Points near infinity in moduli spaces of local systems (Carlos Simpson)

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Points near infinity in moduli spaces of local systems

Plática dada por Carlos Simpson (Centre National de la Recherche Scientifique, CNRS) en el evento Algebraic Geometry in Mexico 2016 el miércoles 1 de noviembre del 2016.

Abstract:
The character variety of representations of the fundamental
group of a Riemann surface has other incarnations with the structure
of algebraic varieties: the moduli spaces of vector bundles with
connection, or Higgs bundles. They have natural compactifications obtained by adding points parametrizing spectral curves.
On the other hand, points in the compactification of the character
variety correspond to actions of the fundamental group on
euclidean buildings. These different compactifications are related by the combinatorial-geometric data of Gaiotto-Moore-Neitzke
spectral networks. Our current work is directed towards making this
precise for SL(3) local systems, and it suggests a strategy for generalizing the construction of stability conditions by Bridgeland-Smith.