## Algebraic Geometry Seminar

"Geometric representation theory" should perhaps be called instead

"homological"; it is concerned with constructing representations

of important groups and algebras on the homology (of various types)

of certain algebraic varieties, even when the groups don't act

on the varieties themselves. I'll talk about one of the main examples,

the action of a simply-laced Lie group on the top homology of its

associated Nakajima quiver varieties (which I'll define from the ground up).

Subtler, but perhaps more natural, is Nakajima's action of the Yangian

algebra on the total homology. I hope to explain Jimbo's construction

of R-matrices from Yangian modules, and Maulik-Okounkov's combination

of these, interpreting R-matrices geometrically (thereby giving a

natural explanation for my puzzle results from Friday).