Morse theory of loop spaces, Hecke algebras, and the higher-dimensional Heegaard Floer homology of cotangent fibers

Tsinghua-BIMSA symplectic geometry seminar

Organizers：

Kenji Fukaya (YMSC)

Honghao Gao (YMSC)

Hang Yuan (BIMSA)

Speaker：

Ko Honda (UCLA)

Time：

Thur., 16:30-18:00, Sept. 18, 2025

Venue：

B725, Shuangqing Complex Building A

Title:

Morse theory of loop spaces, Hecke algebras, and the higher-dimensional Heegaard Floer homology of cotangent fibers

Abstract:

Given a smooth closed $n$-manifold $M$ and a $\kappa$-tuple of basepoints ${\bf q}\subset M$, we define a Morse-type $A_\infty$-algebra called the based multiloop $A_\infty$-algebra and show the equivalence with the higher-dimensional Heegaard Floer $A_\infty$-algebra of $\kappa$ disjoint cotangent fibers of $T^*M$. Along the way, Chas-Sullivan type string operations and Hecke algebras will make appearances.

About the speaker:

Arnaud Plessis is an assistant professor at BIMSA from September 2023. His research is mainly focused on diophantine geometry. He obtained his Phd. thesis in 2019 at Université de Caen Normandie. Before joining BIMSA, he has been Attaché Temporaire d'Enseignement et de Recherche (a kind of postdoctoral with course duties) at Université Grenoble Alpes from September 2019 to August 2020. Then, he has been postdoctor at Morningside Center of Mathematics, Chinese Academy of Sciences, from September 2020 to August 2023.