# Events for June 12, 2017 from General and Seminar calendars

## Linear Analysis Seminar

**Time:** 3:00PM - 4:00PM

**Location:** BLOC 220

**Speaker:** Kunal Mukherjee , Indian Institute of Technology, Madras

**Title:** *Factoriality of q-deformed Araki-Woods von Neumann algebras*

**Abstract:**To any strongly continuous orthogonal representation of the real numbers on a real Hilbert space $H$, Hiai constructed $q$-deformed Araki-Woods von Neumann algebras for $-1< q< 1$, which are $W^{\ast}$-algebras arising from non tracial representations of the $q$-commutation relations, the latter yielding an interpolation between the Bosonic and Fermionic statistics. We show that these von Neumann algebras are factors whenever $dim(H)\geq 3$ and for all $q\in (-1,1)$. In some cases we also determine the type of the von Neumann algebras and show that they satisfy the bicentralizer conjecture of Connes.