Representation Theory & Noncommutative Geometry
An AIM Research Community
This research community, sponsored by AIM and the NSF, brings together researchers to develop connections between representation theory, operator algebras and noncommutative geometry.
Current Organizers:
Monica Nevins (U. of Ottawa), Angela Pasquale (U. de Lorraine), and Haluk Şengün (U. of Sheffield)
Previous Organizers:
Pierre Clare (William & Mary), Nigel Higson (PennState) and Birgit Speh (Cornell U.)
Contact: aimrtncg@gmail.com
Ongoing and Upcoming Activities
In the Winter of 2024, we'll continue our popular This is what I do series, and have a couple of tiny series of wee lectures on selected topics. We'll also introduce a new series: This is my thesis, where two or three students will let us spotlight on their exciting new work.
A look ahead:
May 1: Labour Day, no talk.
May 8: This is What I Do, by Peter Uttenthal (Cornell University):
Title: Whitney extension theorems on symmetric spaces
Abstract: In 1934, H. Whitney introduced the problem of extending a function on a set of points to an analytic function on the ambient space. If the points are invariant under a group of symmetries, it is natural to study the Whitney extension problem on a symmetric space. In joint work with Birgit Speh, we prove a Whitney extension theorem on anti de Sitter space, whose group of symmetries is the noncompact Lie group SO(2,2). A key ingredient in the proof is that Flensted-Jensen functions have an explicit description resembling spherical harmonics for the compact group SO(3). In particular, we construct a Whitney function which is analytic, square integrable, and K-finite. As a corollary, we associate a unique representation to the points which we call its Whitney representation.
May 15: This is What I Do, by Salah Mehdi.
Related Events and News
BIRS Workshop on Branching Problems for real, p-adic and adelic groups, Kelowna, Canada July 7-12, 2024.
Thematic Programme at Institut Henri Poincaré:
Representation Theory & Noncommutative Geometry, January - April, 2025The COST grant CaLISTA, which provides amongst other things, mobility grants for people in Cartan geometry, quantum groups, noncommutative geometry, and related fields to travel between two different European countries for conferences or research collaborations.
Past Activities
Fall 23: Mini-mini-mini series: AQFT and causal symmetric spaces
Fall 23: Mini-mini-mini series: Classification of representations of reductive p-adic groups
January 23: In-person conference Noncommutative Geometry and Analysis on Homogeneous Spaces, William & Mary
Fall 22: Mini-mini-mini series: Elements of the history of representation theory (1950 - 1980)
Fall 22: Mini-mini-mini series: RTNCG before 1950
Spring 22: Mini-mini-mini series: Proper actions and representation theory
Winter 22: Mini-mini-mini series: Index theory
September 21: Workshop Seminar in Representation theory
August 21: Language school Representation theory for C*-theorists
June 21: Language school C*-algebras for representation theorists
June 21: Workshop Branching problems and symmetry-breaking
Spring 21 - present: This is what I do series