# Abstracts for Oberseminar Representation Theory

Alternatively have a look at the program.

## Decomposition numbers for rational Cherednik algebras

Posted in
Speaker:
Emily Norton
Organiser(s):
Prof. C. Stroppel
Affiliation:
MPIM
Date:
Tue, 2016-12-20 14:15 - 15:15
Location:
MPIM Seminar Room

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

Posted in
Speaker:
Dennis Gaitsgory
Affiliation:
Harvard University
Date:
Tue, 2017-01-10 16:30 - 18:30
Location:
MPIM Lecture Hall

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

Posted in
Speaker:
Dennis Gaitsgory
Affiliation:
Harvard University
Date:
Fri, 2017-01-13 12:30 - 14:30
Location:
MPIM Lecture Hall

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

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