Functional analysis seminar @UCSD 2025-2026

Unless otherwise noted, talks will happen in AP&M 6402 on Tuesdays at 11AM. Lunch after at Taco Villa.  🌮

Some of the talks will be in a hybrid form where the speaker is on zoom [this link], and we meet and watch it together 🍿

If you'd like to join our mailing list, send me an email ivigdorovich@ucsd.edu 

Winter 

January 6
Speaker: Junchen Zhao (Texas A&M University)
Title: Free products and rescalings involving non-separable abelian von Neumann algebras
Abstract: For a self-symmetric tracial von Neumann algebra $A$, we study rescalings of $A^{*n}*L\mathbb F_r$  for $n\in\mathbb N$ and $r\in (1,\infty]$ and use them to obtain an interpolation $\mathcal F_{s,r}(A)$ for all real numbers $s > $0 and $1 − s < r \leq\infty$. In this talk, I will first review the literature around this topic and explain well-definedness of the family $\mathcal F_{s,r}(A)$. I will discuss our definition of self-symmetry which includes all diffuse abelian tracial von Neumann algebras regardless of separability, and then focus on free products of infinitely many members of the family $\mathcal F_{s,r}(A_i)$. This is joint work with Ken Dykema.

January 13
Speaker: Patrick DeBonis (Purdue University)
Title: The W* and C*-algebras of Similarity Structure Groups.
Abstract: Countable Similarity Structure (CSS) groups are a class of generalized Thompson groups. I will introduce CSS$^*$ groups, a subclass, that we prove to be non-acylindrically hyperbolic, that includes the Higman-Thompson groups $V_{d,r}$, the countable R\"over-Nekrashevych groups $V_d(G)$, and the topological full groups of subshifts of finite type of Matui. I will discuss how all CSS$^*$ groups give rise to prime group von Neumann algebras, which greatly expands the class of groups satisfying a previous deformation/rigidity result. I will then discuss how CSS$^*$ groups are either C$^*$-simple with a simple commutator subgroup, or lack both properties. This extends C$^*$-simplicity results of Le Boudec and Matte Bon and recovers the simple commutator subgroup results of Bleak, Elliott, and Hyde. This is joint work with Eli Bashwinger.

January 20
Speaker: Amos Nevo (University of Chicago / Technion)
Title: Analysis on spaces with exponential volume growth.
Abstract: We consider ball averages on discrete groups, and associated Hardy-Littlewood maximal operator, with the balls defined by invariant metrics associated with a variety of length functions. Under natural assumptions on the rough radial structure of the group under consideration, we establish a maximal inequality of weak-type for the Hardy-Littlewood operator. These assumptions are related to a coarse radial median inequality, to almost exact polynomial-exponential growth of balls, and to the rough radial rapid decay property. We give a variety of examples where the rough radial structure assumptions hold, including any lattice in a connected semisimple Lie group with finite center, with respect to the Riemannian distance on symmetric space restricted to an orbit of the lattice. Other examples include right-angled Artin groups, Coxeter groups and braid groups, with a suitable choice of word metric. For non-elementary word-hyperbolic groups we establish that the Hardy-Littlewood maximal operator with respect to balls defined by a word metric satisfies the weak-type (1,1)-maximal inequality, which is the optimal result. This is joint work with Koji Fujiwara, Kyoto University.

January 27
Speaker: Ben Major (UCLA)
Title: TBA
Abstract: TBA

February 3
Speaker: TBA
Title: TBA
Abstract: TBA

February 10
Speaker: Paolo Leonetti (Università degli Studi dell’Insubria)
Title: TBA
Abstract: TBA

February 17
Speaker: Bill Helton (UCSD)
Title: TBA
Abstract: TBA

February 24
Speaker: Matt Kennedy (University of Waterloo)
Title: TBA
Abstract: TBA

March 3
Speaker: Linfeng Zang (UCSD)
Title: TBA
Abstract: TBA

March 10
Speaker: Hui Tan (UCLA)
Title: TBA
Abstract: TBA

Speaker: Changying Ding (UCLA)
Title: TBA
Abstract: TBA

Fall 

September 30
Speaker: Hans Wenzl (UCSD)
Title: Subfactors and tensor categories
Abstract: We give an introductory talk about the interplay between the study of subfactors and tensor categories. We will sketch some recent results, time permitting.

October 7
Speaker: Nina Kiefer (Universität des Saarlandes). Hybrid
Title: Complete Classification of Quantum Graphs on M2
Abstract: Over the past few years, the theory of quantum graphs has emerged as a field of growing interest. In 2022, Matsuda and Gromada have given concrete examples by classifying the undirected quantum graphs on the quantum space M2. Based on the solid theory of directed quantum graphs developed in 2024, it became possible to complete the classification of quantum graphs on M2 also in the directed case. We observe that there is a far bigger range of directed quantum graphs than of undirected quantum graphs on M2. This talk is based on a joint work with Björn Schäfer.

October 14
Speaker: Konrad Aguilar (Pomona)
Title: Christensen–Ivan spectral triples on AF algebras and Latrémolière's Gromov–Hausdorff propinquity
Abstract: We provide convergence in the quantum Gromov–Hausdorff propinquity of Latrémolière of some sequences of infinite-dimensional Leibniz compact quantum metric spaces of Rieffel given by AF algebras and Christensen–Ivan spectral triples. The main examples are convergence of Effros–Shen algebras and UHF algebras. We will also present some of the results that laid the groundwork for this result. (This includes joint work with Clay Adams, Esteban Ayala, Evelyne Knight, and Chloe Marple, and this work is partially supported by NSF grant DMS-2316892.)

October 21
Speaker: Tom Hutchcroft (Caltech)
Title: Stationary measures for co-compact group actions
Abstract: Here are two classical facts about actions of countable group Γ on topological spaces: 1. Every action of Γ on a compact space admits an invariant probability measure if and only if Γ is amenable. 2. If μ is a probability measure on Γ then every action of Γ on a compact space always admits a stationary measure. We are interested in how these theorems generalize to actions on non-compact spaces, where measures are required to give compact sets finite mass.

October 28
Speaker: David Jekel (University of Copenhagen). Hybrid
Title: The unitary group of a II₁ factor is SOT-contractible
Abstract: I show that the unitary group of any SOT-separable II₁ factor M, with the strong operator topology, is contractible.

November 4
Speaker: Therese Basa Landry (UCSB)
Title: Quantum Wasserstein Distance on the Quantum Permutation Group
Abstract: We investigate quantum compact groups which support quantum metric space structure.

November 11

Veterans Day

November 18
Speaker: Koichi Oyakawa (McGill)
Title: Hyperfiniteness of the boundary action of virtually special groups
Abstract: A Borel equivalence relation on a Polish space is called hyperfinite if it can be approximated by equivalence relations with finite classes.

November 25

Thanksgiving

December 2
Speaker: Daniel Drimbe (University of Iowa)
Title: Von Neumann equivalence rigidity
Abstract: The notion of measure equivalence of discrete groups was introduced by Gromov as a measurable variant of quasi-isometry.

Thursday, December 11, 3pm (APM 6402)
Speaker: Juan Felipe Ariza Mejia (University of Iowa)
Title: McDuff superrigidity for group II₁ factors
Abstract: Developing new techniques at the interface of geometric group theory and von Neumann algebras, we identify the first examples of ICC groups G whose von Neumann algebras are McDuff.