Speaker:   Ivan Cherednik (University of North Carolina at Chapel Hill)

Where:      In-Person at MIT Room 2-135 and on

Zoom         https://mit.zoom.us/j/94469771032?pwd=d3JaSVhVV0xDOGpkUDdveXdOYmNXQT09

Title:          “From DAHA superpolynomials for algebraic links to motivic ones"

Abstract:  

The focus will be on a recent construction of the motivic superpolynomials far arbitrary singularities (multi-branch  and non-square-free). They will be introduced from scratch, which includes the definition of varieties of torsion-free sheaves of any rank over curve singularities.  Our motivic superpolynomials are q,t,a-generalizations of orbital integrals associated with affine Springer fibers of type A, in the case of the most general characteristic polynomials. I will not use the theory of AFS. The key conjecture is their coincidence with the DAHA superpolynomials of the corresponding (colored) algebraic links. The latter (due to Cherednik-Danilenko) will be defined. This coincidence can be seen as a high-level Shuffle Conjecture. As an application, the DAHA vertex will be considered and its relation to the q-theory of Riemann’s zeta.  Also, q,t,a-deformations of the modified rho-invariants of algebraic knots will be discussed;  classically, rho is defined via the APS eta invariant. See https://arxiv.org/abs/2304.02200 .