# Math Calendar

### Upcoming Events

## Topology & Group Theory Seminar

## Small cancellation methods in probabilistic group laws – Location- SC 1432

Gil Goffer – UCSD

In various cases, a law (that is, a quantifiers free formula) that holds in a group with high probability, must actually hold for all elements. For instance, a finite group in which the commutator law [x,y]=1 holds with probability larger than 5/8, must be abelian.

In the talk I will give an overview of probabilistic laws (namely, laws that hold with high probability) on finitely generated groups, and illustrate how small cancellation methods and partial Burnside groups can reveal unexpected phenomena. For instance, I will present a partial Burnside group in which the law x^p=1 holds with probability 1, but yet the group does not satisfy this law, or any other law, globally, and a partial burnside group in which the probability that the law x^p=1 is satisfied oscillates between 0 and 1. This work, joint with Be’eri Greenfeld, is answering questions of Amir, Blachar, Gerasimova, and Kozma.

## Computational Analysis Seminar

## Two algorithms for one-bit phase retrieval- SC 1320

Dylan Domel-White – Vanderbilt University

Phase retrieval is the problem of reconstructing a vector in a Hilbert space (or rather, its equivalence class) from magnitudes of linear measurements. Rank-one measurements such as magnitudes of frame coefficients are most commonly used, but higher rank measurements have also been studied. Recently, there has been interest in algorithms that perform accurate phase retrieval when the magnitude measurements are coarsely quantized, such as for one-bit measurements. We discuss two algorithms for one-bit phase retrieval in finite-dimensional Hilbert spaces using higher rank maps, along with error bounds for each. The first, Principal Eigenspace Programming (PEP) uses all one-bit measurements at once in a non-adaptive way to approximate the measured vector. The second, Iteratively Consistent Quantized Phase Retrieval (ICQPhase) uses the one-bit measurements in a streaming way to approximate the vector.

## Shanks workshop- Dynamical Sampling, Frame Theory, Harmonic Analysis and Applications

## Subfactor Seminar

## Von Neumann Algebras from Thompson-like Groups-Location-SC 1432

Eli Bashwinger, University of Albany

In this talk, I will discuss some results concerning the von Neumann algebras of Thompson-like groups arising from $d$-ary cloning systems (for $d \ge 2$). This talk will essentially be a survey of some of the many results coming from three papers I have written so far on this topic, the first two of which I wrote with Matthew Zaremsky, who invented cloning systems with Stefan Witzel in 2018. Given a $d$-ary cloning system on a sequence of groups $(G_n)_{n \in \mathbb{N}}$, we can form a Thompson-like group denoted by $\mathscr{T}_d(G_*)$, and this group canonically contains $F_d$, the smallest of the Higman-Thompson groups. The group inclusion $F_d \le \mathscr{T}_d(G_*)$ translates to an inclusion of their group von Neumann algebras $L(F_d) \subseteq L(\mathscr{T}_d(G_*))$. We have several results concerning this inclusion as well as some results concerning the von Neumann algebra $L(\mathscr{T}_d(G_*))$ itself, some of which will have group-theoretic consequences for these Thompson-like groups and how $F_d$ sits inside them.

## Shanks Workshop- Dynamical Sampling, Frame Theory, Harmonic Analysis and Applications

This marquee event marks the culmination of a one-month visit to the Department of Mathematics at Vanderbilt University by global scholars Ursula Molter and Carlos Cabrelli from the University of Buenos Aires, Argentina. Designed to foster collaboration among researchers from various U.S. universities, Vanderbilt researchers across different departments, and the visiting scholars, the primary focus…

This marquee event marks the culmination of a one-month visit to the Department of Mathematics at Vanderbilt University by global scholars Ursula Molter and Carlos Cabrelli from the University of Buenos Aires, Argentina. Designed to foster collaboration among researchers from various U.S. universities, Vanderbilt researchers across different departments, and the visiting scholars, the primary focus of the event is addressing unsolved challenges in dynamical sampling, particularly its implications for climate science. By amalgamating diverse perspectives, the workshop aims to stimulate insightful exchanges of ideas, enabling both researchers and graduate students to leverage each other’s expertise. Furthermore, the event anticipates forging enduring collaborations between the participating institutions and catalyzing joint research endeavors in the future.

**Date:** March 1-3, 2024

**Location:** Vanderbilt University

Website: https://math.vanderbilt.edu/aldroua/workshop.html