Abstract
We will discuss recent work on the relations between the intersection theory of homogeneous spaces (and their quantum, and higher genus generalizations), invariant theory, and non-abelian theta functions. The main theme is that the analysis of transversality in enumerative problems can be viewed as a bridge from intersection theory to representation theory. Some of the new results proved using these ideas are reviewed: multiplicative generalizations of the Horn and saturation conjectures, generalizations of Fulton’s conjecture, the deformation of cohomology of homogeneous spaces, and the strange duality conjecture in the theory of vector bundles on algebraic curves.
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