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Topology, Algebraic Geometry, and Dynamics Seminar (TADS): A singular journey with Morse, Bott, Smale, and Witten

Mar 7, 2025, 1:30 - 2:30 PM

 

Speaker: Hadrian Quan, University of California Santa Cruz

Title: A singular journey with Morse, Bott, Smale, and Witten

Abstract: Morse theory is a flexible approach to studying the topology of manifolds by decomposing these spaces along the isolated critical points of certain nice functions ("Morse functions"), and relates such geometric decompositions to other invariants such as cohomology groups, e.g. through the Morse inequalities. Witten, inspired by ideas from quantum mechanics, later gave new analytic proofs of the Morse inequalities and thus related the analysis of the Hodge Laplacian to the topology and dynamics of Morse theory. In this talk I will present recent joint work with Jayasinghe and Yu, which extend these ideas in two directions. We broaden the dynamical setting by considering Morse-Bott functions (which have more complicated critical point sets), and the geometric setting to consider not just manifolds but also singular stratified spaces (e.g. singular projective varieties).

 

Date/Time: March 7, 1:30pm

Location: Exploratory Hall, Room 4208

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