Spectral data for Higgs bundles

September 28 to October 2, 2015

at the

American Institute of Mathematics, San Jose, California

organized by

Joergen Ellegaard Andersen, David Baraglia, Philip Boalch, and Laura Schaposnik

Original Announcement

This workshop will be devoted to applications of Higgs bundles and their spectral data to the study of geometric questions in the Langlands program and Topological Quantum Field Theory. The purpose of the workshop is to bring the leading key researchers of related fields together with young mathematicians and physicists to establish and investigate new problems and applications of the theory of Higgs bundles and spectral data.

Spectral data for Higgs bundles has recently found applications in different areas of mathematics and physics, the principal focus of the workshop will be to use spectral data associated to Higgs bundles as a framework for understanding open problems in the study of dualities between branes and the geometry and topology of 3-manifolds, as well as brane and curve quantization. The workshop will discuss the ideas behind the study of spectral data, and explore possible applications to new problems. More specifically, the main topics for the workshop are:

  1. Spectral data for Higgs bundles; in particular, its relation to Cameral covers, as well as representation theory of surfaces and 3-manifolds.
  2. The geometric Langlands program; especially, the construction and correspondence between branes in the moduli space of Higgs bundles, and the wild case and the link to Legendrian knots.
  3. Topological Quantum Field Theory; more specifically, the relation between quantization of moduli spaces of Higgs bundles through brane and curve quantisation, as well as the study of formulas for the WRT-TQFT Chern-Simons boundary states associated to 3-manifolds.
An overall aim of the workshop will be to consolidate and disseminate the variety of different techniques, heuristics, and approaches that have been applied to the study of Higgs bundles and spectral data in recent years by the mathematics and physics communities.

The workshop participants include experts from string theory, algebraic geometry, representation theory, integrable systems, topological recursion, and complex geometry. We believe they present the necessary background and familiarity with open questions in their field to make of the workshop a successful week.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Papers arising from the workshop:

Rational points of quiver moduli spaces
by  Victoria Hoskins and Florent Schaffhauser
Group actions on quiver varieties and applications
by  Victoria Hoskins and Florent Schaffhauser
Opers versus nonabelian Hodge
by  Olivia Dumitrescu, Laura Fredrickson, Georgios Kydonakis, Rafe Mazzeo, Motohico Mulase, and Andrew Neitzke