GEMS March 1st Session
2025-03-01 10:00 - 12:00 (America/Los_Angeles) | Shanahan 1480, Harvey Mudd College, 301 Platt Blvd., Claremont, CA, 91711, United States
This GEMS session will be facilitated by Professor Jemma Lorenat from Pitzer College.

Title: Playing with the Rules of Geometries

Abstract: This session will explore how a small set of rules can be used to build and investigate geometrical objects. Through drawing, folding, and imagining, we will see how a limited number of possible actions ground a wide range of mathematical creations.

Enumerative Invariants from Derived Categories III (Reginald Anderson, CMC)
2025-03-02 12:15 - 2025-03-04 13:10 | Estella 2113
We’ll first define the two-point gravitational correlators which appeared last week as descendant Gromov-Witten invariants. By request, we’ll then introduce Gromov-Witten invariants as they appear in the expository work https://arxiv.org/abs/2501.03232 and give CP^1 to demonstrate some of the identities which GW invariants satisfy. If time allows, we’ll also give the small and big quantum cohomology for CP^1.

Applied Math Seminar: Efstratios Tsoukanis (Claremont Graduate University)
2025-03-03 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Title: Bi-Lipschitz Invariants
Abstract: Consider a finite-dimensional real vector space and a finite group acting unitarily on it. We investigate the general problem of constructing Euclidean stable embeddings of the quotient space of orbits. Our embedding relies on subsets of sorted coorbits with respect to chosen window vectors. Our main injectivity results examine the conditions under which such embeddings are injective. We establish these results using semialgebraic techniques. Furthermore, our main stability result states and demonstrates that any embedding based on sorted coorbits is automatically bi-Lipschitz when injective. We establish this result using geometric function techniques. Our work has applications in data science, where certain systems exhibit intrinsic invariance to group actions. For instance, in graph deep learning, graph-level regression and classification models must be invariant to node labeling.

Claremont Topology Seminar: Carrie Frizzell (Scripps College)
2025-03-04 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: Carrie Frizzell (Scripps College)
Title: A Primer on Tropical Geometry
Abstract: Max-plus and min-plus semifields—coined tropical semifields—appeared in the 1970s in the work of the computer scientist Imre Simon. Since then, the field of tropical geometry has developed rapidly. In this talk, we’ll present some basics of tropical geometry, starting with tropical algebra and then passing to the geometric side via a few examples of tropical hypersurfaces. We will also discuss the relationship between classical algebraic curves and tropical curves.

No CCMS Colloquium!
2025-03-05 16:15 - 17:30 | Argue Auditorium, Pomona College, 610 N. College Ave., Claremont, CA, 91711, United States

N+12th Southern California Topology Colloquium
2025-03-08 08:00 - 17:00 | Benson Auditorium, 1050 N Mills Ave., Claremont, CA, 91711, United States
The Claremont Topology Seminar, with funding from Pitzer College and the NSF, is pleased to sponsor the N+12th Southern California Topology Colloquium (SCTC). SCTC is a one-day conference primarily attended by mathematicians from the Southern California area. This year, the colloquium will be held at the Benson Auditorium at Pitzer College on
Saturday, March 8th, 2025.
All talks will take place in Benson Auditorium on the Pitzer College campus. Light breakfast, lunch, coffee and snacks will be served in the foyer of Benson Auditorium. The speakers are
Dror Bar-Natan, University of Toronto
Patrick Orson, California Polytechnic State University, San Luis Obispo
Rhea Palak Bakshi, University of California, Santa Barbara
Sucharit Sarkar, University of California, Los Angeles
There is no registration fee, but you must register to attend. More information can be found at the SCTC website below:
https://sites.google.com/view/socaltopology/home

Contact SCTC 2025 organizers for more questions:
Bahar Acu, <Bahar.Acu@pitzer.edu>, Pitzer College, Claremont Colleges
Ko Honda, <honda@math.ucla.edu>, University of California, Los Angeles
Yi Ni, <YiNi@caltech.edu>, California Institute of Technology
Helen Wong, <Helen.Wong@claremontmckenna.edu>, Claremont McKenna College, Claremont Colleges

Applied Math Seminar: Sarah Robinson (Claremont McKenna College)
2025-03-10 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Title: Do Taxes Affect Pre-Tax Income Inequality? Evidence from 100 Years of U.S. States
Abstract: We study how U.S. state taxes have affected pre-tax income inequality during the last century. Our primary analysis focuses on the top marginal personal income and corporate income tax, and their effect on top incomes and top income shares within each state. The long panel nature of our data, from 1917 to 2018, allows us to study the effect of tax adoptions, tax cancellations, and tax changes, and furthermore to assess both immediate and long-term relationships. With event study and synthetic control designs, we generally find no statistically significant relationship between tax measures and inequality. Some of our point estimates, as well as a simple two-way fixed effects analysis, suggest that higher income taxes may reduce top incomes and income shares.

Claremont Topology Seminar: Iris Yoon (Wesleyan University)
2025-03-11 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: Iris Yoon (Wesleyan University)
Title: Dowker duality, profunctors, and spectral sequences
Abstract: I will present three short, new proofs of Dowker duality using various poset fiber lemmas. I will introduce modifications of joins and products of simplicial complexes called relational join and relational product complexes. These relational complexes can be constructed whenever there is a relation between simplicial complexes, which includes the context of Dowker duality and covers of simplicial complexes. In this more general setting, I will show that the homologies of the simplicial complexes and the relational complexes fit together in a long exact sequence. If time permits, I’ll discuss similar results for profunctors, which are generalizations of relations to categories.

CCMS Colloquium: (Iris Yoon, Wesleyan University)
2025-03-12 16:15 - 17:30 | Argue Auditorium, Pomona College, 610 N. College Ave., Claremont, CA, 91711, United States
Speaker: Iris Yoon, Professor of Mathematics, Wesleyan University
Title: How Topology Reveals Structure in Neuroscience Data
Abstract: We live in an exciting time where new data is generated at an exponential rate. Such data explosion necessitates the development of novel methods for studying large, noisy, and complex data. One interesting aspect of data is its shape and structure. In this talk, I will discuss recent developments in applied topology that studies the structure of data. In particular, I will show how constructions in topology, such as homology and Dowker complexes, reveal interesting structures in data. I will discuss the mathematical challenges of extending these constructions to data science, specifically in neuroscience.
Bio: Iris Yoon is an assistant professor of mathematics at Wesleyan University. She develops novel applications of algebraic topology to data science.

Claremont Topology Seminar: NO SEMINAR
2025-03-18 08:00 - 17:00
No seminar this week due to Spring break!

No Colloquium: Spring Break
2025-03-19

Applied Math Seminar: Ryan O'Dowd (Claremont Graduate University)
2025-03-24 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Title: Learning on manifolds without manifold learning
Abstract: Function approximation based on data drawn randomly from an unknown distribution is an important problem in machine learning. The manifold hypothesis assumes that the data is sampled from an unknown submanifold of a high dimensional Euclidean space. A great deal of research deals with obtaining information about this manifold, such as the eigendecomposition of the Laplace-Beltrami operator or coordinate charts, and using this information for function approximation. This two-step approach implies some extra errors in the approximation stemming from estimating the basic quantities of the data manifold in addition to the errors inherent in function approximation. In this paper, we project the unknown manifold as a submanifold of an ambient hypersphere and study the question of constructing a one-shot approximation using a specially designed sequence of localized spherical polynomial kernels on the hypersphere. Our approach does not require preprocessing of the data to obtain information about the manifold other than its dimension. We give optimal rates of approximation for relatively “rough” functions.

Some Diophantine analogies between Dirichlet series and polynomials (Vesselin Dimitrov, Caltech)
2025-03-25 12:15 - 13:10 | Estella 2113
I will present an integral — requiring no character twists — converse theorem for recognizing when is a Dirichlet series with algebraic integer coefficients equal to the L-function of a modular form. This refines the unbounded denominators conjecture of Atkin and Swinnerton-Dyer. Analogies with basic function field arithmetic then suggest a quantitative refinement which precludes a pair of GL(2) automorphic L-functions with closely matched up zeros. I will explain how to get at such a theorem.

Claremont Topology Seminar: Reginald Anderson (Claremont McKenna College)
2025-03-25 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: Reginald Anderson (Claremont McKenna College)
Title: Kontsevich’s Recursive Formula for Rational Plane Curves
Abstract: Gromov-Witten theory was developed in the 1990s as a curve-counting theory by integrating cohomology classes against a virtual fundamental class for a moduli space of stable maps. One early success of the theory was Kontsevich’s recursive formula for enumerating the number of rational plane curves through 3d-1 points in general position. Starting from a consideration of which genus 0 Gromov-Witten invariants for the complex projective plane can possibly be non-zero, we will assemble a generating function for these invariants, called the genus 0 Gromov-Witten potential for the complex projective plane. If time allows, we will also use the fact that the potential satisfies a partial differential equation called the Witten-Dijkgraaf-Verlinde-Verlinde equation to solve for N_d, the coefficients of the generating function, which give the number of rational plane curves through 3d-1 points.
This talk follows p. 24-26 of these notes, available at https://arxiv.org/abs/2501.03232.
All are welcome.

CCMS Colloquium: Brownian Motion, Random Fractals, and Beyond (Yimin Xiao, Michigan State Uni)
2025-03-26 16:15 - 17:30 | Argue Auditorium, Pomona College, 610 N. College Ave., Claremont, CA, 91711, United States
Speaker: Yimin Xiao, Professor of Statistics and Probability, Michigan State University
Title: Brownian Motion, Random Fractals, and Beyond
Abstract: Brownian motion is not only a fascinating object in mathematics but also a powerful stochastic model that has been applied in many scientific fields, from physics to finance, to biological sciences. The sample function of Brownian motion is nowhere differentiable and generates various interesting fractal sets and measures. It is natural to apply tools from Fractal Geometry (e.g. Hausdorf dimension, packing dimension) to study the fine properties of Brownian motion. There is an enormous literature on sample path properties of Brownian motion, including many fractal and multifractal properties.
In this talk, we first provide an overview of some regularity and fractal properties of Brownian motion and its local times. These results are fundamental for the development of related theories for other stochastic processes. We then describe extensions of these results to Levy stable processes and fractional Brownian motion, which are two important relatives of Brownian motion in the areas of Markov processes and Gaussian processes, respectively.
Bio: Yimin Xiao is an MSU Research Foundation Professor in Statistics and Probability at Michigan State University. He received his Ph.D. from the Ohio State University in 1996. After completing his postdocs at the University of Utah and Microsoft Research, he joined Michigan State University in 2000. His research interests include random fields, Gaussian and Lévy processes, stochastic partial differential equations, extreme value theory, random fractals, and statistical analysis of spatial and spatio-temporal models. He has published about 160 articles in peer-reviewed journals.
Dr. Xiao has been a visiting professor at several universities in China, France, Germany, Hong Kong, Sweden, and Switzerland and has been invited as a speaker at various international conferences. He is a Fellow of the Institute of Mathematical Statistics.

Permutation pattern avoidance, alternating sign matrices, and asymptotics (Justin Troyka, Cal State LA)
2025-04-01 12:15 - 13:10 | Estella 2113
A big area in combinatorics over the last several decades has been the study of pattern-avoiding permutations, whose enumeration is exciting and mysterious. Alternating sign matrices (ASMs) are a generalization of permutations whose study in combinatorics has also been exciting and mysterious. In this talk, I will explain some new asymptotic results involving the number of ASMs that avoid a given permutation pattern, from my joint work with Mathilde Bouvel, Eric Egge, Rebecca Smith, and Jessica Striker. I will also show some of the highlights in the histories of both pattern-avoiding permutations and ASMs.

Claremont Topology Seminar: Scott Taylor (Colby College)
2025-04-01 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: Scott Taylor (Colby College)
Title: Genus 1 Bridge Number of Satellite Knots in Lens Spaces
Abstract: In the mid-1950s, Horst Schubert introduced two ideas which turned out to have lasting impact in knot theory: satellite knots and bridge number. A Satellite knot is a knot which is tied in the shape of another knot (its companion). Wrapping number is one way of measuring how complicated the satellite knot is with respect to its companion. Bridge number is an invariant for knots and links in the 3-sphere. Schubert showed that the bridge number of a satellite knot is at least the wrapping number times the bridge number of the companion. I’ll give an overview of recent joint work with Maggy Tomova where we extend Schubert’s result to knots in lens spaces.

CCMS Colloquium: (Scott Taylor, Colby College, Maine)
2025-04-02 16:15 - 17:30 | Argue Auditorium, Pomona College, 610 N. College Ave., Claremont, CA, 91711, United States
Speaker: Scott Taylor, Professor of Mathematics, Colby College, Maine
Title: Sums and Symmetries
Abstract: Adding is one of the fundamental mathematical operations and we like it so much, we can’t help but add all kinds of things including knots, surfaces, and 3-dimensional spaces. Symmetry is also a fundamental mathematical concern. How well do sums and symmetries play together? In this talk, I’ll survey some of the ways in which, in low-dimensions, sums and symmetries are frenemies: sometimes it all works beautifully and other times, well, it’s complicated.
Bio: Scott is a geometric topologist who studies knots and 3-dimensional spaces. He is the producer of Sum Camp, a summer day camp for public elementary school children that uses the arts and math games to help instill a basic sense of numeracy. He is also the author of the forthcoming textbook “Introduction to Mathematics: Number, Space, and Structure” from the American Mathematical Society.

GEMS April 5th Session
2025-04-05 10:00 - 12:00 | Shanahan 1480, Harvey Mudd College, 301 Platt Blvd., Claremont, CA, 91711, United States
This GEMS session will be facilitated by Professor Bahar Acu from Pitzer College.

Title: The Hole Truth: When is a Coffee Mug a Donut?

Abstract: In mathematics, topology is the study of properties of shapes that remain unchanged when shapes are bent, stretched, or deformed—so long as they aren’t torn or punctured. To a mathematician studying topology, a donut and a coffee cup (with a handle) are considered the “same” shape because one can be continuously deformed into the other without cutting or gluing.

In this interactive session, we will explore the concept of shape equivalence by counting holes—an essential feature in topology. Using Play-Doh and Wikki Stix, we will model different shapes, test their flexibility, and determine whether they can be transformed into one another. Join us for a hands-on journey into the fascinating world of topology, where a simple twist in perspective can redefine how we see the shapes around us!

Applied Math Seminar: Ethan Epperly (Caltech)
2025-04-07 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Title: Randomly pivoted Cholesky: Fast, accurate matrix approximation for scientific machine learning
Abstract:
Low-rank approximation of positive semidefinite matrices is a basic problem in computational mathematics, with many applications to machine learning and scientific computing. Existing approaches for this problem largely fall into two categories: simple, fast, but sometimes inaccurate methods and sophisticated, slower methods with accuracy guarantees. To achieve the best of both worlds, this talk introduces randomly pivoted Cholesky, an algorithm for positive semidefinite low-rank approximation that is simple, fast, and accurate. We demonstrate the effectiveness of randomly pivoted Cholesky for spectral clustering of molecular dynamics data, achieving an order of magnitude lower clustering error than previous methods. We then go on to discuss theoretical guarantees for randomly pivoted Cholesky. Using a matrix concavity argument, we show that randomly pivoted Cholesky has nearly optimal low-rank approximation properties. We conclude by discussing extensions and future prospects for this simple, yet effective, algorithm.

The ANTC of ChatGPT: On the Mathematical Foundations of Large Language Models (Gizem Karaali, Pomona)
2025-04-08 12:15 - 13:10 | 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).
