Title: Eisenstein sheaves and canonical bases associated with a curve

Abstract: In the representation theory of quantum groups, the discovery of canonical bases was a milestone. For the quantum group associated with a quiver, Lusztig constructed canonical bases by considering Hall algebras and the geometry of representation stacks. In my talk, I will present an analogous construction in the setting of curves, follow the idea of Schiffmann. The main contributors of the canonical bases are Eisenstein sheaves, which plays an important role in geometric Langlands program. I will also explain the microlocal behavior of Eisenstein sheaves, from the perspective of Donaldson-Thomas theory.