MOS

Abstract

Classical moduli theory was born with a focus on objects we can easily see: varieties, vector bundles, morphisms, etc. In the last half-century, we have come to perceive a slew of subtler invariants, such as the derived category of coherent sheaves on a variety, that are decidedly murkier. Within the last decade, moduli spaces of objects in the derived category began to appear, drawing inspiration from birational geometry and mathematical physics. It turns out that a systematic approach to constructing these moduli spaces bears fruit in such disparate areas as Gromov-Witten theory, arithmetic geometry, and non-commutative algebra. I will describe some aspects of these moduli problems and a few of their principal applications.