Pseudoholomorphic Curves with Boundary - Can You Count Them? Can You Really? - Sara Tukachinsky

Explore the intricacies of pseudoholomorphic curves with boundary in this Members' Seminar talk by Sara Tukachinsky from the Institute for Advanced Study. Delve into Gromov-Witten theory, examining the moduli space of sphere maps and the challenges of open Gromov-Witten theory. Discover the speaker's approach to the invariance problem, developed jointly with Jake Solomon, including the strong Maurer-Cartan equation and the mapping cone complex. Gain insights into the relative quantum product and its associativity as Tukachinsky addresses the fundamental question: Can we truly count pseudoholomorphic curves with boundary?

Intro
Gromov-Witten theory (g = 0)
The moduli space of sphere maps
Rephrasing the problem
Facts of life
Open Gromov-Witten theory 19 = 0
Compactification of M
Invariance problem
Our approach (Joint with Jake Solomon)
The (strong) Maurer-Cartan equation
Invariance - Part 11
The mapping cone complex
Special case
Relative quantum product (Joint with. Solomon)
Associativity