On some Fukaya categories of singular Lagrangians with coefficients

Abstract: This is about work in progress with Fabian Haiden and Ludmil Katzarkov. We consider the folkloric construction of Fukaya categories over the Novikov ring, for objects that are graphs in a surface (the complex plane) together with sections of a fiber dg-category patched together with A_n-objects at (n+1)-fold vertices of the graph. We discuss aspects of the question of defining these categories, and then look at the case of 6 endpoints on a regular hexagon with A_2 coefficient category. Mirror symmetry already gives a stability condition, and we show that the semistable objects are represented by spectral networks that can be pictured in an explicit way.

algebraic geometrysymplectic geometry

Audience: researchers in the topic

M-seminar