Operator Algebras Seminar Ical Atom

This is a research seminar on operator algebras and noncommutative analysis.

The seminar meets on Wednesdays, 13:00-14:00, in 201

This Week

Mansi Suryawanshi (Technion)

Representations of the Odometer Semigroup: Dilation and Subrepresentations

Given a natural number $n \geq 1$, the odometer semigroup $O_n$, also known as the adding machine or the Baumslag–Solitar monoid with two generators, is a well-known object in group theory. This talk will examine the odometer semigroup in relation to representations of bounded linear operators. We will focus on noncommutative operators and show that contractive representations of $O_n$ always admit nicer representations. A complete description of representations of $O_n$ on the Fock space will be presented, along with connections to odometer lifting and subrepresentations. Along the way, we will also classify Nica–covariant representations of $O_n$.

2025–26–A meetings

Upcoming Meetings

Date
Title
Speaker
Abstract
Nov 19 Representations of the Odometer Semigroup: Dilation and Subrepresentations Mansi Suryawanshi (Technion)

Given a natural number $n \geq 1$, the odometer semigroup $O_n$, also known as the adding machine or the Baumslag–Solitar monoid with two generators, is a well-known object in group theory. This talk will examine the odometer semigroup in relation to representations of bounded linear operators. We will focus on noncommutative operators and show that contractive representations of $O_n$ always admit nicer representations. A complete description of representations of $O_n$ on the Fock space will be presented, along with connections to odometer lifting and subrepresentations. Along the way, we will also classify Nica–covariant representations of $O_n$.
Nov 26 TBA Marcel Sherer (Technion)

TBA

Past Meetings

Date
Title
Speaker
Abstract
Nov 5 Localizations in noncommutative analysis Eli Shamovich (BGU)

In this talk, I will describe some ring theoretic properties of certain rings of noncommutative functions. In particular, I will show that these topological rings are good analogs of the classical rings of analytic functions on discs in the plane. Our rings turn out to be semi-free ideal rings. Namely, every finitely generated right (equivalently, left) ideal is free as a module. In turn, this implies that they admit an embedding into a division ring with a certain universal property (a universal localization). I will explain how this result is a blend of techniques from ring theory and operator algebras and show an application to free probability.

This talk is based on joint work with Meric Augat and Rob Martin.
Nov 12 Isomorphisms between infinite free product C*-algebras Ilan Hirshberg (BGU)

A $C^\ast$-probability space is a pair $(A,\tau)$ consisting of a $C^\ast$-algebra and a tracial state $\tau$ on $A$. For any two $C^\ast$-probability spaces, there’s a definition of a reduced free product $C^\ast$-algebra $(A,\tau) \ast_r (B,\sigma)$. This is a generalization of the case of reduced group $C^\ast$-algebras: if $G$ and $H$ are discrete groups, then the reduced free product of $C^\ast_r(G)$ and $C^\ast_r(H)$ is the reduced group $C^\ast$-algebra of the free product $G \ast H$. We show that if $A$ decomposes as a nontrivial reduced free power of infinitely many copies of separable $C^\ast$-probability spaces, then $C([0,1]) \ast_r A$ is isomorphic to $A$. Several other related isomorphism theorems are obtained as well. I will review some background and outline the proof. This is joint work with N. Christopher Phillips.

Seminar run by Dr. Eli Shamovich, Prof. Victor Vinnikov, Prof. Ilan Hirshberg and Dr. Daniel Markiewicz