Applications are closed
for this workshop

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

This workshop, sponsored by AIM and the NSF, 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.

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.

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