Published on *Department of Mathematics* (https://math.yale.edu)

October 5, 2021 - 4:15pm

LOM 214

For a finite-type surface S, we study a preferred basis for the commutative algebra C[R_SL3(S)] of regular functions on the SL3(C)-character variety, introduced by Sikora-Westbury. These basis elements come from the trace functions associated to certain tri-valent graphs embedded in the surface S. We show that this basis can be naturally indexed by positive integer coordinates, defined by Knutson-Tao rhombus inequalities and modulo 3 congruence conditions. These coordinates are related, by the geometric theory of Fock-Goncharov, to the tropical points at infinity of the dual version of the character variety. This is joint work with Zhe Sun.