Introduction to Soergel Bimodules

Part I: The classical theory of Soergel bimodules 1 How to think about Coxeter groups.- 2 Reflection groups and Coxeter groups.- 3 The Hecke algebra and Kazhdan-Lusztig polynomials.- 4 Soergel bimodules.- 5 The "classical" theory of Soergel bimodules.- 6 Sheaves on moment graphs. Part II: Diagrammatic Hecke category 7 How to draw monoidal categories.- 8 Frobenius extensions and the one-color calculus.- 9 The Dihedral Cathedral.- 10 Generators and relations for Bott-Samelson bimodules and the double leaves basis.- 11 The Soergel categorification theorem.- 12 How to draw Soergel bimodules. Part III: Historical context: category and the Kazhdan-Lusztig conjectures 13 Category and the Kazhdan-Lusztig conjectures.- 14 Lightning introduction to category.- 15 Soergel's V functor and the Kazhdan-Lusztig conjecture.- 16 Lightning introduction to perverse sheaves. Part IV: The Hodge theory of Soergel bimodules 17 Hodge theory and Lefschetz linear algebra.- 18 The Hodge theory of Soergel bimodules.- 19 Rouquier complexes and homological algebra.- 20 Proof of the hard Lefschetz theorem. Part V: Special topics 21 Connections to link invariants.- 22 Cells and representations of the Hecke algebra in type A.- 23 Categorical diagonalization.- 24 Singular Soergel bimodules and their diagrammatics.- 25 Koszul duality I.- 26 Koszul duality II.- 27 The p-canonical basis.