Chris Grossack (Dept. of Mathematics, University of California Riverside)

08/25/2025 4:10 pm

Abstract: 

Gentle algebras are a class of algebras whose representation theory is particularly well understood. In the last 10 years we've learned the "real reason" for their relative simplicity -- they're derived equivalent to Fukaya categories of surfaces. This means we can classify indecomposables by curves in a surface, we can compute Ext groups between two indecomposables by counting intersection points, and we can compute mapping cones by resolving singularities. Together, these allow us to do surprisingly delicate computations with the derived category by drawing curves and counting intersection points. In this talk we'll explain how to work with these doodles, and how to translate them into more impressive looking calculations with chain complexes. Given time, we'll explain the speaker's PhD thesis, where she uses this machinery to compute the Hall algebra of gentle algebras in terms of local skein relations on a surface.