Academic Year 2020 – 2021

Yangians in geometry and representation theory

Instructors:

Andrea Appel (Università di Parma, Italy)

Martina Lanini (Università di Roma Tor Vergata, Italy)

Francesco Sala (Università di Pisa, Italy)

Dates: January – April, 2021

Description:

The course will be divided in three parts. The first part will describe Yangians and Quantum Loop Algebras as algebraic objects, focusing on their definitions (motivated by mathematical physics), their several presentations, and their category of finite-dimensional representations. The second part will focus on developing the necessary tools to study the geometry of Nakajima quiver varieties and the structure of their equivariant cohomology. Finally, in the last part, these two aspects will come together, showing the natural appearance of Yangians in the context of algebraic geometry, following the approach of Maulik-Okounkov which led to discovery of new kind of Yangians.