Heidelberg Mathematics Physics Lectures
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Andy Neitzke (UT Austin)
"Spectral networks and their uses"
Time and venue of the three lectures:
- May 13, 14, 15, 2014, 14:00 - 15:30 h
- Institut für Theoretische Physik, Philosophenweg 12 Room 106
The series is aimed at advanced undergraduate and graduate students of physics and mathematics. Postdocs and faculty members are welcome to attend.
The poster for this lecture series can be found here.
Spectral networks are certain networks of codimension-1 'walls' on manifolds. Spectral networks on 2-manifolds have appeared in many places, e.g. in the theory of cluster varieties, Donaldson-Thomas theory, Hitchin systems, and 4-dimensional supersymmetric quantum field theory. One key idea is that the spectral network gives a way of reducing nonabelian phenomena to abelian ones, e.g. replacing GL(K) connections over some space by GL(1) connections over a K-fold covering space. I will describe what a spectral network is, how they give rise to nice 'cluster-like' coordinate systems on moduli spaces of complex flat connections over 2-manifolds (character varieties), and how they can be used to study the solutions of Hitchin equations themselves. The relation to Donaldson-Thomas theory and quantum field theory will be discussed more briefly. The main part of the story is joint work with Davide Gaiotto and Greg Moore, motivated by work of many other people, especially Fock-Goncharov, Kontsevich-Soibelman, Joyce-Song.