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Workshop

Equivariant Euler characteristics on permutohedral varieties

  • Vincenzo Galgano (MPI-CBG Dresden, Germany)
Felix-Klein-Hörsaal Universität Leipzig (Leipzig)

Abstract

In the literature cohomology has been shown to be a useful tool for detecting invariants in combinatorics. Moreover, equivariant cohomology provides even finer invariants, and it becomes particularly practical for toric varieties. Binomial coefficients can be interpreted as a solution to an intersection problem on a permutohedral variety X. Via Hirzebruch-Riemann-Roch, this is equivalent to computing Euler characteristic of a specific element of K-theory of X which admits a natural lifting to equivariant K-theory. Thus the Euler characteristic (and hence binomial coefficients) may be upgraded to a Laurent polynomial. We provide and implement three different approaches, in particular a recursive one, to computing these polynomials. This is a joint work with Hanieh Keneshlou and Mateusz Michałek.

conference
29.07.24 02.08.24

MEGA 2024

MPI für Mathematik in den Naturwissenschaften Leipzig (Leipzig) E1 05 (Leibniz-Saal)
Universität Leipzig (Leipzig) Felix-Klein-Hörsaal

Mirke Olschewski

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Saskia Gutzschebauch

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Christian Lehn

Ruhr-Universität Bochum

Irem Portakal

Max Planck Institute for Mathematics in the Sciences

Rainer Sinn

Universität Leipzig

Bernd Sturmfels

Max Planck Institute for Mathematics in the Sciences

Simon Telen

Max Planck Institute for Mathematics in the Sciences

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