Description
The purpose of this mini-course is two-fold.
In the first half I plan to start by (very briefly!) recalling some basic notions of the theory of constructible sheaves on complex algebraic varieties (such as, for example, equivariant derived categories of constructible sheaves, perverse sheaves etc.) and then apply this formalism to the study of certain derived category of equivariant sheaves on the affine Grassmannian of a complex reductive group G (here the main goal will be to explain the formulation of the so called derived geometric Satake equivalence due to Drinfled and Bezrukavnikov-Finkelberg).
In the 2nd half I plan to explain applications of the above to the subject of symplectic duality. I plan to discuss topics such as (conical) symplectic resolutions and their quantizations, formulations of (various aspects of) symplectic duality,Braverman-Finkelberg-Nakajima construction of Coulomb branches of 3d N=4 gauge theories via the affine Grassmannian and its relation to symplectic duality.
Some further topics might be discussed depending on how much time is left.
