David Hernandez will speak on "Small property for resolutions of quiver varieties."

ABSTRACT: The geometric small property (Borho-MacPherson) of projective morphisms implies a description of their singularities in terms of intersection homology. We present a solution of the smallness problem raised by Nakajima for certain resolutions of (graded) quiver varieties (analogs of the Springer resolution). The proof relies on the deep relations between quiver varieties and the representation theory of quantum affine algebras : for Kirillov-Reshetikhin modules of simply-laced quantum affine algebras, we characterize explicitly the Drinfeld polynomials corresponding to the small resolutions.

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Pasha Pylyavskyy will speak on "Towards skew total positivity"

ABSTRACT: I will talk about generalizing the theory of total positivity to skew-symmetric matrices. The role of Lindstrom lemma is played by a network interpretation of pfaffian discovered by John Stembridge. The question of semialgebraic description remains open. I will describe an attempt to address it by constructing a family of polynomials called Temperley-Lieb pfaffinants, inspired by Temperley-Lieb immanants of Rhoades and Skandera. The talk is based on joint work with Thomas Lam.

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