#
Spectral data for Higgs bundles

September 28 to October 2, 2015
at the

American Institute of Mathematics,
Palo Alto, 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:

- Spectral data for Higgs bundles; in particular, its relation to Cameral
covers, as well as representation theory of surfaces and 3-manifolds.
- 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.
- 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: