Moduli spaces are solutions to geometric classification problems.  The word "moduli" was first used in this context by Riemann in 1857.  Each point in a such a space is a placeholder for an equivalence class of geometric objects, such as curves or bundles.  Moduli spaces tend to arise naturally in physics as solution spaces to differential equations.  It is often the case that a moduli space will possess its own interesting geometric structure, such as a special metric, the data of an integrable system, or a fibration that can be dualized to give rise to "mirror symmetry".  The moduli space of Higgs bundles on a Riemann surface, also known as the Hitchin system, is an example that embodies all of these features.

In the past few years, there have been significant developments in understanding the topology and geometry of moduli spaces through novel uses of techniques from both mathematics and physics.   These spaces include moduli spaces of bundles and sheaves, the Hitchin system, and quiver varieties.   Very recently, work by Gaiotto-Moore-Neitzke and by Mazzeo-Swoboda-Weiss-Witt has led to a better understanding of the hyperkaehler metric on the Hitchin system.  (The title of this workshop is inspired by the related paper "Ends of the moduli space of Higgs bundles" by the latter group.)

While the study of moduli spaces is certainly not new, many basic questions surrounding them are still unresolved.  This workshop focuses on both the beginnings of moduli spaces (their topologies and local structure) and on the ends of moduli spaces (the asymptotic geometry of noncompact moduli spaces). 

Program Details

All talks will occur in the Bahen building (BA) adjacent to the Fields Institute.  (See schedule below for room numbers.)  Participants are encouraged to use Room 210 in Fields for discussion sessions between the talks.