anisotropy argument: using a generic Artinian reduction, identities for the volume map, and differentiation identities, one proves that nonzero elements up to the middle degree have nonzero squares, which is eventually used to prove that a generic linear form is a Lefschetz element.

The webpage of the seminar is at
math.aalto.fi/en/research/discrete/seminars/agc/<https://math.aalto.fi/en/research/discrete/seminars/agc/>
and we have a mailing list at
https://list.aalto.fi/mailman/listinfo/agc-math-aalto


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