$SL_3$-laminations as bases for $PGL_3$ cluster varieties for surfaces

Abstract: I will recall Fock-Goncharov's duality conjecture for cluster $A$- and $X$-varieties, and Fock-Goncharov's solution for the case of certain enhanced moduli spaces of $G$-local systems on a punctured surface when $G$ is $SL_2$ and $PGL_2$. Then I will explain how Kuperberg's web can be used to extend this result to the case when $G$ is $SL_3$ and $PGL_3$.

algebraic geometrycombinatoricsdifferential geometrygeometric topologyquantum algebrarepresentation theorysymplectic geometry

Audience: researchers in the topic

Legendrians, Cluster algebras, and Mirror symmetry

Series comments: Schedule
School: January 4–8, 2021
Conference: January 11–15, 2021