Witten deformation and Morse inequalities on singular spaces Gayana Jayasinghe, University of Illinois at Urbana Champaign Host: Preston Kelley This is a virtual talk. Zoom link TBA.
Abstract: Morse theory is an important tool in understanding the topology of spaces. In his classic paper, "Supersymmetry and Morse theory", Witten gave a novel take on Morse theory which has been the motivation for various developments in many areas of mathematics and physics.
I will discuss a generalization of the Morse inequalities to stratified pseudomanifolds. I'll also explain some corollaries, including versions of the Arnold-Floer theorem in L2 cohomology, focusing on how the singularities change the formulations of these results. This is based on part of the work in https://arxiv.org/abs/2309.15845.
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