# News & Events

## Seminar

Date/Time:
Thursday, January 3, 2019 - 11:30
Venue:
M1
Speaker:
Affiliation:
ISI Kolkata
Title:
Free-type rigid C*-tensor categories and their annular representations

C*-tensor categories are important descriptors of generalized symmetries appearing in non-commutative analysis and mathematical physics. An important algebra associated to a rigid semisimple C*-tensor category $\mathcal{C}$ is the tube algebra $\mathcal{A}\mathcal{C}$. The tube algebra admits a universal C*-algebra, hence has a well behaved representation category. Further, this representation category provides a useful way to describe the analytic properties of initial C*-tensor categories, such as amenability, the Haagerup property, and property (T).With a brief motivation from different directions, in this talk, I will move on to describing the annular algebra $\mathcal{A}\Lambda$ associated to a rigid C*-tensor category $\mathcal{C}$. The annular representation category of $\mathcal{C}$ is the category of $*$-representations of the annular algebra $\mathcal{A}\Lambda$. I will then present a description of the annular representation category of free product of two categories with an application to the Fuss-Catalan subfactor planar algebra.We then move onto oriented extensions of subfactor planar algebras (or equivalently singly generated C*-2-categories), which are a class of singly generated C*-tensor categories (or equivalently oriented factor planar algebras). I will end the talk with few problems which could extend this work.