In this working group we'll read through Abouzaid's proof of Viterbo's theorem, which identifies the symplectic cohomology ring of a cotangent bundle with the string topology of the base. This will be a weekly-ish seminar at IMJ-PRG, Sorbonne running from November 2025 - January 2026.
Here is a tentative schedule:
(Maral, Nov. 5) Section 1, symplectic topology of cotangent bundles and definition of SH using direct limits.
(Salammbo, Nov. 12) Section 2, BV algebra structure
(Luis, Nov. 19) Section 3, string topology using piecewise geodesics
(? Nov. 15) Open discussion OR Russell gives an introduction to string topology from Chas-Sullivan's point of view.
(Amanda, Dec. 3) Orientations and gluing compatibility for Sections 1+2.
(Vincent, Dec. 10) Section 4, definition to SH to string topology homomorphism.
(?, Dec. 17) Open discussion if desired.
(Nikolas, Jan. 14) Section 5, part 1, foundations of Lagrangian wrapped Floer homology.
(Jianqiao, Jan. 21) Section 5, part 2, definition of string topology to SH map and essential properties.
(Lukas, Jan. 28) Section 6, completed proof of the isomorphism.