The application of the factorization method in the study of the Gaiotto conjecture

The Gaiotto conjecture says that the category of representations of the quantum supergroup is equivalent to the category of certain sheaves on the affine Grassmannian. It is the quantum version of a particular case of the relative Langlands conjecture by Ben-Zvi-Sakellaridis-Venkatesh.

In the first half of this talk, we will review the background and explain the statement of the Gaiotto conjecture. In the second half, we will sketch the proof with a focus on the factorization method. If time permits, we will also explain the application of the method in related questions. The talk is based on work and ongoing work joint with Michael Finkelberg and Roman Travkin.