UTK Student-led Graduate Seminar

M597 is a student-led seminar for graduate students supported by the Department of Mathematics at the University of Tennessee. Each week, one graduate student presents a talk, often expository and informal. Attendees are encouraged to ask questions and engage in discussion, with the level of interaction guided by the speaker.

In Spring 2026 we are meeting on Mondays 4:10PM - 5PM EDT at AYR 121.

If you’re interested to give a talk, fill out the sign-up form. If you want to be included on the mailing list please include your name in the following link.

Feb 9, 2026 - Ernesto Ugona Santana  

Title:  An introduction to topological data analysis

Feb 23, 2026 : Dominic Bair 

Title:  Graphons and random graphs 

Abstract: Graphons (or graph functions) are a class of measurable symmetric functions on the unit square which have many applications to sequences of graphs, random graph models, and network theory. In this talk, we will discuss what a graphon is, explore their relationship to graphs, sequences of graphs, and random graphs, and discuss problems people investigate using graphons.

Apr 06, 2026- Aaratrick Basu (UVA)

Title: A Glimpse at Mapping Class Groups of Surfaces

Abstract: Mapping class groups of surfaces are one of the most well-studied classes of groups that are immensely important in branches as diverse as geometric group theory, low dimensional topology, representation theory, algebraic geometry and operator algebras! In my talk, I will attempt to sketch some of the main highlights of their theory, and showcase a few beautiful ideas that go into proving these results. Time permitting, I will talk about a group-theoretic conjecture about the Torelli subgroup, and sketch the proof of a closely related result about braid groups due to Leininger and Margalit.

Apr 09, 2026- Joint with PDE seminar: Nicholas Dominic Gismondi (Purdue) 

Apr 13, 2026- Kesavan Mohana Sundaram (Nebraska)

Title: The arithmetic rank of residual intersections of a complete intersection ideal

Abstract: The arithmetic rank of a variety is the minimal number of equations needed to define it set-theoretically, i.e., the smallest number of polynomials generating the defining ideal up to radical. Computing this invariant is notoriously difficult: the minimal generators up to radical often bear little relation to the given ideal generators and can vary unpredictably across characteristics. The residual intersections provide a natural extension of the classical notion of algebraic links. In a different direction, this residual intersection also arises as the defining ideal of a variety of complexes, a notion introduced by Buchsbaum and Eisenbud. We establish a general upper bound for the arithmetic rank of any residual intersection of a complete intersection ideal in an arbitrary Noetherian ring, and we show that this bound is sharp under specific characteristic assumptions.  The methods used includes topological and combinatorial techniques: a computation of singular cohomology provides a lower bound for the critical arithmetic rank, while the theory of Algebras with a Straightening Law yields the corresponding upper bound. This work is joint with Manav Batavia, Taylor Murray, and Vaibhav Pandey. 

Apr 27, 2026- Alexi Reed (ASU)

Title: Advancing a novel performance-based test of cognition and daily functioning for preclinical Alzheimer’s disease screening using secondary data: Bridging the computational and clinical gap

Abstract: Clinical trials for Alzheimer’s disease (AD) prevention face major challenges due to high screen-failure rates and substantial variability in disease progression, limiting their efficiency and statistical power. While blood-based biomarkers can identify underlying pathology, they do not reliably predict near-term cognitive decline. In this talk, I will present a complementary, low-cost approach to trial enrichment using the Brief Evaluation of Cognition and Daily Function (BEan), a rapid, performance-based assessment of real-world cognitive functioning. Leveraging existing longitudinal cohort data, I will demonstrate how secondary data analysis can be used to evaluate and refine the BEan as a prognostic tool, showing its associations with cognitive and functional decline in asymptomatic older adults. I will also discuss how integrating behavioral measures with biomarker and imaging data can improve participant selection. More broadly, this work highlights how secondary data and computational methods can be used to bridge the gap between scalable measurement and clinical trial design in preclinical AD.

May 4, 2026- Roxana Barrios Rosales