LGRT 1621
The Khovanov-Rozansky homology categorifies the classical Jones and HOMFLY-PT polynomials. In this talk, we will explore how the Khovanov-Rozansky homology of the (m,n)-torus knot can be derived from the finite-dimensional representation of the rational Cherednik algebra at slope m/n, equipped with the Hodge filtration. This result confirms a conjecture by Gorsky, Oblomkov, Rasmussen, and Shende. Our approach involves the geometry of Hilbert schemes of points and character D-modules. Numerous examples will be provided to introduce and clarify the main concepts.