#### Room 326

#### Soergel bimodules and Kazhdan-Lusztig theory

#### Ben Elias

##### Massachussets Institute of Technology

*Recently, Geordie Williamson and I proved Soergel's conjecture, which is the generalization to arbitrary Coxeter systems of the Kazhdan-Lusztig conjecture, thus realizing Soergel's dream. Our proof was an algebraic adaptation of de Cataldo and Migliorini's Hodge-theoretic proof of the Decomposition Theorem in geometry. Our goal in this lecture series is to provide a thorough introduction to Hecke algebras, Soergel bimodules, and the Hodge-theoretic techniques which went into the proof of the Soergel conjecture. We will also introduce the diagrammatic tools which are used to study Soergel bimodules.*

For more details, see www.imsc.res.in/~knr/elias/

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