[Topology.beta] FW: DDT&G seminar on March 15 @Amsterdam: Francesco Lin on Topology of the Dirac equation

[Rot, T.O. (Thomas)]

Dear all,

This is happening tomorrow.  We’ll have drinks and dinner after.

Best,
Thomas

From: Federica Pasquotto <f.pasquotto at math.leidenuniv.nl>
Date: Thursday, 7 March 2024 at 23:05
To: Federica Pasquotto <f.pasquotto at math.leidenuniv.nl>
Subject: DDT&G seminar on March 15 @Amsterdam: Francesco Lin on Topology of the Dirac equation


Dear colleagues,



You are cordially invited to attend the next Dutch Differential Topology and Geometry seminar, which will take place next week in Amsterdam.



Speaker: Francesco Lin<https://www.math.columbia.edu/~flin/>

Title: "Topology of the Dirac equation on spectrally large three-manifolds" (see below for the abstract)

Date: Friday 15 March, 14:00-16:30

Location: VU Amsterdam, NU 9-A46



The schedule will be as follows:



2:00-3:00 p.m.: first part of the seminar (little to no prior knowledge assumed)

3:30-4:30 p.m.: second part of the seminar (slightly more advanced level)



Please notice that the first part of the seminar (2:00-3:00 p.m.) is intended for general mathematical audience, and master students with an interest in geometry and topology are especially encouraged to participate.



Please visit the seminar's webpage for additional information and an overview of past and upcoming talks:

https://www.few.vu.nl/~trt800/<https://www.few.vu.nl/~trt800/ddtg.html>ddt<https://www.few.vu.nl/~trt800/ddtg.html>g.html<https://www.few.vu.nl/~trt800/ddtg.html>



We hope to see many of you next week!



Alvaro, Federica and Thomas


Abstract
In the first talk, I will review the classical work of Atiyah and Singer describing the homotopy type of the family of Dirac operators on a spin Riemannian manifold, and its consequences regarding metrics of positive scalar curvature. In the second talk, I will discuss how one can exploit the Seiberg-Witten equations and Floer theory to obtain more detailed information about the structure of the family in the case of a three-manifold for which the spectral gap of the Hodge Laplacian on coexact 1-forms is large compared to the curvature. For concreteness, we will have a special focus on the case of the n-torus throughout the talks.

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