Doppio Seminario di Geometria

Martin Ulirsch e Samouil Molcho

30-09-2021 - 14:00
Largo San Leonardo Murialdo,1 - Pal.C

M. Ulirsch: Buildings, parabolic bundles, and toroidal bordifications of reductive groups

Abstract: Bruhat-Tits buildings are natural piecewise-linear analogues of symmetric spaces for semi-simple (or more generally reductive) groups. In this talk we show how a variation on the theme of Bruhat-Tits buildings can be used to define a natural tropicalization of a reductive group G. We explain how the choice of a stacky fan structure on the tropicalization gives rise to a toroidal bordification of G and how to prove a version of faithful tropicalization. Finally, we combine this story with methods from logarithmic geometry to give a new perspective on parabolic principal bundles.

2. S. Molcho: Logarithmic Geometry, universal stability conditions and Abel-Jacobi theory.

Abstract: The classical Abel-Jacobi theorem gives necessary and sufficient conditions for a divisor on a Riemann surface to be the divisor of zeros and poles of a rational function. The modern counterpart of this question leads to the study of the "double ramification cycles", which are, roughly speaking, the loci of curves in ar{M}_{g,n} which admit a rational function with prescribed zeros and poles along their markings. The DR cycles have been extensively studied in recent years for a variety of reasons -- their connection with Gromov-Witten theory, strata of meromorphic differentials. In this talk I will discuss how approaching the problem from the perspective of logarithmic geometry reveals additional structure on these cycles, and how it naturally connects them to the theory of universal stability conditions, yielding new formulas in the process. This is joint work with Holmes, Pandharipande, Pixton and Schmitt.

I seminari saranno presentati in presenza nell'aula 211. Tutti gli afferenti all'università Roma Tre potranno accedere previa esibizione del greenpass. Gli esterni che fossero interessati a partecipare possono contattare gli organizzatori all'email amos.turchet@uniroma3.it.

Il seminario sarà anche seguibile via Teams seguendo il seguenteLink identifier #identifier__144167-1 link:
org: Turchet Amos

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