Mathematics Colloquia and Seminars
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Categorical diagonalization of the full twistAlgebra & Discrete Mathematics
I will discuss recent joint work with Ben Elias in which we introduce a theory of diagonalization of functors. Our main application is the diagonalization of the the Rouquier complex associated to full-twist braid, acting on the category of Soergel bimodules. The ``eigenprojections'' yield categorified Young symmetrizers, which can be used to give a construction of an arbitrarily colored triply-graded link homology theory, and are also important in the categorical representation theory of Hecke algebras. I will mention a beautiful recent conjecture of Gorsky-Rasmussen relating the categorified Young symmetrizers to the flag Hilbert scheme. There is also a relationship with the stable homology of torus links, which was recently investigated by myself and Michael Abel.