[Topology.beta] DDT&G seminar on April 14 in Amsterdam: Nils Waterstraat

[Rot, T.O. (Thomas)]

Dear colleagues,

Please see the announcement below. The spectral flow is a nice topological tool for differential equations.

I therefore hope to see not only topologists, but also dynamicists in the audience.

Please note that the talks should be accessible to master students. Please forward this to any master students that might be interested.

Best,
Thomas


From: Federica Pasquotto <f.pasquotto at math.leidenuniv.nl>
Date: Wednesday, 5 April 2023 at 18:17
To: Federica Pasquotto <f.pasquotto at math.leidenuniv.nl>
Subject: DDT&G seminar on April 14 in Amsterdam: Nils Waterstraat


Dear all,



You are kindly invited to attend the next Dutch Differential Topology and Geometry seminar:



Speaker: Niels Waterstraat (MLU Halle-Wittenberg)

Title: "Spaces of Self-adjoint Fredholm Operators and the Spectral Flow" (see below for the abstract)

Date: Friday 14 April, 14:00-16:30

Location: VU Amsterdam, NU building, room 9-A46



It will also be possible to attend remotely (login details to be provided shortly).

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)



Master students with an interest in topology and geometry are strongly 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/ddtg.html



We would also like to remind you that most of the previous lectures are available on the YouTube channel of the seminar:

https://www.youtube.com/channel/UCN0o3PUqaC_ZhPNuM846kgg/


We hope to see many of you next week!



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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