We are entering a new era of electrification, marked by the widespread adoption of lithium-ion batteries across critical sectors such as transportation, renewable energy, and grid infrastructure. Despite their advantages, lithium-ion batteries still grapple with notable performance and safety issues, casting doubt on their long-term role in future electrification efforts. This raises an urgent question: how can we improve batteries to meet the diverse demands of real-world applications? Systems theory, control strategies, and learning-based approaches have emerged as powerful tools in the search for effective solutions. We aim to make the batteries more efficient by creating more accurate models that are battery specific and adjustable. Specifically, we introduce an interpretable, physics-inspired, data-driven approach for discovering governing equations and estimating the state-of-charge (SOC) and voltage dynamics of Li-ion batteries. SOC estimation is a key challenge in battery management systems, particularly for high-demand applications like electric vehicles, where errors in low and high SOC regions can limit performance. The proposed method leverages sparse identification, using a physics-based library of electrochemical functions to uncover governing equations that accurately capture battery dynamics. This approach ensures interpretability and physical consistency, addressing common issues in purely data-driven models, such as overfitting and lack of generalizability.

This week's meeting will feature a talk by Professor Dolgushev giving an introduction to SageMath. And, of course, there will be free pizza!

Abstract: Sage (or SageMath) is free, open-source math software that supports research and teaching in algebra, geometry, number theory, cryptography and numerical computation. Although the syntax of Sage is similar to that of Python, it runs much faster than Python with its libraries (e.g. SymPy). In my talk, I will show how SageMath can be used in number theory and group theory. I will encourage participants of the Math Club to experiment with writing a simple Sage code (if some participants will come with laptops and their laptops can be connected to the internet). 

For d>= 1, it is an easy fact that a graph G must have minimum degree at least d in order to be rigid in R^d. In the talk I will present a recent work, joint with A. Lew, E. Nevo and Y. Peled, where we show that the threshold probability for a random graph G(n, p) to be d-rigid, coincides with the known threshold for having minimum degree d. This extends the classical proof for a random graph to be connected, which corresponds to the case d=1.

Vasily Dolgushev, Temple University

I will introduce the action of the groupoid of GT-shadows on child's drawings and discuss how this is related to the action of the Grothendieck-Teichmueller group and the action of the absolute Galois group (of rational numbers) on child's drawings. My talk is loosely based on this paper.  If time permits, I will mention an open question motivated by the paper by J. Ellenberg.

This week's meeting will be a talk by Andrew Clickard on braid groups and knot invariants. And, of course, there will be free pizza!

Abstract: Braid groups are the algebraic codification of the ways you can braid together several strands. By gluing the top of a braid to the bottom, you also get a knot/link, but does every link have a braid presentation? And is that presentation unique? We answer both of these questions and use the answers to define a family of knot invariants in this beginner-friendly talk.

We study a Coulomb gas on a sufficiently smooth Jordan arc in the complex plane, at arbitrary positive temperature. We show that, as the number of particles tends to infinity, the partition function converges to an expression involving the partition function of the gas on [−1,1], a power of the capacity of the curve, and the Fredholm determinant of the arc-Grunsky operator. We also obtain an asymptotic formula for the Laplace transform of linear statistics for sufficiently regular test functions. This shows that the centered empirical measure converges to a Gaussian field with explicit asymptotic mean and variance given by the Dirichlet energy of the test function. Based on joint work with Kurt Johansson and Fredrik Viklund.

Vasily A. Dolgushev, Temple University

Grothendieck's child's drawings (a.k.a. dessins d'enfant) connected topology to number theory in a fascinating way. In my first talk, I will present several equivalent definitions of a child's drawing. You will see permutation pairs, bipartite ribbon graphs and finite index subgroups of the free group on two generators. If time permits, I will start talking about Belyi pairs. The absolute Galois group of rational numbers acts on child's drawings and Belyi pairs allow us to introduce this action.   

Thomas Hill (Utah)

For a locally finite, connected graph $\Gamma$, let $\operatorname{Map}(\Gamma)$ denote the group of proper homotopy equivalences of $\Gamma$ up to proper homotopy.  Excluding sporadic cases, we show $\operatorname{Aut}(\mathcal{S}(M_\Gamma)) \cong \operatorname{Map}(\Gamma)$, where $\mathcal{S}(M_\Gamma)$ is the sphere complex of the doubled handlebody $M_\Gamma$ associated to $\Gamma$.  We also construct an exhaustion of $\mathcal{S}(M_\Gamma)$ by finite strongly rigid sets when $\Gamma$ has finite rank and finitely many rays, and an appropriate generalization otherwise. This is joint work with Michael Kopreski, Rebecca Rechkin, George Shaji, and Brian Udall.  

Join us for an insightful session with Terry Dougherty and Anne Beeman, where they will share valuable career advice for math students.

Terry will kick off the talk with a 10–15 minute session on interview preparation, focusing on structure, soft skills, and strategies to effectively answer the question: What makes you stand out from other math majors?

Anne will then discuss her career journey with a math degree, the choices she made along the way, and practical advice for succeeding in Temple’s math program.

This is a great opportunity to gain career insights and ask questions in an informal setting. And, of course, there will be free pizza! Don’t miss out!

Ian Whitehead, Swarthmore College

Abstract: I will discuss joint work in progress with Will Sawin on function field multiple Dirichlet series constructed based on a set of axioms from algebraic geometry. These series have applications to moments of Dirichlet L-functions for characters of fixed order. We prove functional equations that imply meromorphic continuation for many of these series. The most striking feature of our work is a set of detailed predictions for the symmetries involved in any given moment computation. We find a complete tabulation of moments that are possible to compute via known multiple Dirichlet series methods, including several new moments.