Alexei Oblomkov: Coinvariants and Affine Springer fibers (ASF), Part II

Speaker: Alexei Oblomkov, UMass

This talk, a continuation of last week's talk, is based on joint work with Carlsson. We give a geometric construction of a monomial space of the space of double coinvariants DH_n. The space is the quotient of the ring C[x₁,..,x_n,y₁,..y_n] by the ideal generated by the S_n-symmetric polynomials without a constant term. Our basis gives an elementary proof of the shuffle conjecture. The key idea is to study a flag version of the compactified Jacobian for xⁿ=yⁿ⁺¹, also known as ASF. We show that this ASF is a bouquet of Hessenberg varieties.