Following a quick summary of exponential networks, I will describe in some detail the explicit correspondence, obtained in collaboration with Banerjee, Romo and Senghaas, between torus fixed points of the Hilbert scheme of points in the plane and anomaly-free finite webs attached to the quadratically framed pair of pants.
I will describe exponential networks and its uses in defining (some version of) Donaldson-Thomas invariants and BPS quivers. If time allows I will present some other interpretation of these invariants as Euler characteristic of certain families of special Lagrangians.
Higher Teichmüller spaces are connected components in the space of representations from a surface group into a higher rank Lie group. The first examples of these are Hitchin components for split real Lie groups. I will give an overview of the known examples of higher Teichmüller spaces, via the notion of Theta-positivity introduced by Guichard-Wienhard to generalize Fock-Goncharov and Lusztig...
I will describe a role of spectral networks in 2-dimensional conformal field theory: they can be used as "screening contours" in a new construction of Virasoro conformal blocks from branched double covers. The key new point is that, when three exponentiated screening contours end on a branch point of the cover, they cancel an unwanted singularity of the conformal block there. The talk is...
Given a bipartite graph G on a possibly punctured surface S, there is a (non-commutative) cluster Poisson variety X(G,S). It depends only on the equivalence class of G under certain elementary transformations. A threefold M which bounds the surface S with filled punctures gives rise to a Lagrangian in the generic symplectic fibers of X(G,S). I will explain that it carries a natural...