The Purdue Operator Algebra Seminar will be held on Tuesdays (not every week) from 13:30–14:20 in LILY G458. If you are interested in giving a talk, please send an email to either Thomas Sinclair or me.
The Purdue Operator Algebra Seminar will be held on Tuesdays (not every week) from 13:30–14:20 in LILY G458. If you are interested in giving a talk, please send an email to either Thomas Sinclair or me.
Sep 01, 2026: Andrew S. Toms, Purdue
Title: A simple amenable C*-algebra without uniform property Gamma.
Abstract: Uniform property Gamma is a regularity property for C*-algebras which entails a positive solution to the Toms-Winter conjecture. Until recently, it was an open question as to whether every simple separable amenable infinite dimensional C*-algebra enjoys this property. We resolve this question negatively, using tools from classical algebraic geometry and intersection theory.
Feb 10, 2026: M. Ali Asadi-Vasfi, Purdue
Title: How Do Group Actions Affect the Radius of Comparison?
Abstract: In this talk, I will discuss the structure of crossed products arising from group actions with different properties. I will then explain how the radius of comparison behaves for fixed-point algebras and crossed products coming from these actions. In particular, I will explain when we should expect the radius of comparison of a crossed product can be larger than that of the original C*-algebra, and when it can be smaller. This work is based on different joint works with several coauthors.
Feb 24, 2026: Thomas Sinclair, Purdue
Title: Kirchberg's Embedding Problem
Abstract: The problem is whether every separable C*-algebra embeds into an ultrapower of the Cuntz algebra O_2. This is an analog of Connes' Embedding Problem, which was famously refuted by the complexity theory result MIP*=RE. So far, Kirchberg's problem has resisted attacks trying to leverage similar strategies. I'll give a history of the problem and possible approaches towards its resolution.
Mar 03, 2026: Ajay Kumar Karri, Texas A&M University
Title: Results on General Toeplitz Random Matrices
Abstract: We prove the convergence of $*$-moments of Toeplitz matrices in two cases: (1) matrix entries are independent Gaussian random variables and (2) matrix entries are free semicircular entries. We also study joint $*$- moments of Toeplitz matrices in both cases with $ L^\infty[0,1]$ functions.
Apr 07, 2026: Zhiyuan Yang, Texas A&M University
Title: On von Neumann algebras generated by noncommutative free Poisson random measure
Abstract: The Marchenko-Pastur distribution is widely recognized as the free probability counterpart to the classical Poisson distribution. In this talk, we discuss the corresponding free analogue for Poisson random measures, alongside a noncommutative generalization constructed via a natural Fock space representation. The von Neumann algebras generated by these noncommutative random measures provide examples of type II_1 and type III_λ (λ nonzero) factors. Using the Fock space construction, we study a family of completely positive maps between those free Poisson algebras called the second quantizations.
We also examine the Lévy-Khintchine decomposition of an additive free Lévy process and its Fock space representation. We provide an operator-algebraic proof of this decomposition via left Hilbert algebras in Tomita-Takesaki theory. As an application, we prove that the filtration algebras of a free Lévy process are always interpolated free group factors (possibly with an additional atom).
Apr 21, 2026: Martin Peev, University of Oxford
Title: Renormalising Noncommutative SPDEs
Abstract: When attempting to construct QFTs that include Fermions using the methods of Stochastic Quantisation, one is naturally forced to consider noncommutative stochastic PDEs. I shall show how to formulate SPDEs driven by noncommutative noises in terms of algebra-valued singular PDEs. Furthermore, I will describe how one can renormalise singular products appearing in such equations, using the example of free probability and q-Gaussian noises. Finally, I will show how one can derive operator insertion estimates, which are crucial in solving singular SPDEs, such as the \Phi^4_2-equation, by changing the topology on the algebra of q-Gaussian. This talk is based on joint work with Ajay Chandra and Martin Hairer.
The Purdue Operator Algebra Seminar will be held on Tuesdays (not every week) from 1:30–2:20 PM in SCHM 103. If you are interested in giving a talk, please send an email to either me, Thomas Sinclair , or Patrick DeBonis.
Sep 09, 2025: M. Ali Asadi-Vasfi, Purdue University
Title: The Rank Ratio Function and the Radius of Comparison Function
Abstract: In this talk, for any given Cuntz semigroup, we introduce an associated function, called the Rank Ratio Function. This function plays a very important role in computing the relative radii of comparison of Cuntz semigroups. Time allowing, we will discuss both the C*-algebraic and algebraic aspects of the relative radius of comparison, and introduce another function called the Radius of Comparison Function.
This function provides a method for constructing non-classifiable C*-algebras with distinct relative radii of comparison.
Sep 23, 2025: Laurent Cantier, University of Zaragoza(Online)
Title: C*-algebras over the circle: some classification and limitation
Abstract: We first review the traditional Elliott classification program for AT-algebras, i.e. C*-algebras that are obtained as inductive limits of building blocks over C(T). After recalling earliest satisfactory results in both the simple and real rank zero case, we turn to more recent developments involving the Cuntz semigroup and its refined versions.
In particular, we discuss the classification of *-homomorphisms from C(T) into various codomains, and highlight current limitation to complete the classification of these C*-algebras.
Oct 07, 2025: Aldo Garcia Guinto, Michigan State University
Title: Projective representations of almost unimodular groups
Abstract: Given a locally compact group $G$ with a 2-cocycle $\omega: G\times G\to \mathbb{T}$, Colin Sutherland showed that any left Haar measure uniquely determines a faithful normal semifinite weight on the associated twisted group von Neumann algebra. This weight, which we call the twisted Plancherel weight, is tracial if and only if $G$ is unimodular, and for countable discrete groups it is the usual tracial state. In the setting of non-unimodular groups, the modular automorphism group of the necessarily non-tracial twisted Plancherel weight is explicitly determined by the so-called modular function of $G$. The twisted group von Neumann algebra is generated by the left regular $\omega$-projective representation of $G$. In 1958, George Mackey showed that $\omega$-projective representations of $G$ are connected to the representations of the central extension of $G$ by $\mathbb{T}$, when $G$ is second countable. In this talk, we will introduce the class of "almost unimodular groups" for which the twisted Plancherel weight is almost periodic, in the sense of Connes from 1972. We will also give some examples of such groups admitting a 2-cocycle such that the group von Neumann algebras are purely infinite and not factors, but the twisted group von Neumann algebras are semifinite factors.
Nov 04, 2025: Felipe Flores, University of Virginia
Title: Discrete measured groupoid von Neumann algebras via the Gaussian deformation.
Abstract: During this talk, we will discuss recent results on von Neumann algebras associated with discrete groupoids. Indeed, the work discussed involves defining the Gaussian deformation for discrete p.m.p. groupoids and using the techniques of Popa's deformation/rigidity theory to obtain results related to primeness, fullness and unique prime factorizations for these algebras. This talk is based on joint work with James Harbour.
Dec 02, 2025: Alonso Delfín Ares de Parga, University of Colorado, Boulder
Title: Twisted Crossed Products of Banach Algebras
Abstract:
Abstract: The main goal of this talk is to introduce twisted crossed products of Banach algebras by locally compact groups. Classical crossed products of Banach algebras have been extensively studied for different classes of representations, including contractive representations on L^p-spaces. In this talk, we will give a general formulation for Banach algebras associated with twisted dynamical systems. Recent developments in L^p-twisted crossed products have mostly focused on situations where either the algebra is the complex numbers or when the group is discrete (more generally for étale groupoids). We present a universal characterization of the twisted crossed product when the acting group is locally compact and the Banach algebra has a contractive approximate identity. As an application, we focus on the case when the representations are contractive ones acting on L^p spaces. We briefly discuss a reduced version for L^p-operator algebras. Time permitting, we will present a generalization of the so called Packer–Raeburn trick to the L^p-setting, by showing that the universal L^p twisted crossed product is ``stably'' isometrically isomorphic to an untwisted one.
This is joint work with Carla Farsi and Judith Packer.
Dec 09, 2025: Christopher Phillips, University of Oregon
Title: An isomorphism theorem for infinite reduced free products
Abstract: Let C be a separable unital C*-algebra, not isomorphic to the complex numbers, equipped with a faithful tracial state. Let A be a unital direct limit of one dimensional NCCW complexes, also equipped with a faithful tracial state. Suppose there is a unital trace preserving embedding of A in the Jiang-Su algebra which is an isomorphism on K-theory. (For example, A could be C ([0, 1]) with Lebesgue measure, or the Jiang-Su algebra itself.) Let D be the infinite reduced free product of copies ofC. Then the reduced free product of A with D is isomorphic to D.
If D has real rank zero, then in place of A we can use C (X) for any contractible compact metric space X and any faithful tracial state on C (X).
An example consequence is that the reduced free product of infinitely many copies of C ([0, 1]) with Lebesgue measure is isomorphic to the reduced free product of infinitely many copies of the Jiang-Su algebra.
This is joint work with Ilan Hirshberg.