International Laboratory of Cluster Geometry: Andrew Nietzke (Yale University, USA)
Spectral networks and some applications I
I will describe the notion of "spectral network." These objects appeared in WKB theory under the name "Stokes graphs," and later arose in my joint work with Gaiotto and Moore on BPS states in supersymmetric field theory. They are generalizations of the critical graph of a meromorphic quadratic differential. It has turned out that they are connected to various different subjects: e.g. analysis of ODEs, hyperkahler geometry, Donaldson-Thomas invariants, cluster varieties, quantum topology. I will define what they are and explain as many applications as I can.