[Topology.beta] DDT&G this week

[Rot, T.O. (Thomas)]

Dear all,

I am sad to not be present! I am sure you will enjoy the talks of luca without me.

Say hi from me?

Best,
Thomas

On 26 Nov 2024, at 09:29, Rot, T.O. (Thomas) <t.o.rot at vu.nl> wrote:


Dear all,

Next week Luca Asselle (Bochum) will visit Gabriele and he will speak in the DDT&G. Abstract is below.

I think the talk should be interesting to those of us who care about variational ODE’s and PDE’s, which is why I post this on both lists. Please encourage your master students to attend.

06-12-2024: 14:30-17:00 location Utrecht BBG 083: Luca Asselle <https://sites.google.com/site/lucaasselle/> : A Tour of Morse Theory: From Its Origins to the Present Day
Abstract. The Morse theory of critical points, originally developed by Morse in his study of closed geodesics and later extended by Palais and Smale to a class of functionals on Hilbert manifolds, does not apply to problems defined in a Banach setting. One of the reasons is the fact that the standard notion of non-degeneracy for critical points cannot be satisfied in this context. Also, even in a Hilbert setting, the theory proves inadequate when dealing with critical points that have infinite Morse index and co-index, as the critical groups in such cases always vanish. One way to address these limitations is through the Morse complex approach, which uses the intersections between the stable and unstable manifolds to construct a chain complex generated by critical points. In the first of two talks, I will introduce the Morse complex approach in a finite-dimensional setting and discuss the challenges that arise when attempting to extend this method to infinite-dimensional spaces. In the second talk, I will explore how some of these challenges can be tackled, both from a general perspective and in the context of specific examples, such as the Hamiltonian action functional on cotangent bundles, functionals involving the p-Laplacian or p-area, and functionals for Dirac-harmonic maps.

This Friday there will be more factorization homology as well:

https://sites.google.com/view/miguelbarata/seminars


Best,
Thomas



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