Geometric Structures - Ursula Ludwig - June 1st - 4:15 pm (Rome Time)

[Miruna - Stefana Sorea]

Dear All, 

This is a reminder of today's seminar from the series "Geometric
Structures".

Speaker: URSULA LUDWIG  [1]( [1]Universität Duisburg-Essen and [1] MPIM
Bonn [1]) [1] 

Title:       The Witten deformation on singular spaces 

Time:      June 1, 2021, 4:15 pm (Rome Time)  

Venue:    from remote only, on zoom at this link 
https://sissa-it.zoom.us/j/85675591787?pwd=TUo2VXpmcEhOU1paRzBXUWp2MU1odz09
[2]
Passcode: geometry

Abstract:  
In his seminal paper "Supersymmetry and Morse theory" (Journal Diff.
Geom. 1982) Witten, inspired by ideas from quantum field theory, gave a
new analytic proof of the famous Morse inequalities. The Witten
deformation plays an important role in the generalisation by Bismut and
Zhang of the comparison theorem between analytic and topological torsion
of a smooth compact manifold, aka Cheeger-Mu ̈ller theorem. 

The aim of this talk is to explain the generalisation of the Witten
deformation to certain singular spaces. We will explain the case of
singular spaces with conical singularities equipped with a radial Morse
function as well as the case of singular algebraic complex curves
equipped with a stratified Morse function in the sense of Goresky and
MacPherson. A first result in both situations is the proof of the Morse
inequalities for the L2-cohomology (or equivalently the intersection
cohomology). A much stronger result is the generalisation of the
comparison between the so called Witten complex and an appropriate
singular Morse-Thom-Smale complex. 

In the first part of this talk, I will give a gentle introduction to the
Witten deformation for a smooth compact manifold.

More information can be found here:
https://sites.google.com/view/geometric-structures/ [3] 

Everyone is welcome! 
-- 
_Miruna-Stefana Sorea_
_Postdoctoral Researcher_
_Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste,
Italy_
_HTTPS://SITES.GOOGLE.COM/VIEW/MIRUNASTEFANASOREA/_ 

Links:
------
[1]
https://www.google.com/url?q=https%3A%2F%2Fwww.uni-due.de%2F~hm0213%2F&sa=D&sntz=1&usg=AFQjCNEMOwokYziDIctuDaIk486elg_XAw
[2]
https://sissa-it.zoom.us/j/85675591787?pwd=TUo2VXpmcEhOU1paRzBXUWp2MU1odz09
[3] https://sites.google.com/view/geometric-structures/