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SUMMARY:Schottky problem\, Siegel modular forms and quadratic forms
DTSTART:20171005T141500
DTEND:20171005T151500
DTSTAMP:20260511T204832Z
UID:c671eb6d1154c71c99e91ab81973579df2c1ea759758eca7d32f3979
CATEGORIES:Conferences - Seminars
DESCRIPTION:Giulio Codogni (EPFL)\nThe Schottky problem is about understan
 ding when a principally polarised abelian variety is the Jacobian of a cur
 ve. There is a classical way to approach this problem using modular forms.
  More generally\, there is a very rich interplay between modular forms\, m
 oduli space of curves and moduli space of abelian varieties. We are partic
 ularly interested in theta series\, these are modular forms associated to 
 convenient quadratic forms. By proving some geometrical results about the 
 singularities of the Satake compactification of the moduli space of curves
 \, we will show that any given linear combination of theta series is not i
 dentically zero on the moduli space of curves of high enough genus\; this 
 can be rephrased by saying that there are no stable solutions to the Schot
 tky problem. We are able to make this result effective just for quadratic 
 forms of rank at most 24. This is a joint work with N. Shepherd-Barron. We
  will also report about a work in progress on the connection between confo
 rmal vertex algebras and modular forms defined on the moduli space of curv
 es.
LOCATION:BI A0 448 https://plan.epfl.ch/?room==BI%20A0%20448
STATUS:CONFIRMED
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