Geometry & Geometric Analysis Seminar
Main Content
The Geometry and Geometric Analysis (GAGA) Seminar is an opportunity for geometers, topologists, and others from TCU and other campuses to learn about new topics of mutual interest. GAGA meets most weeks during the school year. You can find notes from past talks at the GAGA Note Repository, located in a secure off-campus location.
The Fall 2026 GaGA seminar is Fridays at 1 pm in TUC 352 on TCU campus, and also the seminar will be available on Zoom. Contact Ken Richardson with any questions or issues with the link.
No talk on Friday, October 23
Next talk: Monday, October 26, 4 pm
Speaker: Pradyut Karmakar (Sam Houston State University)
Next talk: Monday, October 26, 4 pm
Speaker: Pradyut Karmakar (Sam Houston State University)
Title: Rapid Decay Property of Fell bundles over étale groupoids
Abstract:
We extend the theory of RDP to Fell bundles over locally compact Hausdorff groupoids. As an application, we show that RDP for a group, together with a free action on a space X, does not imply RDP for the associated crossed product: our main example is the crossed product with a free group (with respect to a partial action). We further investigate the Fourier series problem in the setting of Fell bundles.
The Rapid Decay Property (RDP) is closely tied to approximation properties and the
convergence of Fourier series: in general, one cannot recover an element from its
Fourier coefficients, but RDP is the key tool for doing this. Moreover, RDP is used
to construct smooth subalgebras inside C*-algebras, reducing the study of K-theory
into smooth subalgebras. RDP has also recently attracted attention in the study of
strict comparison and selflessness for C*-algebras. While RDP is well understood for
groups and groupoids separately, it has not previously been studied for Fell bundles.
Fell bundles provide a unifying framework for many important C*-algebras, including
group C*-algebras, groupoid C*-algebras, and crossed product C*-algebras: objects
that arise naturally in both group theory and dynamical systems.We extend the theory of RDP to Fell bundles over locally compact Hausdorff groupoids. As an application, we show that RDP for a group, together with a free action on a space X, does not imply RDP for the associated crossed product: our main example is the crossed product with a free group (with respect to a partial action). We further investigate the Fourier series problem in the setting of Fell bundles.