Oded Yacobi (The University of Sydney) Friday 11 May, 12-1pm, Place: Carslaw 375 Title: On the category O of affine Grassmannian slices Abstract: Affine grassmannian slices are varieties which appear naturally in geometric representation theory. Their quantisations are given by truncated shifted Yangians. I will describe a recent result which gives an equivalence of categories between modules for truncated shifted Yangians and modules for Khovanov-Lauda-Rouquier-Webster algebras. We use this theorem to a) resolve a conjecture describing the highest weights of truncated shifted Yangians, and b) prove the so-called "symplectic duality" between affine Grassmannian slices and Nakajima quiver varieties. The latter result provides a link between two very different geometric models for representations of semisimple Lie algebras. This is joint work with Kamnitzer, Tingley, Webster, and Weekes.