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Richard Thomas: Lectures

January 8 and January 10, 2018
TITLE: Introduction to coherent sheaves

ABSTRACT: I will try to give a coherent introduction to sheaf theory.

Coherent sheaves can be thought of as singular holomorphic vector bundles on complex manifolds, and can be used to compactify moduli of bundles. They thus give a way to define higher dimensional gauge theory invariants on projective varieties, and give examples that demonstrate some of the phenomena that can arise on more general manifolds of special holonomy.

After an introductory first lecture I will focus on some of (depending on audience tastes): curve counting via sheaves, stable pairs, the relationship to GW theory (MNOP conjecture) and Gopaukmar-Vafa invariants, the Serre construction relating codimension two subvarieties to rank 2 bundles, smoothing of singularities of reflexive sheaves.

January 10, 2018:

 

January 8, 2018: