[Topology.beta] FW: DDT&G seminar tomorrow in Amsterdam: Niels Waterstraat

[Rot, T.O. (Thomas)]

Dear all,

This is happening today. Fun with analysis and topology. I hope to see you there!

Best,
Thomas

From: Federica Pasquotto <f.pasquotto at math.leidenuniv.nl>
Date: Thursday, 13 April 2023 at 13:28
To: Federica Pasquotto <f.pasquotto at math.leidenuniv.nl>
Subject: DDT&G seminar tomorrow in Amsterdam: Niels Waterstraat


Dear all,



This is to remind you that Niels Waterstraat (MLU Halle-Wittenberg) will speak in the DDT&G seminar tomorrow (Friday) afternoon.



The title of his minicourse will be



"Spaces of Self-adjoint Fredholm Operators and the Spectral Flow"



(see below for the abstract).



We will start at 14:00 in room 9-A46 (NU building, Amsterdam).



It will also be possible to attend remotely using the login details below:



https://us06web.zoom.us/j/85884234839

Meeting ID: 858 8423 4839

Passcode: 304030



We hope to see many of you tomorrow!



Alvaro, Federica, and Thomas.



Abstract:


The spectral flow is an integer-valued homotopy invariant for paths of self-adjoint Fredholm operators that was invented by Atiyah, Patodi and Singer in the seventies, for investigating elliptic differential operators on manifolds. Later it was used by Floer in the construction of his famous homology groups and became a well-known invariant in global and symplectic analysis as well as mathematical physics in the decades since.
In the first part of this lecture, we introduce some basic definitions and concepts of functional analysis like, e.g., Fredholm operators, spectra and functional calculus.
The second part deals with different topologies on the space of self-adjoint Fredholm operators, for which the spectral flow induces an isomorphism between their fundamental groups and the integers.
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