American Institute of Mathematics, San Jose, California
Lara B. Anderson, Jonathan Mboyo Esole, Laura Fredrickson, and Laura Schaposnik
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.
A list of open problems.