# Abstracts for Representation theory learning seminar

Alternatively have a look at the program.

## The Hilbert scheme of points of affine 3-space

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Speaker:
Andrea Ricolfi
Affiliation:
University of Stavanger/MPIM
Date:
Fri, 2018-03-02 14:15 - 16:30
Location:
MPIM Lecture Hall

We describe the scheme structure of the Hilbert scheme of points of affine 3-space,
in terms of representations of the Jacobi algebra of a quiver with potential. This exhibits the Hilbert scheme of points as the critical locus of a regular function on a smooth variety.
We discuss the torus action on the Hilbert scheme and its Euler characteristic.

## Rational Cherednik algebras, Hilbert schemes and combinatorics

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Speaker:
Tomasz Przezdziecki
Affiliation:
MPIM
Date:
Fri, 2018-03-16 14:15 - 16:00
Location:
MPIM Seminar Room

We will discuss the connection between cyclotomic rational Cherednik algebras at t=0 and the Hilbert scheme of points in the plane. In particular, we will explain how the spectrum of the centre of the rational Cherednik algebra is diffeomorphic to a certain component of the Hilbert scheme. Analyzing torus actions we will derive some combinatorial applications such as Bezrukavnikov and Finkelberg's proof of Haiman's conjecture about wreath MacDonald polynomials and a generalization of the q-hook formula.

## Deligne's interpolating categories

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Speaker:
Thorsten Heidersdorf
Date:
Fri, 2018-04-13 14:15 - 16:00
Location:
MPIM Lecture Hall

This is an overview talk about Deligne categories. These categories interpolate (representation) categories to complex parameters (or parameters in any field). Initially Deligne considered the cases $\underline{Rep}(O_t)$, $\underline{Rep}(GL_t)$, $\underline{Rep}(S_t)$ for $t \in \mathbb{C}$ which interpolate representations of the orthogonal groups, the general linear and the symmetric groups (we refer to those as classical Deligne categories).

## Tensor ideals in Deligne's interpolating categories

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Speaker:
Thorsten Heidersdorf
Affiliation:
The Ohio State University/MPIM
Date:
Fri, 2018-04-20 14:15 - 16:00
Location:
MPIM Lecture Hall

I will talk about the classification of tensor ideals in the Deligne categories attached to the symmetric, orthogonal and general linear group and give some applications.

## The blocks and abelian envelope of Deligne's Rep S_t

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Speaker:
Hankyung Ko
Affiliation:
MPIM
Date:
Fri, 2018-04-27 14:15 - 16:00
Location:
MPIM Seminar Room

## Quantum versions of Deligne categories

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Speaker:
Hans Wenzl
Affiliation:
University of California at San Diego/MPIM
Date:
Fri, 2018-05-04 14:15 - 16:00
Location:
MPIM Lecture Hall

## Stability in representation theory and Deligne categories - CANCELLED -

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Speaker:
Hankyung Ko
Affiliation:
MPIM
Date:
Fri, 2018-05-18 14:15 - 16:00
Location:
MPIM Seminar Room

## Deligne categories for rational Cherednik category O

Posted in
Speaker:
Tomasz Przezdziecki
Affiliation:
IMPRS MPIM
Date:
Fri, 2018-05-25 13:30 - 15:15
Location:
MPIM Seminar Room

Posted in
Speaker:
Apolonia Gottwald
Affiliation:
MPIM
Date:
Fri, 2018-06-01 14:15 - 16:00
Location:
MPIM Lecture Hall

## The periplectic Deligne category

Posted in
Speaker:
Emily Norton
Affiliation:
Universität Bonn
Date:
Fri, 2018-06-15 14:15 - 16:00
Location:
MPIM Seminar Room
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