# Geometric and Modular Representation Theory Seminar

## The affine Hecke category is a monoidal colimit

We will discuss the following theorems concerning colimits taken in the infinity-category of monoidal DG-categories. (No familiarity with infinity-categories will be required or assumed.) The affine Hecke category is the monoidal colimit of its finite type Hecke subcategories. The category of D-modules on the loop group is the monoidal colimit of the categories of D-modules on standard parahoric subgroups. These theorems, and many analogous ones, are consequences of a general inductive characterization of colimits indexed by a category of `words' in a Coxeter group. We will also discuss two applications-in-progress: the construction of a functor from the affine to the finite Hecke category in type A, and the construction of new `deformations' of the affine Hecke category.

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Simonyi Hall 101 and Remote Access### Speakers

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Seminar website: /math/sp/geometric_modular_reptheory/seminar