Lecture II: Topological and categorical invariants of quiver varieties (and other symplectic moduli spaces)

There is a long history of efforts to calculate topological invariants (especially cohomology) of moduli spaces in algebraic geometry. I will describe recent work, drawing inspiration from precursors in the moduli of sheaves, that finds generators for cohomology and other invariants—including derived categories—of quiver varieties, and explain how the results fit into general patterns in noncommutative geometry.