This workshop will be primarily based on two papers of myself and Geordie Williamson: Soergel calculus and The Hodge theory of Soergel bimodules. We also have a survey article which roughly covers the content of the Hodge theory of Soergel bimodules.

Soergel calculus has a number of papers which led to it:

Diagrammatics for Soergel categories with Mikhail Khovanov

The two-color Soergel calculus, also known as the

On cubes of Frobenius extensions with Geordie Williamson.

Our proof of the Soergel conjecture was greatly inspired by the excellent work of de Cataldo and Migliorini:

The Hard Lefschetz Theorem and the topology of semismall maps

The Hodge theory of algebraic maps.

Similar workshops have been given twice before:

Aarhus - Videos Lecture notes and Exercises

Chennai - Videos Lecture notes and Exercises.

Required background for the course: General graduate background on algebra. It may help to learn or refresh one's memory of a few concepts:

The idempotent completion. Given a full additive subcategory A of an abelian category C, its idempotent completion is the full additive subcategory of C whose objects are summands of objects in A (i.e. images of idempotents in A). However, there is a formal way to mimic this construction for any additive category A, even without assume it is embedded in an abelian category, known as the Karoubi envelope.

Grothendieck groups of abelian, additive, and triangulated categories. In particular, the Grothendieck group of a Krull-Schmidt additive category has a basis given by indecomposable objects.

The 2-category Bim. See Examples 2.2 in Lauda's paper. This is a formalism for discussing bimodules for various rings, and their tensor products.

Coxeter groups. Coxeter groups are groups with a certain kind of presentation, essentially stating that they are generated by "reflections." We will learn about them in class, but it may help to have some prior awareness of the topic. The exercises will assume the classification of finite Coxeter groups.