Functional analysis seminar @UCSD 2025-2026
Organized by Itamar Vigdorovich and Priyanga Ganesan
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
Jan 06: Junchen Zhao (TAMU)
Jan 13: Partick DeBonis
Jan 20: Amos Nevo
Jan 27: Ben Major (UCLA)
Feb 03:
Feb 10: Paolo Leonetti
Feb 17: Bill Helton
Feb 24: Matt Kennedy
Mar 03: Linfeng
Mar 10: Hui Tan, Changying Ding (two talks)
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.
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.
Speaker: Konrad Aguilar (Ponoma)
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).
Speaker: Tom Hutchcroft (Caltech)
Title: Stationary measures for co-compact group actions
Abstract: Here are two classical facts about actions of countable group Gamma on topological spaces: 1. Every action of Gamma on a compact space admits an invariant probability measure if and only if Gamma is amenable. 2. If mu is a probability measure on Gamma then every action of Gamma on a compact space always admits a stationary measure, that is, an measure that does not change on average when multiplying by a random element of Gamma drawn from mu. We are interested in how these theorems generalize to actions on non-compact spaces, where measures are required to give compact sets finite mass. For co-compact actions, the first question (about invariant measures) was answered by Kellerhals, Monod, and Rørdam (2013) and is closely related to classical results of Tarski. I will review this and then discuss our recent solution of the problem about stationary measures, joint with Alhalimi, Pan, Tamuz, and Zheng, which also involves a stationary analogue of Tarski's theorem.
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 II_1 factor M, with the strong operator topology, is contractible. Combined with several old results, this implies that the same is true for any SOT-separable von Neumann algebra with no type I_n direct summands (n < infinity). The proof for the II_1-factor case uses regularization via free convolution and Popa's theorem on the existence of approximately free Haar unitaries in II_1 factors. I will also explain some of the bigger picture of the free probability ingredients.
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. In our core example, we define an analog of the Hamming metric on the quantum permutation group $S_n^+$. The construction of our quantum metric relies on the work of Biane and Voiculescu. We also obtain an associated quantum 1-Wasserstein distance on the tracial state space of $C(S_n^+)$. This is joint work with David Jekel and Anshu.
Veterans day
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. This notion has long been studied in descriptive set theory to measure complexity of Borel equivalence relations. Recently, a lot of research has been done on hyperfiniteness of the orbit equivalence relation on the Gromov boundary induced by various group actions on hyperbolic spaces. In this talk, I will explain my attempt to explore this connection of Borel complexity and geometric group theory for another intensively studied geometric object, which is CAT(0) cube complexes. More precisely, we prove that for any countable group acting virtually specially on a CAT(0) cube complex, the orbit equivalence relation induced by its action on the Roller boundary is hyperfinite.
Thanksgiving
Speaker: Daniel Drimbe (University of Iowa)
Title: Von Neumann equivalence rigidity
Abstract: The notion of measure equivalence of discrete groups has been introduced by Gromov as a measurable variant of the topological notion of quasi-isometry. Measure equivalence of groups is tightly related to the theory of II_1 factors: if G and H are measure equivalent, then they admit free ergodic probability measure preserving action for which their von Neumann algebras are stably isomorphic. Also, two groups G and H are called W*-equivalent if their group von Neumann algebras are stably isomorphic.
A few years ago, it was discovered that there is an even coarser notion of equivalenceof groups, coined von Neumann equivalence, which is implied by both measure equivalence and W*-equivalence. In this talk I will present a unique prime factorization for products of hyperbolic groups up to von Neumann equivalence. This is joint work with Stefaan Vaes.
Speaker: Juan Felipe Ariza Mejia (University of Iowa)
Title: McDuff superrigidity for group $II_1$ 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 and exhibit a new rigidity phenomenon, termed McDuff superrigidity: any arbitrary group $H$ satisfying $LG\cong LH$ must decomposes as $H=G \times A$ for some ICC amenable group $A$. Our groups appear as infinite direct sums of $W^*$-superrigid wreath-like product groups with bounded cocycle. In this talk I will introduce this class of groups and a natural array into a weakly-$\ell^2$ representation of the group that witnesses the bound on the 2-cocycle. I will then show how this array leads to an interplay between two deformations of the group von Neumann algebra and how these can be used to prove this class of groups satisfies infinite product rigidity. This is joint work with Ionut Chifan, Denis Osin and Bin Sun.