Mathematics Department Colloquium: Fukaya categories with coefficients and spectral networks

Colloquium | February 7 | 4:10-5 p.m. | 60 Evans Hall

 Carlos Simpson, Université de Nice

 Department of Mathematics

A conjecture of Kontsevich says that the Fukaya category of a symplectic manifold having an additional volume form, should have a stability condition where the stable objects are represented by possibly singular "special Lagrangians". This statement has a nice expression, in the case where we look at the Fukaya-Seidel category of a Riemann surface with coefficients in a fiber category. The special Lagrangians are identified with the spectral networks of Gaiotto-Moore-Neitzke. In joint work with Haiden, Katzarkov and Pandit, in progress, we treat a first rather simple case but one that leads already to some interesting pictures.