#
Singular geometry and Higgs bundles in string theory

October 30 to November 3, 2017
at the

American Institute of Mathematics,
San Jose, California

organized by

Lara B. Anderson,
Jonathan Mboyo Esole,
Laura Fredrickson,
and Laura Schaposnik

## Original Announcement

This workshop will be devoted to the
study of exciting developments around Higgs bundles, real algebraic
geometry and string 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.
The proposed workshop focuses on two interrelated themes concerning
Higgs bundles and the Hitchin fibration:

(A) The study of the moduli space of Higgs bundles and its branes
through the Hitchin fibration within the broader setting of integrable
systems and string theory: Hitchin systems and T-branes.

(B) Higgs bundles and algebraic geometry: Invariants of singular
spaces, and in particular Higgs bundles on singular curves. The study
of the geometry of this moduli space, including limits and geometric
structures within the Hitchin fibration.

Although these two themes are closely related, interactions between
them are just in their infancy. A key goal of this meeting would be to
strengthen links among researchers studying Higgs bundles from each of
these perspectives. In particular, one may define Higgs bundles over
singular curves, and also look at Higgs bundles which have singular
spectral data - obtaining a global understanding of these two
situations would be most beneficial from the perspective
of F-theory and superconformal theories in diverse dimensions.

One of the most interesting aspects of the duality revolution in
string theory is the understanding that gauge fields and matter
representations can be described by intersection of branes. This has
opened the door to the geometric engineering of many physical systems
since gauge theory is at the heart of our description of physical
interactions, and in particular it has opened many doors in the study
of Higgs bundles. 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. In particular, we hope to understand further the
role that spectral curves and spectral data plays in string theory, and in
particular for Higgs bundles on higher dimensional spaces.

The workshop participants include experts from string theory,
algebraic geometry, representation theory, integrable systems, quiver
varieties, and singular 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.