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DTSTAMP:20261025T183952Z
UID:69a7ee41f3eb3900041701@ist.ac.at
DTSTART:20261112T131500
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DESCRIPTION:Speaker: Gergely Berczi\nhosted by Tamas Hausel\nAbstract: We r
 eport on a story that began in January with my AlphaEvolve experiments on 
 a conjecture of Aluffi\, Chen and Marcolli: the Poincar polynomials of the
  moduli of genus-zero curves are real-rooted. These experiments uncovered 
 the asymptotic behaviour of the roots\, but no proof.In April a bivariate 
 deformation\, discovered by an internal DeepMind model\, led in joint work
  with Young-Hoon Kiem to a proof of the conjecture. Reinterpreting the def
 ormation as a stratified motivic invariant\, we generalised real-rootednes
 s to that setting and formulated a conjecture on the branches of the real 
 roots of the deformation which implies the real-rootedness of the Chow\, c
 hain and coarse flag polynomials of an arbitrary loopless matroid. We prov
 ed this branch conjecture for broad classes of matroids\, among them the p
 aving matroids.The same machinery then found the limits: in recent joint w
 ork with Basile Coron\, Chris Eur and Shiyue Li\, our agents constructed m
 atroids from finite geometries whose Chow and chain polynomials are not lo
 g-concave\, disproving conjectures of Huh-Stevens\, Ferroni-Schroter and A
 thanasiadis-Kalampogia-Evangelinou. Interestingly\, for genus one curves l
 og-concavity survives but real-rootedness does not.
LOCATION:Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101
 )\, ISTA
ORGANIZER:boosthui@ist.ac.at
SUMMARY:Gergely Berczi: Real-rootedness and log-concavity from moduli of cu
 rves to matroids: an AI-assisted workflow
URL:https://talks-calendar.ista.ac.at/events/6721
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