# Past Workshops

## Seminar in Representation Theory

### September 8-9, 2021

#### Organized by Jan Frahm and Bent Ørsted (Aarhus U.)

The purpose of this seminar is to present recent developments in the representation theory of real reductive groups and related areas. The time slots were chosen so that researchers from both Asia and Europe can attend. We hope that this meeting also helps to bring together Asian and European colleagues within the AIM Research Community Representation Theory & Noncommutative Geometry.

Abstracts

### Schedule

Titles are linked to the video recordings of the talks.

September 8
 T. Kobayashi Tempered representations and limit algebras Slides C.-B. Zhu Theta correspondence and special unipotent representations Slides W. T. Gan Twisted GGP problems and conjectures Slides

September 9

## Branching Problems and Symmetry Breaking

### June 10-11, 2021

#### Organized by Michaël Pevzner (U. of Reims)

In Representation Theory, branching problems ask how a given irreducible representation $\pi$ of a group $G$ behaves when restricted to subgroups $G'\subset G$. The decomposition of the tensor product of two irreducible representations (fusion rule) is a special case of this problem, where $(G,G')$ is of the form $(G_1 \times G_1, \Delta(G_1))$. In the general setting where $(G,G')$ is a pair of reductive groups and $\pi$ is an infinite dimensional representation of $G$, branching problems include various important situations such as theta correspondence and the Gross–Prasad–Gan conjecture, and branching laws may involve "wild behaviors" such as infinite multiplicities and continuous spectrum.
This workshop is devoted to recent progress in this area, with a particular emphasis on new analytical methods.

Abstracts

### Schedule

Titles are linked to the video recordings of the talks.

June 10
 T. Kubo Differential symmetry breaking operators for $(O(n+1,1),O(n,1))$ on differential forms Slides R. Nakahama Computation of weighted Bergman inner products on bounded symmetric domains for $SU(r,r)$ and restriction to subgroups Slides Q. Labriet Symmetry breaking operators and orthogonal polynomials Slides E. Shelburne Toward a holographic transform for the quantum Clebsch-Gordan formula Slides

June 11