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 

Spring

April 7
Speaker: Mikael de la Salle (University of Lyon), zoom.
Title: Kakeya conjecture and High Rank Lattice von Neumann algebras.
Abstract: My talk will be about two open questions and a (perhaps surprising) link between them:

(1) Connes' rigidity conjecture, that in particular predicts that the von Neumann algebras of PSL_n(Z) are not isomorphic for different values of n. Ancient works with Vincent Lafforgue and Tim de Laat suggest a possible approach to it: does the non-commutative Lp space of the von Neumann of SL(n,Z) have the completely bounded approximation property for some non-trivial p?

(2) Kakeya conjecture : every subset of R^d containing a unit segment in every direction has dimension d.Both questions are open for large values of the parameters (n>2 and >3). I will explain why (1) is difficult: it implies some form of (2) for d<=(n+1)/2.

April 14
Speaker: Otte Heinävaara (Caltech)
Title: Convolution comparison measures
Abstract: Free convolution is a fundamental operation in free probability. It expresses the distribution of the sum of two freely independent random variables in terms of the distributions of the summands. Compared to classical convolution of probability measures, free convolution is considerably more difficult to analyze and calculate. To untangle this complicated operation, we introduce a precise functional comparison between free and classical convolutions. This comparison states that the expectation of f w.r.t. classical convolution is larger than the expectation w.r.t. free convolution as long as f has non-negative fourth derivative. The comparison is based on the existence of convolution comparison measures, novel measures on the plane whose positivity depends on a peculiar identity involving Hermitian matrices.

April 21
Speaker: David Gao (UCSD)
Title: A new source of purely finite matricial fields
Abstract: A group G is said to be a matricial field (MF) if it admits a "strongly converging" sequence of approximate homomorphisms into matrices, i.e., norms of polynomials converge to the corresponding value in the left regular representation. G is then said to be purely MF (PMF) if this sequence of maps into matrices can be chosen as actual homomorphisms. G is further said to be a purely finite field (PFF) if the image of each homomorphism is finite. These questions have phenomenal applications to the study of C* and von Neumann algebras, spectral geometry, random walks and random graphs, spectral gaps of hyperbolic manifolds, minimal surface theory and Yau’s conjectures, and applied mathematics including but not limited to signal processing. By developing a new operator algebraic approach to the MF problems, we are able to prove the following result bringing several new examples into the fold. Suppose G is a MF (resp., PMF, PFF) group and H is separable (i.e., H is an intersection of finite index subgroups of G) and K is a residually finite MF (resp., PMF, PFF) group. If either G or K is exact, then the amalgamated free product G *_H (H \times K) is MF (resp., PMF, PFF). Our work has several applications. Firstly, as a consequence of MF, the Brown-Douglas-Fillmore semigroups of many new reduced group C*-algebras are not groups. Secondly, we obtain that arbitrary graph products of residually finite exact MF (resp., PMF, PFF) groups are MF (resp., PMF, PFF), yielding a significant generalization of the breakthrough work of Magee-Thomas. Thirdly, our work resolves the open problem of proving PFF for 3-manifold groups, more generally all RAAGs. Prior to our paper, PFF results remained unknown even in the simple subcase of free products. These results are of further significance since PFF is the property that is used in Antoine Song’s approach towards the existence of minimal surfaces in spheres of negative curvature.

April 28
Speaker: Changying Ding (UCLA)
Title: Structure and non-isomorphisms of q-Araki-Woods factors, Part II
Abstract: This is a continuation of Hui Tan's talk on joint work studying the structure and classification of q-Araki-Woods factors. I will focus on the proofs of the main results: the dichotomy for subalgebras in continuous cores underlying strong solidity, and the failure of biexactness for q-Araki-Woods factors with infinite-dimensional representations via norm estimates from Nou and Hiai.

April 29 (Wedensday 11am, special meeting)
Speaker: Dietmar Bisch (Vanderbilt U)
Title: New Quantum Symmetries from Subfactors
Abstract: Vaughan Jones introduced an index for inclusions of certain von Neumann algebra in the 1980's and proved that it is surpisingly rigid. This rigidity is due to a rich combinatorial structure that is inherent to the representation theory of a subfactor with finite index. Subfactor representations reveal interesting unitary tensor categories, or quantum symmetries, whose algebras of intertwiners always contain the Temperley-Lieb algebras and, if an intermediate subfactor is present, the Fuss-Catalan algebras of Jones and myself. The case of two intermediate subfactors is much more involved and not much progress had been made since the late 1990's. 

I will discuss recent work with Junhwi Lim in which we determine the quantum symmetries of a subfactor when two intermediate subfactors occur, and the four algebras form a cocommuting square. These new symmetries turn out to be related to partition algebras and Bell numbers.

May 5
Speaker: Alonso Delfín (University of Colorado Boulder)
Title: Twisted Crossed Products of Banach Algebras
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 and present conjectures regarding amenability and rigidity when p\neq 2. 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.

May 12
Speaker: Rufus Willet (University of Hawaii at Mānoa)
Title: The LLP, property FD, and representation stability.
Abstract:  Representation stability asks whether an approximate representation of a group can be approximated by an actual representation.  There are many technical variations of this basic question: I will focus mainly on approximate representations into finite-dimensional unitary groups. 

I’ll introduce the two properties in the title - the LLP of Kirchberg and property FD of Lubotzky-Shalom - via group C*-algebras and explain how they imply some fairly weak representation stability results.  I’ll then explain some refinements you can get using K-theory (without assuming any background knowledge of K-theory).  Finally, I'll discuss the known range of validity of the LLP and property FD (I’ll also mention some related properties like Kechris’ property MD).

The non K-theoretic parts are based on joint work with Francesco Fournier-Facio.

May 19
Speaker: Asuman Aksoy (Claremont McKenna College)
Title: From Classical Approximation to Banach Space Geometry: The Evolution of Bernstein’s Lethargy Theorem
Abstract: While Weierstrass’ Approximation Theorem guarantees that continuous functions can be uniformly approximated by polynomials, it provides no information about the rate of this convergence. Bernstein’s Lethargy Theorem (BLT) classically addresses this gap by proving that the error of best polynomial approximation can decay at an arbitrarily slow, prescribed rate. This talk explores the evolution of BLT from its roots in classical approximation theory to its broad applications in functional analysis. We will discuss extensions of BLT to abstract Banach spaces and Frechet spaces. Building on this framework, we will investigate the deep connections between lethargy phenomena and operator ideals, the influence of Banach space reflexivity on the existence of lethargic convergence, and the interplay between BLT and interpolation theory via the Peetre K-functional.

May 26
Speaker: Todd Kemp
Title: TBA
Abstract: TBA

Jun 2
Speaker: Cyril Houdayer (ENS)
Title: TBA
Abstract: TBA

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: New Proofs of Indecomposability Results for Tracial von Neumann Algebras
Abstract: We show that, for many choices of finite tuples of generators $\mathbf{X}=(x_1,\dots,x_d)$ of a tracial von Neumann algebra $(M,\tau)$ satisfying certain decomposition properties (non-primeness, possessing a Cartan subalgebra, or property $\Gamma$), one can find a diffuse, hyperfinite subalgebra in $W^*(\mathbf{X})^\omega$ (often in $W^*(\mathbf{X})$ itself), such that $W^*(N,\mathbf{X}+\sqrt{t}\mathbf{S})=W^*(N,\mathbf{X},\mathbf{S})$ for all $t>0$. (Here $\mathbf{S}$ is a free semicircular family, free from $\{\mathbf{X}\cup N\}$). This gives a short 'non-microstates' proof of strong 1-boundedness for such algebras.

February 3
No seminar.

February 10
Speaker: Paolo Leonetti (Università degli Studi dell’Insubria)
Title: Orbits which are "more than" dense
Abstract: See here

February 17
Speaker: Bill Helton (UCSD)
Title: Parallelizing a Class of Quantum Algorithms
Abstract: Many classical computer algorithms can be paralyzed efficiently; what about quantum computers? An algorithm can be described as having layers, one composed with another, with the depth n of the circuit being the number of layers. An algorithm might be presented as having n simple layers, but if we are able to build more complicated layers, can we construct an equivalent algorithm with a few layers?  This is an issue, which goes back to the early days when people became enthusiastic about the possibility of quantum computers. One of the most straightforward test cases is called the quantum waterfall or quantum staircase. It is a tensor product analog of a matrix of 2 x 2 blocks supported on the diagonal and the first diagonal below it.  It was conjectured in the late 90s that an n layer quantum waterfall cannot be produced with an algorithm having fewer than order n layers. This conjecture (Moore-Nillson 1998) turns out to be way too pessimistic and the talk describes recent work with Adam Bene  Watts, Joe Slote, Charlie Chen on a theorem constructing a parallelization of any n layer quantum waterfall which yields  (asymptotically) log n layers.  Gratifying to  operator theorists is that a substantial ingredient is a matrix decomposition originating with Chandler Davis.

February 24
Speaker: Matt Kennedy (University of Waterloo)
Title: Hyperrigidity and noncommutative Choquet theory
Abstract: Hyperrigidity is an interesting and important approximation-theoretic property of generating sets of C*-algebras. It plays a key role in, for example, the theory of strong convergence. In this talk, I will discuss a new characterization of hyperrigid generating sets in terms of the solvability of a certain noncommutative Dirichlet problem. I will also demonstrate how this result can be applied in practice.
Classical Choquet theory plays a key role in the study of classical Dirichlet problems, so it is perhaps not surprising that our results utilize noncommutative Choquet theory. I will provide a brief overview of some of these ideas.

March 3
Speaker: Linfeng Zang (UCSD)
Title: Von Neumann Morgenstern Theorem for Choquet Simplex
Abstract: In 1944, von Neumann and Morgenstern raised a question in their famous book Theory of Games and Economic Behavior: For a rational agent with preferences over all probabilistic mixtures of finitely many deterministic outcomes, is there always a unique utility function on deterministic outcomes whose expected value on probabilistic mixtures represents the preferences? Under natural assumptions on the preference order, they answered the question positively. We attempt to generalize this result to the case when the outcomes are infinite. We first identify the outcomes with the extreme points of a Choquet simplex, a natural generalization of the classical simplex to infinite-dimensional spaces. We then prove a similar result in the setting of Choquet simplex.

March 10
Speaker: Hui Tan (UCLA)
Title: Structure and non-isomorphisms of q-Araki-Woods factors
Abstract: Hiai’s construction of q-Araki-Woods factors generalizes both Shlyakhtenko’s free Araki-Woods factors and Bozejko-Speicher’s q-Gaussian algebras. I will discuss joint work with Changying Ding where we show the q -Araki-Woods factors are strongly solid if the associated representation U is almost periodic, and the non-isomorphism between q-Araki-Woods factors and free Araki-Woods factors for certain classes of representations, contrasting the case for q-Gaussians.

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.