Alternatively have a look at the program.

## Decomposition numbers for rational Cherednik algebras

In a highest weight category, ''decomposition numbers'' refers to multiplicities of simple objects in standard objects. I will describe results that are known about decomposition numbers for Category O of a rational Cherednik algebra, and mention some questions that remain open.

## Hirzebruch-Riemann-Roch as a categorical trace I

Let X be a smooth proper scheme over a field of characteristic 0, and let E be a

vector bundle on X. The classical Hirzebruch-Riemann-Roch says that the Euler characteristic of the cohomology H^*(X,E) equals \int_X ch(E) Td(X).

Thus, HRR is an equality of numbers, i.e., elements of a set. In these talks,

we will explain a proof of HRR that uses the hierarchy

{2-categories} -> {1-categories} -> {Vector spaces} -> {Numbers}.

I.e., the origin of HRR will be 2-categorical. The procedure by which we

## Hirzebruch-Riemann-Roch as a categorical trace III

Let X be a smooth proper scheme over a field of characteristic 0, and let E be a vector bundle on X. The classical Hirzebruch-Riemann-Roch says that the Euler characteristic of the cohomology H^*(X,E) equals \int_X ch(E) Td(X).

Thus, HRR is an equality of numbers, i.e., elements of a set. In these talks,

we will explain a proof of HRR that uses the hierarchy

{2-categories} -> {1-categories} -> {Vector spaces} -> {Numbers}.

I.e., the origin of HRR will be 2-categorical. The procedure by which we