Alladi Ramakrishnan Hall

Geometry of quiver representations, Kac Conjecture and Donaldson - Thomas Invariants

Janu Verma

Kansas State Univ

Quivers are related to many different areas of mathematics, particularly representation theory, Kac - Moody algebras, quantum groups, algebraic geometry and physics. Using the techniques of GIT, King constructed the moduli space of finite dimensional representations of a quiver over a fixed field. This gives a geometric framework to understand the representation theoretic problems related to quivers.
In this talk, I'll explain King's construction of quiver moduli and Nakajima's construction of quiver variety. I'll talk about the algebraic notion of stability conditions on an abelian category (a la Bridgeland).
An important problem in theory of quiver representations is the conjecture of kac which emerged from his work on Kac - Moody algebras. I'll talk about the recent developments towards the understanding of this conjecture.
If time permits, I'll explain some other aspects of the varieties associated to quivers.