Seminars & Colloquia Calendar
Tropical Fock-Goncharov coordinates for linear bases of SL3-skein algebras of surfaces
Daniel Douglas - Yale University
Location: Hill Center Room 705
Date & time: Wednesday, 27 April 2022 at 2:00PM - 3:00PM
Abstract - 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.