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Seminars

Special Colloquium

Topology of group actions, Morse theory and symplectic invariants

2024/12/12 (Thu.) 15:30~16:30
  • Date : 2024/12/12 (Thu.) 15:30~16:30
  • Location : Auditorium, 6 Floor, Institute of Mathematics (NTU Campus)
  • Speaker : Yusuf Barış Kartal (University of Edinburgh)
  • Abstract : Morse theory provides a method for studying the topology of smooth manifolds through the critical points of a function and its gradient flow. In the 1980s, Andreas Floer applied ideas from Morse theory to the infinite dimensional setting, producing an invariant in symplectic topology that has since become a central tool in this field, and later understood to be closely related to enumerative geometry and mirror symmetry. Inspired by Floer's insight, Cohen-Jones-Segal proposed a framework to obtain finer information from the data arising in Morse and Floer theory. However, neither Morse theory nor the framework of Cohen-Jones-Segal is compatible with compact group actions, which limit their usefulness in the study of equivariant topology and geometry. In this talk, I will explain how, in joint work with Laurent Cote, we extend the Cohen-Jones-Segal setup to study equivariant invariants. I will then discuss applications to topology and symplectic geometry, and explain how tools from homotopy theory can be used to relate symplectic invariants to the topology of the underlying manifold.
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