Abstracts for Representation theory learning seminar

Alternatively have a look at the program.

The Hilbert scheme of points of affine 3-space

Posted in

Vortrag

Speaker:

Andrea Ricolfi

Zugehörigkeit:

University of Stavanger/MPIM

Datum:

Fre, 02/03/2018 - 14:15 - 16:30

Location:

MPIM Lecture Hall

Parent event:

Representation theory learning seminar

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

Posted in

Vortrag

Speaker:

Tomasz Przezdziecki

Zugehörigkeit:

MPIM

Datum:

Fre, 16/03/2018 - 14:15 - 16:00

Location:

MPIM Seminar Room

Parent event:

Representation theory learning seminar

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

Posted in

Vortrag

Speaker:

Thorsten Heidersdorf

Datum:

Fre, 13/04/2018 - 14:15 - 16:00

Location:

MPIM Lecture Hall

Parent event:

Representation theory learning seminar

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).

Weiterlesen

Tensor ideals in Deligne's interpolating categories

Posted in

Vortrag

Speaker:

Thorsten Heidersdorf

Zugehörigkeit:

The Ohio State University/MPIM

Datum:

Fre, 20/04/2018 - 14:15 - 16:00

Location:

MPIM Lecture Hall

Parent event:

Representation theory learning seminar

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.