Title: Quantum Grassmannians, reduced arc schemes and representation theory.


Abstract: An arc scheme of an algebraic variety is obtained by replacing the base field with the ring of series in one variable.
For the Grassmann varieties the corresponding reduced arc schemes are identified with the  Sottile-Sturmfels quantum 
Grassmannians. We will recall the main definitions and constructions of the theory. We will also describe the connection with
the representation theory of type A current algebras.