Lecture series by S. Rayan and H. Weiss 19-21 June 2017

Recordings from the minicourse on Asymptotics of Higgs bundles and hyperpolygons

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The mini-course was held between June 19th and 21st, 2017.

Monday, June 19th

Intro to moduli space of Higgs bundles: gauge theory (Compact Riemann surfaces, Yang-Mills / Hitchin equations and Hermitian metrics, Hitchin's construction, integrable system, etc.) by Hartmut Weiss. Intro to moduli space of Higgs bundles: algebraic geometry (Higgs bundles and stability condition from algebraic point of view, Nitsure construction, spectral curves and Hitchin fibration, C*-action, etc.) by Steven Rayan.

Tuesday, June 20th

Topology of Hitchin system (Morse theory of U(1)-action, fixed points as quivers, calculation of Poincare polynomials in low rank and genus, quivers as motivation for hyperpolygons) by Steven Rayan. Asymptotics of Higgs bundles (Partial compactification of moduli space, limiting configurations) by Hartmut Weiss.

Wednesday, June 21st

Hyperpolygons and parabolic Higgs bundles by Steven Rayan. Asymptotics of Higgs bundles (continued) and asymptotics of hyperpolygons (work in progress) by Hartmut Weiss.