Compactifications and cohomology of quiver varieties
-- Thomas Nevins, April 7, 2017
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Nakajima quiver varieties play a central role in
interactions of algebraic geometry with geometric representation
theory and mathematical physics.  I will introduce quiver varieties
and explain that they admit modular compactifications with good
properties.  As a consequence, the cohomology of quiver varieties is
generated by tautological classes, i.e., they satisfy "hyperkahler
Kirwan surjectivity."  Similar statements hold for generalized
cohomology theories and derived categories.  The preceding is an
instance of a general story about moduli of objects in certain
categories, which I will discuss as time permits (as well as what one
can say about the hyperkahler Kirwan surjectivity problem in general).
The talk is based on joint work with K. McGerty.