The ANTC of ChatGPT: On the Mathematical Foundations of Large Language Models (Gizem Karaali, Pomona)
2025-04-08 12:15 - 13:10 (America/Los_Angeles) | Estella 2113
Large Language Models like ChatGPT rely on surprisingly familiar mathematics. This talk will explore how ideas from (linear) algebra, number theory and combinatorics appear — both directly and indirectly — in the structure and behavior of these models. Along the way, we’ll touch on themes like structure, symmetry, and scale, and consider how abstract mathematical ideas can shed light on systems that process and generate human language. The talk will be self-contained, and no background in machine learning will be assumed. (This abstract was prepared with the assistance of ChatGPT, which seems to be remarkably self-aware of its own mathematical foundations.)

CCMS Colloquium presents "Fall 2025 Course Preview Session"
2025-04-09 16:15 - 17:30
Fall 2025 Course Preview Session
Moderator: Lenny Fukshansky, Professor of Mathematics, Claremont McKenna College, CA
Slide Link: https://docs.google.com/presentation/d/142NF1vUazpGNLF0pfLKc0qhkv4VoMQstSvZ0yKtMfNE/edit?usp=sharing

Applied Math Seminar: Victoria Chebotaeva (USC)
2025-04-14 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Title: Erlang-Distributed SEIR Epidemical Models
Abstract:
We examine the effects of different dynamics in epidemiological models, focusing on two key approaches. The first model incorporates reaction-diffusion dynamics, where susceptible individuals avoid areas with high concentrations of infected individuals. The second model divides exposed and infectious individuals into symptomatic and asymptomatic subclasses.
Our findings emphasize the importance of adaptive control measures, such as targeted testing, contact tracing, and isolation, in effectively containing disease spread while minimizing societal and economic impacts. The models highlight the distinct roles of symptomatic and asymptomatic individuals, demonstrating how tailored public health strategies can improve resource management and mitigate the socio-economic effects of outbreaks.

Jacobians of tropical curves and finite graphs (Carrie Frizzell, Scripps)
2025-04-15 12:15 - 13:10 | Estella 2113
A Jacobian variety is a principally polarized abelian variety (PPAV) associated with a smooth complex algebraic curve. For dimensions less than or equal to 3, every PPAV is either a Jacobian or a product of Jacobians. The Schottky problem concerns dimensions 4 and greater: which PPAVs are Jacobians? The Schottky problem can also be posed in the tropical setting, in which the Jacobian of a tropical curve is a real torus. We will spend most of the talk discussing tropical Jacobians and their discrete counterparts, but we will also survey a few results related to the aforementioned Schottky problem.

Claremont Topology Seminar: Sierra Knavel (Georgia Tech)
2025-04-15 15:00 - 16:00 | Estella 2099, Pomona College, 610 N. College Ave., Claremont, CA, United States
We especially welcome all undergraduates and graduate students to attend topology seminar!
Speaker: Sierra Knavel (Georgia Tech)
Title: Betti Numbers and Indecomposability of Genus-2 Lefschetz Fibrations
Abstract: Symplectic 4-manifolds, smooth 4-manifolds equipped with a closed, nondegenerate 2-form, arise naturally in classical mechanics and have become central objects of study in topology. Following foundational work by Donaldson and Gompf, Lefschetz pencils have been shown to correspond bijectively with symplectic 4-manifolds, making symplectic 4-manifolds a tractable family of smooth 4-manifolds to work with. This talk focuses on genus-2 Lefschetz fibrations obtained by blowing up Lefschetz pencils and presents new bounds on their first Betti number. We will also examine a particularly elusive class of non-simply connected, indecomposable genus-2 fibrations and consider the prospects of extending these results to higher genera.

CCMS Colloquium: (Naneh Apkarian, Arizona State University, Arizona)
2025-04-16 16:15 - 17:30 | Argue Auditorium, Pomona College, 610 N. College Ave., Claremont, CA, 91711, United States
Speaker: Naneh Apkarian Professor of Mathematics, Arizona State University, Arizona
Title: Student Success in an Interactive STEM Ecosystem
Abstract: This talk begins with a discussion of the multifaceted nature of “student success” in STEM, including externally recognized markers (e.g., grades) and internally defined indicators (e.g., enjoyment). Investigations of the factors which contribute to student success along various dimensions, how to improve student success, and how to implement successful interventions at scale reveal the complexities of the STEM higher education ecosystem as well as the critical role of introductory mathematics courses. I will review results along these themes, highlighting interactions which define that ecosystem and support/constrain different aspects of student success, for different populations. This includes the role of intra- and extra-curricular factors such as student-student interactions, course coordination, departmental culture, and instructors’ beliefs. Implications for research and practice will also be discussed.
Bio: Dr. Naneh Apkarian is an Assistant Professor in the School of Mathematical and Statistical Sciences at Arizona State University. She is from California, where she obtained a BA and MA in mathematics prior to completing her PhD in mathematics education. Pursuing departmental change as a strategy for transforming mathematics education, she was for two years a postdoctoral researcher at Western Michigan University. Her research spans many facets of the STEM education ecosystem, including the knowledge, beliefs, practices, and experiences of students and instructors, departmental culture, and interactions within and across levels – always in the service of building inclusive excellence. Outside academia, Dr. Apkarian continues to play competitive water polo across the US and the world.

Applied Math Seminar: Fabio Milner (Arizona State University)
2025-04-21 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Title: Modeling viral STI epidemics
Abstract: We will describe an SIR model of viral sexually transmitted infections in a population structured by sex and sexual preference and its validation in the simple SI case from HIV data incidence. We will also use the model to establish a plausible structure of the U.S. population by sexual preferences for men and women and perform a case scenario analysis of the impact that changes in sexual preferences may have in the incidence of STIs.

Algebraic properties of linguistic structure (Isabella Senturia, Yale / Caltech)
2025-04-22 12:15 - 13:10 | Estella 2113
The recognition that theoretical models of natural language syntax have robust algebraic foundations is longstanding. Both the syntactic structures proposed (trees, semirings, etc.) and metrics developed to understand them (the Chomsky hierarchy, partial orders, and so forth) closely resemble structures and systems familiar to theoretical mathematicians (groups, rings, fields, …). Despite the underlying mathematical tools, rarely do structural properties of language get analyzed at an algebraic level. I use two complementary perspectives, one representational and continuous (spectral graph theory) and one derivational and discrete (Hopf algebras), as lenses to explore mathematical properties of linguistic structure. I will also show a connection between the two approaches through a case study on the problem of learning syntactic parameters.

Claremont Topology Seminar: Sam Nelson (Claremont McKenna College)
2025-04-22 15:00 - 16:00 | Estella 2099, Pomona College, 610 N. College Ave., Claremont, CA, United States
We especially welcome all undergraduates and graduate students to attend topology seminar!
Speaker: Sam Nelson (Claremont McKenna College)
Title: Virtual Biquandle Cocycle Quiver Representations
Abstract: We construct a quiver representation valued invariant of virtual knots and links using virtual biquandle homology.

CCMS Colloquium: Agent-Based and Continuous Models of Locust Hopper Bands (Andrew J. Bernoff, Harvey Mudd College, CA)
2025-04-23 16:15 - 17:30 | Argue Auditorium, Pomona College, 610 N. College Ave., Claremont, CA, 91711, United States
Speaker: Andrew J. Bernoff, Professor of Mathematics, Harvey Mudd College
Abstract: An outstanding challenge in mathematical biology is using laboratory and/or field observations to tune a model’s functional form and parameter values. These problems lie at the intersection of dynamical systems and data science. In this talk I will discuss an ongoing project developing models of the Australian plague locust for which excellent field data is available. Under favorable environmental conditions flightless juveniles aggregate into coherent, aligned swarms referred to as hopper bands. We develop two models of hopper bands in tandem; an agent-based model that tracks the position of individuals and a continuum model describing locust density. By examining 4.4 million parameter combinations, we identify a set of parameters that reproduce field observations.
I will then discuss ongoing efforts to improve these models. The first extends this work by modeling locust alignment via the Kuramoto model of oscillator synchronization. The second uses motion tracking of tens of thousands of locusts to shed light on how locust movement is influenced by social interactions.

Bio: Andrew Bernoff is a Professor of Mathematics whose research focuses on applying dynamical systems to physical and biological phenomena, with notable international recognition for his work on swarming. He earned degrees in math and physics from MIT and a PhD from the University of Cambridge as a Marshall Scholar. With over 50 published papers and multiple NSF and Simons Foundation grants, his interdisciplinary collaborations span physics, engineering, chemistry, and biology.
A dedicated educator, Bernoff has mentored over 60 undergraduate research projects at Harvey Mudd College, with many students pursuing PhDs at top institutions. He has served in leadership roles including Director of the Claremont Center for Mathematical Sciences, Chair of the SIAM Dynamical Systems Group, and a co-author of the Putnam Exam (2019–2021).

Data Science / Statistics Seminar: Ana Maria Kenney (UC Irvine)
2025-04-25 13:15 - 14:15 | Roberts North 15, CMC, 320 E. 9th St., Claremont, 91711, United States
Speaker: Ana Maria Kenney, Assistant Professor, Department of Statistics, UC Irvine
Title: Distilling heterogeneous treatment effects: Stable subgroup estimation in causal inference
Abstract: Recent methodological developments have introduced new black-box approaches to better estimate heterogeneous treatment effects; however, these methods fall short of providing interpretable characterizations of the underlying individuals who may be most at risk or benefit most from receiving the treatment, thereby limiting their practical utility. In this work, we introduce a novel method, causal distillation trees (CDT), to estimate interpretable subgroups. CDT allows researchers to fit any machine learning model of their choice to estimate the individual-level treatment effect, and then leverages a simple, second-stage tree-based model to “distill” the estimated treatment effect into meaningful subgroups. As a result, CDT inherits the improvements in predictive performance from black-box machine learning models while preserving the interpretability of a simple decision tree. We derive theoretical guarantees for the consistency of the estimated subgroups using CDT, and introduce stability-driven diagnostics for researchers to evaluate the quality of the estimated subgroups. We illustrate our proposed method on a randomized controlled trial of antiretroviral treatment for HIV from the AIDS Clinical Trials Group Study 175 and show that CDT out-performs state-of-the-art approaches in constructing stable, clinically relevant subgroups.
Bio: Ana Maria Kenney is an Assistant Professor in the Department of Statistics at UC Irvine. She works at the interface of statistics, interpretable machine learning, and large-scale optimization to advance biomedical research. She has been on several interdisciplinary teams across institutions spanning cardiovascular genetics, “Omics” contributions to early infant growth, and early cancer screening. She completed a postdoc at UC Berkeley and previously received a dual title Ph.D. at Penn State in Statistics and Operations Research. There she was a Biomedical Big Data to Knowledge Training Fellow and Alfred P. Sloan Ph.D. Scholar.

Applied Math Seminar: Alejandra Castillo (Pomona College)
2025-04-28 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Title: Randomized Kaczmarz Methods for Corrupted Tensor Linear Systems
Abstract: Recovering tensor-valued signals from corrupted measurements is a central problem in various applications such as hyperspectral image reconstruction and medical imaging. This talk considers tensor linear systems of the form AX = B, that contain observations potentially affected by sparse, large-magnitude corruptions. A quantile-based randomized Kaczmarz algorithm, called quantile tensor randomized Kaczmarz (QTRK), is discussed to address this challenge. By integrating quantile statistics into the iterative update process, QTRK improves robustness against adversarial errors. A variant selectively omits unreliable measurements to enhance stability further.

Claremont Topology Seminar: David Bachman (Pitzer College)
2025-04-29 15:00 - 16:00 | Estella 2099, Pomona College, 610 N. College Ave., Claremont, CA, United States
We especially welcome all undergraduates and graduate students to attend topology seminar!
Speaker: David Bachman (Pitzer College)
Title: Learning optimal knot projections
Abstract: We use techniques from Reinforcement Learning to find knot projections which minimize crossing number.

CCMS Colloquium presents the Second Barbara Beechler Talk: Deanna Needell (UCLA)
2025-04-30 16:15 - 17:30 | Argue Auditorium, Pomona College, 610 N. College Ave., Claremont, CA, 91711, United States
CCMS Colloquium invites you to the Second Barbara Beechler Lecture by Professor Deanna Needell, Professor of Mathematics, Dunn Family Endowed Chair in Data Theory
Executive Director, Institute for Digital Research and Education (IDRE) at UCLA.
Title: Fairness and Foundations in Machine Learning
Abstract: In this talk, we will address areas of recent work centered around the themes of fairness and foundations in machine learning as well as highlight the challenges in this area. We will discuss recent results involving linear algebraic tools for learning, such as methods in non-negative matrix factorization that include tailored approaches for fairness. We will showcase our approach as well as practical applications of those methods. Then, we will discuss new foundational results that theoretically justify phenomena like benign overfitting in neural networks. Throughout the talk, we will include example applications from collaborations with community partners, using machine learning to help organizations with fairness and justice goals. This talk includes work joint with Erin George, Kedar Karhadkar, Lara Kassab, and Guido Montufar.
Speaker Bio: Deanna Needell earned her PhD from UC Davis before working as a postdoctoral fellow at Stanford University. She is currently a full professor of mathematics at UCLA, the Dunn Family Endowed Chair in Data Theory, and the Executive Director for UCLA’s Institute for Digital Research and Education. She has earned many awards including the Alfred P. Sloan fellowship, an NSF CAREER and other awards, the IMA prize in Applied Mathematics, is a 2022 American Mathematical Society (AMS) Fellow and a 2024 Society for industrial and applied mathematics (SIAM) Fellow. She has been a research professor fellow at several top research institutes including the SLMath (formerly MSRI) and Simons Institute in Berkeley. She also serves as associate editor for several journals including Linear Algebra and its Applications and the SIAM Journal on Imaging Sciences, as well as on the organizing committee for SIAM sessions and the Association for Women in Mathematics.

Applied Math Seminar: Evan Rosenman (Claremont McKenna College)
2025-05-05 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Title: TBA
Abstract: TBA

CCMS Colloquium presents "Career Panel"
2025-05-07 16:15 - 17:30 | Argue Auditorium, Pomona College, 610 N. College Ave., Claremont, CA, 91711, United States
TBA

Categorification of biquandle arrow weight invariants via quivers (Migiwa Sakurai, Shibaura Institute of Technology)
2025-09-02 12:15 - 13:10 | Estella 2099
Biquandle arrow weights invariants are enhancements of the biquandle counting invariant for oriented virtual and classical knots defined from biquandle-colored Gauss diagrams using a tensor over an abelian group satisfying certain properties. In this talk, we categorify the biquandle arrow weight polynomial invariant using biquandle coloring quivers, obtaining new infinite families of polynomial invariants of oriented virtual and classical knots.

The Shooting Method in the Analysis of Two-Point Boundary-Value Problems (Adolfo J. Rumbos, Pomona College)
2025-09-08 16:15 - 17:15
Abstract:
Two-point boundary-value problems (BVPs) appear frequently in applied mathematics. When looking for solutions of boundary-value problems for some partial differential equations (PDEs) in mathematical physics, two-point BVPs come up as a result of applying the method of separation of variables, for instance. In the case of linear PDEs, the resulting two-point BVPs fall into a class of problems known as Sturm-Liouville eigenvalue problems.
This presentation deals with the use of the shooting method to prove existence of solutions of two-point BVPs. The shooting method is a numerical technique used to estimate solutions of two-point BVPs once a solution is known to exist. In this talk we illustrate how the shooting method can be used to prove existence of eigenvalues of linear Sturm-Liouville problems. We also show how the shooting method can be applied to prove existence and uniqueness of solutions for some nonlinear, two-point BVPs, and existence of eigenvalues for some nonlinear eigenvalue problems.
The presentation describes research conducted with collaborators Vaidehi Srinivasan (Pomona College class of 2027) and Gavin Zhao (Pomona College class of 2029) in the summer of 2025 with the support of the Summer Undergraduate Research Program at Pomona College.

CCMS Colloquium: Morse theory, Floer homology, and string topology (Ko Honda, UCLA)
2025-09-12 11:00 - 12:00 | Davidson Lecture Hall, CMC, 340 E 9th St, Claremont, CA, 91711, United States
CCMS Colloquium invites you to a talk by Professor Ko Honda, Professor of Mathematics at UCLA.
Title: Morse theory, Floer homology, and string topology
Abstract: One of the most important theories in geometry/topology is Floer homology, which can be viewed as a Morse theory of a loop space of a manifold (a generalization of a surface to higher dimensions). The aim of this talk is to give a gentle pictorial introduction to Morse theory for surfaces and then upgrade it in two steps: to Morse theory of loop spaces (e.g., of the 2-dimensional sphere) and then to “multiloops” (collections of many loops). The last upgrade is intimately related to a mathematical model for string theory called “string topology”, due to Chas-Sullivan, and to quantum topology via the HOMFLY polynomial of knots/links.
Speaker Bio: Ko Honda is an entirely American-trained mathematician, receiving his BA and MA from Harvard University in 1992 and PhD from Princeton University in 1997. After postdocs/visiting positions at Duke, the University of Georgia, the American Institute of Mathematics, and IHES, he arrived in LA in 2001, was a faculty member at USC for 12.5 years, and then moved across town to UCLA, where he has been for the last 11.5 years. Sometime during his postdoc at Duke, he discovered/invented an object called a “bypass” in contact geometry, which allowed him to simplify the analysis of 3-dimensional contact manifolds and solve several open problems in that area, some in joint work with Colin, Etnyre, and Giroux. He has been working on contact and symplectic geometry ever since, gradually branching out into adjacent areas (e.g., low-dimensional topology, Floer theory, and quantum topology) in the intervening years.

LA City Council Reform: A Statistical Study of Alternatives (Evan Rosenman & Sarah Cannon, Claremont McKenna College)
2025-09-15 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Abstract:
The 2022 Los Angeles City Council scandal intensified public demand for governance reform, leading to the creation of the Los Angeles Charter Reform Commission. The commission is now considering proposals from civic and academic groups. Major recommendations include: eliminating the automatic election of candidates who win a primary majority, expanding the size of the City Council, and adopting alternative electoral systems such as multimember districts and ranked-choice voting.
This project offers a rigorous, data-driven evaluation of these proposals, focusing on their implications for proportionality, racial representation, and electoral responsiveness. We combine methods from Statistics and Computer Science, including Bayesian ethnicity imputation, ecological inference, and advanced graph-sampling algorithms to explore district boundaries. This hybrid approach provides new insights into Los Angeles’s political geography and the challenges of building a fair, representative City Council. By providing empirical evidence on the strengths and weaknesses of various districting systems, our work aims to inform policymaking and advance democratic representation in Los Angeles.

A non-uniformly inner amenable group (Isaac Goldbring, UC Irvine)
2025-09-16 12:15 - 13:10 | Estella 2099
An inner amenable group is one in which there is a finitely additive conjugation-invariant probability measure on the non-identity elements. In this talk, we show that inner amenability is not preserved under elementary equivalence. As a result, we give the first example of a group that is inner amenable but not uniformly inner amenable.

NO CCMS Colloquium this Friday!
2025-09-19 11:00 - 12:00 | Davidson Lecture Hall, CMC, 340 E 9th St, Claremont, CA, 91711, United States
We’ll be back next week!

Graphical designs: combinatorics and applications (Catherine Babecki, Caltech)
2025-09-23 12:15 - 13:10 | Estella 2099
A graphical design is a quadrature rule for a graph inspired by classical numerical integration on the sphere. Broadly speaking, that means a graphical design is a relatively small subset of graph vertices chosen to capture the global behavior of functions from the vertex set to the real numbers. We first motivate and define graphical designs for graphs with positive edge weights. Through Gale duality, we exhibit a combinatorial bijection between graphical designs and the faces of certain polytopes associated to a graph, called eigenpolytopes. This polytope connection implies a variety of beautiful consequences, including a proof of existence, an upper bound on the cardinality of a graphical design, methods to compute, optimize, and organize graphical designs, the existence of random walks with improved convergence rates, and complexity results for associated computational problems. We conclude with applications to the equitable facility location problem.

Analysis seminar: Geometric classification problems with the Bergman metric (John Treuer, UCSD)
2025-09-25 16:00 - 17:00 | Davidson Lecture Hall, CMC, 340 E 9th St, Claremont, CA, 91711, United States
Title: Geometric classification problems with the Bergman metric
Abstract: One of the common problems in mathematics is the classification problem: When are two mathematical structures really the same? The classification problem appears throughout undergraduate mathematics courses in different forms. For example, in an abstract algebra course, one asks when are two groups isomorphic? In a geometry course, one asks when are two surfaces isometric? In a discrete math course, one asks when are two sets bijective? The version in complex analysis is when are two domains (open, connected sets) biholomorphic to each other?
In this talk, we will begin by defining the primarily studied functions in complex analysis, the complex differentiable functions also known as the holomorphic functions. We will then study the classification problem through the Bergman kernel and the Bergman metric. Towards the end of the talk, recent progress on classifying domains and complex manifolds with Bergman metrics of constant holomorphic sectional curvature will be presented.

CCMS Colloquium: Robert Cass (CMC)
2025-09-26 11:00 - 12:15 | Davidson Lecture Hall, CMC, 340 E 9th St, Claremont, CA, 91711, United States
CCMS Colloquium invites you to a talk by Assistant Professor of Mathematics Robert Cass of Claremont McKenna College:

Title: An introduction to the Langlands program

Abstract: Class field theory, which was established in the early 20th century, has its origins in Gauss’s law of quadratic reciprocity. As such, it allows one to determine whether certain integer polynomials have a root mod p. The Langlands program is a vast area of current research in number theory that can be viewed as a generalization of class field theory to all integer polynomials. In this talk, I will give a leisurely introduction to this circle of ideas by way of some concrete examples. I will conclude with my own work, which includes a result on the independence of the cohomology theory chosen in a geometric and categorical analogue of the Langlands program.

Brief Bio: Robert Cass joined the Mathematical Sciences Department at CMC as an Assistant Professor of Mathematics this fall. He received his B.S. from the University of Kentucky and his Ph.D. from Harvard University. After that, he was an NSF postdoctoral fellow at Caltech and the University of Michigan. He is interested in the Langlands program and arithmetic geometry, as well as related problems in algebraic geometry and representation theory. He enjoys mathematical questions that are simple to state but whose solutions involve tools from multiple disciplines, especially those with unexpected connections to geometry.

Bounds and Extremal Examples for the Hot Spots Ratio (Alex Hsu, University of Washington)
2025-09-29 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Abstract: The shape of the fluctuations as heat approaches equilibrium in an insulated body are governed by the first Neumann eigenfunction of the Laplacian. Rauch’s hot spots conjecture states that the extrema of the first nontrivial Neumann Laplacian eigenfunction for a Lipschitz domain lies on the boundary. While this conjecture is false in general, its failure can be measured by the hot spots ratio, defined as the maximum over the entire domain divided by the maximum on the boundary. We determine the supremum of this quantity over all Lipschitz domains in every dimension $d$ and construct a sequence of sets for which the hot spots ratio approach this supremum. As $dto infty$, this maximal ratio converges to $sqrt{e}$, which matches the previously best known upper bounds.

Algebraic lattices and Pisot polynomials (Lenny Fukshansky, CMC)
2025-09-30 12:15 - 13:10 | Estella 2099
A Z-module M in a number field K gives rise to a lattice in the corresponding Euclidean space via Minkowski embedding. Such lattices often carry inherited structure from the number field in question and can be attractive from both, theoretical and applied perspectives. We consider this construction when M is spanned by the set of roots of an irreducible polynomial f(x) of prime degree n. In this case, the resulting lattice has rank n or n-1 and includes the Galois group of f(x) as a subgroup of its automorphism group. Of particular interest is the case of Pisot polynomials, i.e., polynomials with one positive real root and the rest of the roots in the unit circle. We construct infinite families of such polynomials of any prime degree for which the resulting lattices have bases of minimal vectors, a property of interest in coding theory and cryptography applications. In case of the Galois group being cyclic, A_n, or S_n we derive formulas for the determinant of the lattice in terms of the symmetric functions of the roots of f(x). This is joint work with Evelyne Knight (Pomona College).

Analysis seminar: Transfinite Apollonian metric (Zair Ibragimov, CSU Fullerton)
2025-10-02 16:00 - 17:00 | Davidson Lecture Hall, CMC, 340 E 9th St, Claremont, CA, 91711, United States
Title: Transfinite Apollonian metric
Abstract: The concept of transfinite diameter of compact sets in the complex plane was introduced by Fekete in 1923. It is a generalization of the standard diameter of sets and has found many applications in the study of conformal mappings. The Apollonian metric was introduced by A. Beardon in 1995 and has since been used in the study of non-Euclidean geometries, hyperbolic-type metrics, and quasiconformal mappings. After a brief introduction to these concepts, we will discuss in some details the constructions of Apollonian metrics of order k and the transfinite Apollonian metric. Time permitting, we will discuss several properties, connections to other hyperbolic-type metrics, and some open problems.

CCMS Colloquium: Ruby Kim (University of Michigan)
2025-10-03 11:00 - 12:15 | Davidson Lecture Hall, CMC, 340 E 9th St, Claremont, CA, 91711, United States
CCMS Colloquium invites you to a talk by Ruby Kim (University of Michigan)
Title: Mathematical Models of Circadian Rhythms and Seasonal Timing

Abstract: The circadian clock shapes nearly 24-hour periodic rhythms throughout the body, from the activity of individual cells to our daily sleep/wake cycles. These rhythms can be self-sustained (for example, people still show circadian patterns even in total darkness), but they are also strongly influenced by the environment, especially light. Mathematical models of circadian rhythms have provided insight into many intriguing phenomena, including jet lag, mid-afternoon fatigue, and how animals sense the changing seasons. In this talk, I will introduce how mathematical models of circadian rhythms are constructed and used. Then, I will share recent work on seasonal timing in a large population of medical interns, using data collected from wearable devices. Our results suggest that seasonal timing plays a key role in how people respond to shift work. Overall, the goal of this talk is to introduce how mathematical modeling can be used to better understand biological rhythms and their impact on daily life.

Bio: I am originally from Koreatown, Los Angeles. I did my undergraduate studies at Pomona College (Class of ’17), where I majored in math and completed a thesis under the mentorship of Dr. Ami Radunskaya. I enjoyed teaching mathematics and doing research, so I decided to pursue graduate studies in math at Duke University. During my PhD, I fell in love with biological rhythms and mathematical neuroscience. Currently, I am a postdoc at the University of Michigan using mathematical modeling and data science to study biology and health. During my free time, I enjoy playing pool, hanging out with my dog, and reading.

GEMS October 4th Session
2025-10-04 10:00 - 11:55 | Shanahan B450, Harvey Mudd College, 301 Platt Blvd., Claremont, 91711, United States
This GEMS session will be facilitated by Professor Chiu-Yen Kao from Claremont McKenna College.

Title: Finding Your Optimal Paths

Abstract: Path planning plays an important role in many aspects of our daily life, among which are transportation, robotics, and optics. In this session, we will explore the mathematics behind path planning including the Dijkstra’s algorithm for finding the shortest paths between nodes in a graph and Fermat’s principle on the least time path taken between two points by a ray of light. Students will get hands-on experience on building a graph network on a real map and study different path planning problems. To inspire students to explore more advanced topics, some complicated path planning questions in high dimensions will be discussed at the end.
