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Title:
Higgs bundles on the affine line and wild surface groups
Speaker:
Abstract:
After the work of Seiberg-Witten mathematicians focused on meromorphic Higgs bundles leading to the work of Markman and Bottacin showing they are algebraic integrable systems, and in turn to the wild nonabelian Hodge correspondence showing they admit complete hyperkahler metrics and relate to meromorphic connections. In turn this implies that the underlying moduli spaces have a simple intrinsic topological description generalising the familiar fundamental group representations appearing in the non-singular case. The best known approaches are the Stokes filtrations and the Stokes local systems (or wild monodromy representations). In this talk I will explain how to formalise the notion of {\em Stokes decompositions}, to intermediate between them. This is part of an attempt (the Lax project) to understand the bestiary of complete hyperkahler manifolds that occur as moduli spaces of algebraic Higgs bundles on the affine line (i.e. on R^2).
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