Mini-courses of Mini-lectures

These short courses of short lectures will lie somewhere between the This is what I do talks and the language schools. They will aim to be informal and understandable introductions to subjects of likely interest to many members of the RTNCG community. There will be few prerequisites, and questions and digressions will be welcomed. Meetings will generally be held during Sococo tea times.

Mini-course of Mini-lectures: RTNCG before 1950

by Alexandre Afgoustidis (CNRS - Institut Élie Cartan de Lorraine)
September-October 2022

When operator algebras and the representation theory of locally compact groups both took off around 1950, they were very much two faces of the same subject — they have common origins in the rise of spectral theory in the wake of Hilbert, the mathematical analysis of quantum physics in the wake of Von Neumann, and other topics. I will discuss some of the main episodes of their common early history, beginning with the Peter-Weyl theorem around 1926, and stopping before the appearance of the Plancherel formula of Segal and Mautner. No special historical knowledge will be required.

Next talk: October 10 at 11:00 EDT

For additional information and further reading, see this companion page.

9/12Compact Lie groups in the 1920s RecordingSlides
9/19Abelian locally compact groups in the 1930s RecordingSlides
10/03Beginnings of operator algebras RecordingSlides
10/10General theory of locally compact groups and other topics

Mini-course of Mini-lectures on Proper Actions and Representation Theory

by Toshiyuki Kobayashi (U. of Tokyo)
April-May 2022

I plan to introduce some topics on proper actions with emphasis on their relation to representation theory. No special background knowledge will be required. The lectures will be short without details, but with elementary examples so that they fit into teatime. The lectures are loosely related but are mostly independent of one another. The first two topics are of more geometric nature, and the last two are of more analytic nature.

Discontinuous dual and properness criterion RecordingSlides
The Mackey analogy and proper actions RecordingSlides
Tempered subgroups à la Margulis RecordingSlides
Tempered homogeneous spaces RecordingSlides

Mini-course of Mini-lectures on Index Theory

by Nigel Higson (Penn State)
February-March 2022

My goal will be to introduce some topics in index theory and K-theory that might be of interest in representation theory. No background knowledge will be required from index theory or K-theory.
Some overall principles: The lectures will be short. They will be independent of one another, mostly. They will be aimed at representation theorists. They will avoid details. Finally, I will lie wherever necessary in order to tell the truth.

Fixed points formulas and index theory RecordingSlides
The Oka principle and the Langlands classification RecordingSlides
An index theorist reads the Green Book RecordingSlides
Bismut’s hypoelliptic Laplacian RecordingSlides