Spectral networks and G2

Abstract: Spectral networks are a combinatorial tool consisting of labelled lines on a Riemann surface. They have a surprising amount of applications and are intimately linked to non-Abelianization of flat connections, Fock–Goncharov cluster coordinates, exact WKB theory, etc. After reviewing this story for the SL(2) and SL(3) case, I will describe this is in detail for the group G2. Time permitting, I will give as an application a concrete parametrization of the nonabelian Hodge correspondence for the Hitchin component of the split real form of G2. This is joint work with Andy Neitzke.

mathematical physicsalgebraic topologycategory theoryquantum algebra

Audience: researchers in the topic

Topological Quantum Field Theory Club (IST, Lisbon)

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