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Explore the categorical analogue of symmetric functions through a lecture on Soergel bimodules and the Carlsson-Mellit algebra. Delve into the dg cocenter of the category of Soergel bimodules in type A and its connection to the ring of symmetric functions. Discover how various algebras, such as affine Lie algebras and the Heisenberg algebra, act on symmetric functions, and investigate their potential categorical counterparts acting on the cocenter of SBim. Learn about a Soergel bimodule interpretation of the Carlsson-Mellit algebra's action on symmetric functions, and examine the concept of "dg cocentralizers" to obtain a categorical analogue of the full polynomial representation. Gain insights into the skein theoretic interpretation of the polynomial representation of the Carlsson-Mellit algebra, which plays a crucial role in this research. This talk presents joint work with Nicolle Sandoval Gonzalez and builds upon previous collaborations with Eugene Gorsky and Paul Wedrich.
