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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

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

p-adic dimentions

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

The periplectic Deligne category

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