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DTSTAMP:20261106T001110Z
UID:69a7ee41f3eb3900041701@ist.ac.at
DTSTART:20261112T131500
DTEND:20261112T161500
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
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20261106T001110Z
UID:69a7ee4200403374631665@ist.ac.at
DTSTART:20261119T131500
DTEND:20261119T161500
DESCRIPTION:Speaker: Leonardo Francisco Cavenaghi\nhosted by Tamas Hausel\n
 Abstract: In this talk\, we quickly recall a weaker notion of the Hodge at
 oms of Katzarkov--Kontsevich--Pantev--Yu which suffices to solve the irrat
 ionality of wide interesting varieties\, such as very general smooth cubic
  4-folds. This is done by introducing a super-analytic manifold (in the se
 nse of Berkovich)\, which should be thought of as the parameter space for 
 the Gromov--Witten potential. This supermanifold carries a natural action 
 of the Hodge group\, and at fixed points\, the isomorphism classes (partit
 ioned as generalized eigenspaces for the quantum multiplication action) of
  the isotropy representations are called coarse Hodge atoms''. We explain 
 to what extent this data can be read from Lie-theoretic content in the cas
 e of complete intersections in flag varieties\, present an algorithm to co
 mpute atomic decomposition (implemented at https://leonardofcavenaghi.gith
 ub.io/atomicdecompositions/)\, and present some theoretical results to obs
 truct the rationality of 4-folds and some 5-folds.This is based on two joi
 nt works: the in-progress 9.5-lecture series on the theory of atoms with L
 . Katzarkov and M. Kontsevich\, and a recent work with B. Alexeev\, G. Gal
 indo\, L. Katzarkov\, and P. A. M. Martins.
LOCATION:Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101
 )\, ISTA
ORGANIZER:boosthui@ist.ac.at
SUMMARY:Leonardo Francisco Cavenaghi: On the atomic decomposition of some c
 omplete intersections
URL:https://talks-calendar.ista.ac.at/events/6723
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