Mathematics Colloquium

Upcoming Colloquium

Strict Comparison in C*-algebras
Gregory Patchell, Ph.D. candidate, UC San Diego

February 21, 2025
12:00pm-1:00pm in FO3-200A and via Zoom

Join 2/21 Zoom
Meeting ID: 859 2099 6105

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Abstract

One of the most fundamental ways to compare matrices is via their rank. For two matrices X and Y, rank(X) is less than or equal to rank(Y) if and only if there are matrices S and T such that X = SYT. C*-algebras are infinite-dimensional analogs of matrix algebras. The rank can be generalized to C*-algebras using dimension functions and the latter algebraic condition can be generalized to a condition known as Cuntz subequivalence. C*-algebras for which the dimension functions recover Cuntz subequivalence are said to have strict comparison. Strict comparison is known to have applications to the classification of C*-algebras, including the influential Toms-Winter conjecture. In 1998 Dykema-Rørdam showed that infinite reduced free products have strict comparison, but even for the free group on two generators strict comparison of the reduced group C*-algebra was a long-standing open problem. In our work (joint with Tattwamasi Amrutam, David Gao, and Srivatsav Kunnawalkam Elayavalli) we show that the reduced group C*-algebra of the free group on two generators has strict comparison. Our methods are very general and lead to proving strict comparison for all acylindrically hyperbolic groups with rapid decay.

Biosketch

Gregory Patchell is a PhD Candidate at UC San Diego and he will be a Postdoctoral Research Associate at Oxford University starting this fall. He grew up in Canada and attended the University of Waterloo for his undergraduate. His research is in operator algebras, especially when there are connections with analytic and geometric properties of groups.

About the Colloquium

The Mathematics Colloquium is a unique opportunity for students to learn about new developments in mathematics and what mathematics and statisticians do after they graduate. Hosted by the Department of Mathematics and Statistics at California State University, Long Beach, the weekly meetings invite guests from universities, research laboratories, and industry to present and discuss current topics in mathematics. All students are encouraged to attend.

Schedule

The Spring 2025 will be posted as it becomes available.

Previous Colloquia

February 14, 2025

Topological Deep Learning in Computer-Aided Drug Discovery and Beyond
Dr. Yuzhou Chen, UC Riverside

Abstract

In computer-aided drug discovery (CADD), virtual screening (VS) is used for identifying the drug candidates that are most likely to bind to a molecular target in a large library of compounds. Most VS methods to date have focused on using canonical compound representations or generating alternative fingerprints of the compounds by training progressively more complex variational autoencoders (VAEs) and graph neural networks (GNNs). Although VAEs and GNNs led to significant improvements in VS performance, these methods suffer from reduced performance when scaling to large virtual compound datasets. The performance of these methods has shown only incremental improvements in the past few years. To address this problem, we developed a novel method using multiparameter persistence (MP) homology that produces topological fingerprints of the compounds as multidimensional vectors. We further establish theoretical guarantees for the stability properties of our proposed MP signatures, and demonstrate that our models, enhanced by the MP signatures, outperform state-of-the-art methods on benchmark datasets by a wide and highly statistically significant margin.

Biosketch

Dr. Yuzhou Chen is an Assistant Professor in the Department of Statistics at University of California, Riverside. He is also an Adjunct Assistant Professor in the Department of Computer and Information Sciences at Temple University and a Visiting Research Collaborator in the Department of Electrical and Computer Engineering at Princeton University. Before joining Temple, he worked as a postdoctoral scholar in the Department of Electrical and Computer Engineering at Princeton University. He received his Ph.D. in Statistics at Southern Methodist University in 2021. His research focuses on geometric machine learning, topological data analysis, knowledge discovery in graphs and spatio-temporal data, with applications to biosurveillance, energy systems, intelligent transportation, cryptocurrency, and environmental sciences. His research has appeared in the top machine learning and data mining conferences and journals, including ICML, ICLR, NeurIPS, AAAI, PNAS, etc. He won 2022 and 2021 Best Paper Awards of the Section for SDNS of ASA and the 2021 Chateaubriand Fellowship from the Embassy of France in the United States. 

January 31, 2025

Innovative Approaches to Mathematics Assessment Development for Linguistically Diverse Students
Dr. Melissa Gallagher, US Math Recovery Council

Abstract

Traditional assessments that are used to determine mathematics interventions for students have high language demands (Trakulphadetkrai et al., 2020), focus on deficits (Hunt et al., 2019; Myers, 2022; Rodríguez et al., 2022), and present learning in a linear progression, despite evidence that learning trajectories (LTs) are nonlinear (Confrey, 2018; Confrey & Maloney, 2012). The available evidence suggests that multilingual learners (MLs) are over-represented in pull out interventions and particularly impacted by the limitations of high language demand assessments. This presentation will describe an innovative measure development project aimed at overcoming the challenges of traditional assessments.

Biosketch

Melissa A. Gallagher, Ph.D., is the senior research and evaluation specialist at the US Math Recovery Council. Her research focuses on the knowledge, beliefs, and practices that teachers need to support multilingual students in the mathematics classroom. She enjoys learning about new research methods and employing them in novel ways to answer research questions.

The Mathematics Colloquium Archive has the Colloquia from previous semesters.

Colloquium Committee

For Spring 2025:

• Dr. Pavneet Kaur Bharaj
• Dr. Seungjoon Lee
• Dr. Rolando de Santiago