Geometric Structures seminar - Alexis Aumonier, March 17, 2022

[Miruna - Stefana Sorea]

Dear All,

This is to announce the next seminar from the series "Geometric Structures".

Speaker:   Alexis Aumonier<https://isomorphisme.github.io/> (University of Copenhagen)

Title:          An h-principle for complements of discriminants

Time:*       March 17, 2022, 2:00 pm (Rome Time)



Venue - hybrid:

  *   at room 134 at SISSA
  *
  *   from remote, on zoom at this link

https://sissa-it.zoom.us/j/85675591787?pwd=TUo2VXpmcEhOU1paRzBXUWp2MU1odz09
Passcode: geometry


Abstract:
In classical algebraic geometry, discriminants appear naturally in various moduli spaces as the loci parametrising degenerate objects. The motivating example for this talk is the locus of singular sections of a line bundle on a smooth projective complex variety, the complement of which is a moduli space of smooth hypersurfaces.
I will present an approach to studying the homology of such moduli spaces of non-singular algebraic sections via algebro-topological tools. The main idea is to prove an "h-principle" which translates the problem into a purely homotopical one.
I shall explain how to talk effectively about singular sections of vector bundles and what an h-principle is. To demonstrate the usefulness of homotopical methods, and using a bit of rational homotopy theory, we will prove together a homological stability result for moduli spaces of smooth hypersurfaces of increasing degree.



More information can be found here: https://sites.google.com/view/geometric-structures/

Everyone is welcome!


--
Miruna-Stefana Sorea
Postdoctoral Researcher
Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste, Italy
https://sites.google.com/view/mirunastefanasorea/