CCMS Colloquium: Mary Lou Zeeman (Bowdoin College)
2026-02-20 11:00 - 12:15 (America/Los_Angeles) | Davidson Lecture Hall, CMC, 340 E 9th St, Claremont, CA, 91711, United States
CCMS Colloquium invites you to a talk by Mary Lou Zeeman (Bowdoin College)

Title: A new framework for studying transient reactivity in two-dimensional systems.

Abstract: Even if a linear system of ordinary differential equations (ODEs) has a globally attracting equilibrium, solutions of the ODEs may grow arbitrarily large in the short-term before returning to the equilibrium in the long-term. This counter-intuitive phenomenon of transient amplification is called reactivity. It is especially important in ecological resilience and other applications where disturbances of a system may be transiently magnified to undesirable levels. In this talk we introduce a new framework for analyzing reactivity in two-dimensional linear systems of ODEs. While the eigenstructure of the system captures the long-term dynamics, we use the new framework to define an orthostructure, dual to the eigenstructure, that captures transient reactivity dynamics of the system. By interweaving the eigen- and ortho-structures, we are able to exactly quantify the maximum disturbance amplification possible.

Bio: Mary Lou Zeeman is the Wells Johnson Professor of Mathematics at Bowdoin College. Her research is in dynamical systems with applications to biology, sustainability and resilience. She is known for collaboratively building cross-disciplinary research communities focused on the health of the planet. She helped found and co-lead the Mathematics and Climate Research Network, the Computational Sustainability Network and the SIAM Activity Group on Mathematics of Planet Earth.

CCMS Colloquium: Harrison Li (HMC)
2026-02-27 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 Harrison Li (HMC)

Title: Precise analysis of blocked randomized experiments

Abstract: I recently finished a multi-year project with collaborators analyzing a blocked randomized experiment to evaluate the effectiveness of a government job training program for unemployment insurance (UI) recipients in Rhode Island. In presenting the results, I will focus on some methodological considerations that arose organically in this context. I will start by providing an introduction to the potential outcomes framework in causal inference and show how it enables us to formulate a precise mathematical description of what exactly it is we want to estimate when running a randomized experiment. Then, we will see some principled and less principled methods for performing this estimation in the setting of a block randomized experiment. Some directions for ongoing and future research will be discussed.

Bio: Harrison Li is in his first year as an Assistant Professor of Mathematics at Harvey Mudd College. He comes to Claremont after finishing his graduate studies in statistics at Stanford University in 2025, and previously worked full time as a quantitative trader on Wall Street. His research interests center around variance reduction in randomized experiments through experimental design and/or novel estimation procedures. He is also very passionate about developing sound statistical methodology in the service of other disciplines, including climate science, agronomy, and economics, and about exposing more students to the mathematical aspects of probability and statistics.

Structure-Preserving Discretizations for Fokker–Planck Equations via the Energy Dissipation Law (Satish Chandran, UCR)
2026-03-02 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Abstract: We present a new approach for deriving structure-preserving numerical discretizations of Fokker-Planck equations by establishing a connection between the Fokker-Planck equation and its semi-discrete master equation at the level of the energy-dissipation law. We determine the transition rate in the master equation via the detailed balance condition and the spatial discretization of the continuous energy-dissipation law. This approach ensures that the semi-discrete master equation satisfies the detailed balance condition and converges to the correct equilibrium. In addition to recovering existing transition rates proposed in earlier works, our framework uncovers new transition rates that have not been discussed in the current literature. This work is joint with Dr. Yiwei Wang (UCR).

On a new version of Siegel’s lemma (Lenny Fukshansky, CMC)
2026-03-03 12:15 - 13:10 | Estella 2099
The classical Siegel’s lemma (1929) asserts the existence of a nontrivial integer solution to an underdetermined integer homogeneous linear system, whose “size” is small as compared to the size of the coefficients of the system. Far-reaching generalizations of this theorem, producing a full basis for the solution space, were obtained over number fields by Bombieri & Vaaler (1983), and over the field of algebraic numbers by Roy & Thunder (1996), where the “size” was measured by a height function. We obtain a new version of Siegel’s lemma, bridging the Bombieri & Vaaler and Roy & Thunder results in two ways: (1) our basis lies over a fixed number field as in Bombieri & Vaaler’s theorem; (2) our height-bound does not depend on the number field in question as in Roy & Thunder’s theorem. Our result does not imply the previously established ones and is not implied by them, and our basis has some additional interesting properties. Our method is quite different from the previous ones, using only linear algebra. Joint work with Max Forst.

CCMS Colloquium: Lihong Zhao (Kennesaw State University)
2026-03-06 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 Lihong Zhao (Kennesaw State University)

Title: Capturing heterogeneity in malaria transmission: an age-structured model with immune feedback and seasonality

Abstract: Malaria remains a major global health burden, causing more than 600,000 deaths and over 249 million cases globally each year. Heterogeneity in malaria transmission is a critical factor that influences the dynamics of disease emergence and the effectiveness of possible control strategies. In this talk, I will present an age-structured model that couples vector-host epidemiological dynamics with immune feedback and how we use it to characterize seasonal malaria transmission and assess the impact of vaccination strategies. We also extend this model to explore how different mobility patterns and immunity profiles interact to impact the risk of severe infection and prevalence.

Bio: Dr. Lihong Zhao is an Assistant Professor of Mathematics at Kennesaw State University (KSU). Prior to her position at KSU, she was a Visiting Assistant Professor in the Department of Mathematics at Virginia Tech and an NSF DIRAC-RTG postdoctoral fellow in the Department of Applied Mathematics at the University of California, Merced. She develops and analyzes mathematical and computational models to examine questions in life sciences. Most of her work focuses on infectious disease epidemiology and ecology.

GEMS March 7th Session
2026-03-07 10:00 - 11:55 | Shanahan 1480, Harvey Mudd College, 301 Platt Blvd., Claremont, CA, 91711, United States
This GEMS session will be facilitated by Robbie Tran from Claremont Graduate University.

Title: Formulating Equations as a Medium for Digital Art and Design

Abstract:
As we can utilize letters and words to write out mathematics (e.g. 2+2=4 can be written as “two plus two is equal to four”), this session seeks to explore the near reverse: how can we use mathematics to some extent graph letters and words? Rather, could we formulate equations of curves that visually resemble text on a 2D-plane? If we include both conventional and nonconventional shapes too, this question is not only an interesting curiosity, but a question whose answer is quite prevalent in programs for computer graphics, animation, digital art, and font design!

We will approach this question by highlighting and constructing Bézier curves, which can approximate smooth curves by control (anchor) points on the plane. Furthermore, this session will showcase the mathematics of these curves, covering polynomials, linear interpolation, and parametrization (no prior knowledge assumed). Ultimately, we will simulate how graphs of Bézier curves can be drawn for various letters and shapes by applying a recursive method called de Casteljau’s algorithm. Join us to explore an example of how mathematics can serve as a gateway to art and design!

An Odd Estimator for Shapley Values (Teal Witter, CMC)
2026-03-09 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Abstract: The Shapley value is a ubiquitous framework for attribution in machine learning, encompassing feature importance, data valuation, and causal inference. However, its exact computation is generally intractable, necessitating efficient approximation methods. While the most effective and popular estimators leverage the paired sampling heuristic to reduce estimation error, the theoretical mechanism driving this improvement has remained opaque. In this work, we provide an elegant and fundamental justification for paired sampling: we prove that the Shapley value depends exclusively on the odd component of the set function, and that paired sampling orthogonalizes the regression objective to filter out the irrelevant even component. Leveraging this insight, we propose OddSHAP, a novel consistent estimator that performs polynomial regression solely on the odd subspace. By utilizing the Fourier basis to isolate this subspace and employing a proxy model to identify high-impact interactions, OddSHAP overcomes the combinatorial explosion of higher-order approximations. Through an extensive benchmark evaluation, we find that OddSHAP achieves state-of-the-art estimation accuracy.

Joint work with Fabian Fumagalli, Landon Butler, Justin Singh Kang, and Kannan Ramchandran.

Hecke algebras and motives (Robert Cass, CMC)
2026-03-10 12:30 - 13:10 | Estella 2099
Hecke algebras play a central role in both number theory and representation theory. While some Hecke algebras have explicit descriptions in terms of generators and relations, others are understood through structure constants that encode multiplicities in tensor products of representations. In this talk, I will discuss several projects with Thibaud van den Hove and Jakob Scholbach aimed at using geometry and motives to give a uniform categorification of Hecke algebras. Along the way, we will encounter the geometric Satake equivalence, Gaitsgory’s central functor, and Iwahori-Whittaker models.

NO CCMS Colloquium: Pi Day at CMC
2026-03-13 11:00 - 12:15 | Davidson Lecture Hall, CMC, 340 E 9th St, Claremont, CA, 91711, United States
No lecture today.

Quantitative and Computing Lab (QCL) Math Club Pi Day celebration at Claremont McKenna College at Kravis Lower Court from 11am to 12:30pm.

NO CCMS Colloquium - SPRING BREAK
2026-03-20 11:00 - 12:15

A Regularity Criterion for the 3-D Navier-Stokes Equations Based on Finitely Many Observations (Abhishek Balakrishna, USC)
2026-03-23 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Abstract: This talk presents a regularity criterion for the three-dimensional Navier–Stokes equations based on finitely many observations of the flow. Motivated by data assimilation, we study a nudging algorithm that incorporates coarse spatial measurements through general interpolation operators.
We show that suitable conditions on the observed data guarantee global regularity of the associated system and yield an exponential tracking property. As a consequence, we obtain a new regularity criterion for weak solutions formulated entirely in terms of finitely many observables, covering modal, volume, and nodal measurements.

Computing certificates for complete positivity (Achill Schürmann, University of Rostock)
2026-03-24 12:15 - 13:10 | Estella 2099
A key problem in computer proofs based on solutions from copositive optimization, is checking whether or not a given quadratic form is completely positive or not. In this talk we describe the first known algorithm for arbitrary rational input. It is based on a suitable adaption of Voronoi’s Algorithm and the underlying theory from positive definite to copositive quadratic forms. We observe several similarities with the classical theory, but also some differences, in particular for three and more variables. A key element and currently the main bottleneck in our algorithm is an adapted shortest vector computation, asking for all nonnegative integer vectors attaining the copositive minimum of a given copositive quadratic form.
(based on joint work with Valentin Dannenberg, Alexander Oertel, Mathieu Dutour Sikiric and Frank Vallentin)

Analysis Seminar: Metrics on quantum channels from noncommutative geometry (Tron Omland, University of Oslo and Norwegian National Security Authority)
2026-03-24 16:15 - 17:15 | Estella 2099, Pomona College, 610 N. College Ave., Claremont, CA, United States
Abstract: We study metrics on completely positive maps, and in particular on quantum channels, induced by seminorms from noncommutative geometry. Using an infinite-dimensional analogue of the Choi–Jamiołkowski correspondence, we construct such metrics and show that, under suitable assumptions, they satisfy stability and chaining. I will present the main ideas and explain how spectral triples and related constructions give rise to distances between quantum processes. This is joint work with Austad, Bedos, Eidesen, and Larsen.

NO CCMS Colloquium - Cesar Chavez Day
2026-03-27 11:00 - 12:15 | Davidson Lecture Hall, CMC, 340 E 9th St, Claremont, CA, 91711, United States

The Euler Equations in Function Spaces of Generalized Smoothness (Zachary Radke, OSU)
2026-03-30 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Abstract: In this talk, we will describe a well/ill-posedness result for the 2D incompressible Euler equations. We investigate solutions in a setting logarithmically smoother than previously done, in a hope to identify the key dynamics leading to a breakdown of regularity in 2D fluid flow. When order of the logarithmic derivative is sufficiently large one obtains global well posedness, however, below this threshold, one can construct initial data for which the corresponding solution blows up instantaneously in the logarithmic Sobolev norm. In this sense, the result is sharp at this logarithmic scale, but by no means is the story completed by it so we will discuss ways to dive deeper.

Central moments of autocorrelation demerit factors of binary sequences (Daniel Katz, CSUN)
2026-03-31 12:15 - 13:10 | Estella 2099
A low autocorrelation binary sequence of length $ell$ is an $ell$-tuple of $+1$s and $-1$s that does not strongly resemble any translate of itself. Such sequences are used in communications and remote sensing for synchronization and ranging, where translation represents time delay. A single number that indicates how good a sequence is for such purposes, called the merit factor, was introduced by Golay. Its reciprocal is the demerit factor, which is more natural to analyze due to its connection with norms of polynomials on the complex unit circle. We consider the uniform probability measure on the $2^ell$ binary sequences of length $ell$ and investigate the distribution of the demerit factors of these sequences. Sarwate and Jedwab have respectively calculated the mean and variance of this distribution. For each positive integer $p$, we derive a formula for the $p$th central moment of the demerit factor for the binary sequences of length $ell$; this is $ell^{-2 p}$ times a quasipolynomial function of $ell$. The derivations rely on new combinatorial techniques, assisted by group theory and Ehrhart theory, and show that all the central moments are strictly positive for $pgeq 2$ and $ell geq 4$. Jedwab’s formula for variance is confirmed, and we go beyond previous results by also deriving an exact formula for the skewness (by hand) and for the kurtosis and the fifth moment (by computer). We obtain asymptotic values for all central moments in the limit as the length $ell$ of the sequences tends to infinity.

Analysis Seminar: Restricted isometries and operator norms on finite-dimensional $L^p$-spaces (Alonso Delfín Ares de Parga, CU Boulder)
2026-04-02 16:15 - 17:15 | Estella 2099, Pomona College, 610 N. College Ave., Claremont, CA, United States
Abstract: An isometry between two normed vector spaces is a linear map that preserves the norm (i.e., the length of each output agrees with the length of its input). For the classical $p$-norms, isometries have a very concrete description when $p
eq 2$: they are given by signed permutations of the coordinates.
In this talk, I will present a generalization of this result to restricted isometries, which are linear maps that preserve the norm only on a fixed subset of coordinates. I will discuss how this generalization could be used in the computation of certain $p$-operator norms, a problem that is known to be NP-hard in general.
This talk includes joint work carried out as part of two REU projects in 2024 and 2025.

CCMS Colloquium: Puttipong Pongtanapaisan (Pitzer)
2026-04-03 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 Puttipong Pongtanapaisan (Pitzer)

Title: Derivatives and the Shape of Graphs

Abstract: Reading the title of this talk, perhaps you think you are going to hear about Calculus I. I stole the title from a section of Stewart’s popular calculus book. But actually, I am going to talk about geometry and topology, and the root idea already appears in Calculus I. In real life, shapes such as proteins and DNA can be tangled up in space. These can be modeled as graphs embedded in three-dimensional space, and some applied mathematicians also call these networks. In calculus, you learn that information about derivatives, such as the number of local maxima and where they appear, tells us a great deal about the graph itself. I am going to apply this same philosophy to knotted graphs in three-dimensional space and demonstrate that one protein is more complexly entangled than another.

Bio: Puttipong Pongtanapaisan obtained his Ph.D. at the University of Iowa, where he studied low-dimensional topology under the supervision of Dr. Maggy Tomova. His previous positions include a PIMS Postdoctoral Fellow at the University of Saskatchewan and a Postdoctoral Associate at Arizona State University. His research explores knotted shapes in confinement by analyzing the arrangement of local maxima and minima.

GEMS April 4th Session
2026-04-04 10:00 - 11:55 | Shanahan 1480, Harvey Mudd College, 301 Platt Blvd., Claremont, CA, 91711, United States
This GEMS session will be facilitated by Evan Rosenman from Claremont McKenna College

Title: Fair Votes? The Mathematics of Elections and Redistricting

Abstract: How do we know if an election is fair? In this interactive session, we’ll explore how math helps us answer that question. Students will experiment with drawing voting districts to see how drawing different district boundaries can change outcomes. They will also learn about alternative voting systems, such as ranked choice voting and approval voting, and how these might yield more representative outcomes than traditional “first-past-the-post” elections. Along the way, we’ll encounter ideas like Condorcet winners, and see how Statistics can help us learn about voting patterns from limited data. Join us to discover how geometry, algorithms, and probability shape modern elections.

Tropical linear series and matroids (Dagan Karp, HMC)
2026-04-07 12:15 - 13:10 | Estella 2099
In this talk, I’ll attempt to give a friendly introduction to tropical linear series and explore their relationship to matroid theory. Along the way, we’ll stop to admire the beautiful view from enumerative geometry and combinatorics. This is joint work with Chih-Wei Chang, Matthew Dupraz, Hernan Iriarte, David Jensen, Sam Payne, and Jidong Wang, and also with Jenna Luo.

CCMS Colloquium: Course Preview
2026-04-10 11:00 - 12:15 | Davidson Lecture Hall, CMC, 340 E 9th St, Claremont, CA, 91711, United States
Please join us for the course preview of all the math courses for Fall 2026.

Join us to hear from faculty about the exciting math courses being offered this upcoming fall. It’s a great opportunity to learn more, ask questions, and plan your schedule!
Please see the presentation below.
https://docs.google.com/presentation/d/1zpXAPZv34v3CWK3Ic-aGedRaJRIEt2BywVJJ4LlJnp0/edit?usp=sharing

The alchemy of mixing mathematics: The second annual CCMS workshop in the history and philosophy of mathematics
2026-04-11 10:00 - 15:30 | Argue Auditorium, Pomona College, 610 N. College Ave., Claremont, CA, 91711, United States
This one-day workshop assembles diverse perspectives from the history and philosophy of mathematics to examine ways in which mathematics interacts and expands across other fields of study.
Please RSVP here by Monday, April 6th to attend the workshop and lunch.

Schedule
10:00 to 10:05 Welcome!
10:05 to 11:05 Otávio Bueno (University of Miami & Tohoku University), “Why there are no styles of mathematical reasoning”
11:10 to 12:10 E. L. Meszaros (Brown University), “Algorithmic translations and interpretations of late Babylonian mathematics”
12:10 to 1:20 Lunch
1:25 to 2:25 Jed Buchwald (CalTech), “The winding trail to Newton’s Principia”
2:30 to 3:30 Mate Szabo (University of Southern California), “Turing’s machines and Max Newman’s symbolic machinery for mathematical physics”

Abstracts

Otávio Bueno (University of Miami & Tohoku University), “Why there are no styles of mathematical reasoning”
The notion of style of scientific reasoning has been used as an analytical tool for the characterization of significant features of scientific practice (in particular, by Crombie [1994], Hacking [2002], and Granger [1988]). Styles of scientific reasoning are different from scientific theories in a given domain of inquiry: styles are broader than theories, and they are not so dependent on features of the particular domain. In this work, I have two main goals. I’ll first provide a characterization of the concept of style of reasoning that overcomes some difficulties that have been raised against this tool (by Bolduc [2014]). I’ll then argue that, despite the broad conception of style I defend, there is no suitable way of formulating a notion of style of mathematical reasoning. Mathematics, I’ll argue, is too malleable, and attempts at characterizing a notion of style in geometry, analysis, algebra or set theory end up yielding just more mathematical theories particular to these domains. Mathematical practice is significantly different from scientific practice in this respect.
E. L. Meszaros (Brown University), “Algorithmic translations and interpretations of late Babylonian mathematics”
Initial investigations into Babylonian mathematics as “algorithms” began, intuitively, by interrogating the large corpus of Old Babylonian mathematical texts. Donald Knuth viewed these prose maths problems as examples of algorithms, though many scholars of Babylonian cultures and languages disagreed with this characterization. However, recent studies have demonstrated the value of looking for algorithms among other corpora, particularly astronomical texts. While astronomical procedures demonstrated more algorithmic characteristics, they also highlighted uniquely Babylonian tendencies. Whether these texts can be truly considered “algorithmic” becomes less important than whether the algorithmic lens as a tool of analysis can shed light on new aspects of the science and mathematics contained within the tablets. This talk examines the application of the term “algorithm” to less frequently considered Late Babylonian mathematics. While this corpus remains small, the few examples that have been recovered show characteristic differences from their Old Babylonian counterparts, making it valuable to reconsider the application of the term algorithm and the algorithmic lens of investigation. Beginning with an introduction to the corpus and what makes it different from earlier mathematical texts, this talk then makes the case for viewing these later texts algorithmically. Comparisons to Babylonian algorithmic forms and cultures, particularly arising from the astronomical sciences, will be made and evaluated for use within the field.
Jed Buchwald (CalTech), “The winding trail to Newton’s Principia“

Throughout the years between his first engagement with mathematics under Isaac Barrow and the production of the manuscript that evolved into Book I of the Principia, Newton was only sporadically engaged by issues of motion, whether earthly or astronomical. His first concerted interest involved collisions, which he modeled on the material circumstances of a springlike mechanism. In doing so, and in a subsequent turn to circular motion, the young Newton presumed without comment what would later be formalized as the Principia‘s three laws of motion. He was hardly the only one, at least in England, to make such presumptions. We will discuss this early work in order to unpack what transpired when, in 1679, Newton responded to a letter from Robert Hooke, his former critic in optics. We’ll then consider what in consequence took place following the famous visit to Newton by Edmond Halley in 1684. If time allows, we’ll conclude with a brief examination of the interesting reaction of the mathematician John Wallis to Newton’s manuscript account of fall under resistance, sent to Wallis for comment by Halley two years before the Principia. In so doing we will see that the fundamental key to the novelty of Newton’s work at that time consisted in the specific manner according to which he discretized motion change.
Mate Szabo (University of Southern California), “Turing’s machines and Max Newman’s symbolic machinery for mathematical physics”
While Turing’s “On Computable Numbers…” from 1936 and its impact is well studied, much less is known about Turing’s early influences. The aim of this talk is to show how Max Newman, who taught Turing in Cambridge and was later his boss in Bletchley Park and at the University of Manchester, influenced his early work. Indeed, Turing’s interest in the “Entscheidungsproblem” stemmed from Newman’s lectures on the foundations of mathematics he attended in 1935. While Newman is known as a combinatorial topologist, he was the first to teach a modern, Hilbert style mathematical logic course in the UK. In addition, he frequently engaged with the Cambridge philosophers during the 1920s and 1930s. His interest in scientific philosophies most likely stems from his visit to Vienna during the 1922/1923 academic year, where he came in touch with members of the famous Vienna Circle. Indeed, his unpublished dissertation, The Foundations of Mathematics from the Standpoint of Physics (1923), shows strong influences of the Vienna Circle. Newman’s aim in the dissertation is to build up mathematical physics as a “symbolic machinery” for manipulating “a body of ‘logical axioms’ and a set of ‘physical assumptions’”. This leads to the parallel development of an ‘epistemic logic’ to deal with ‘beliefs’ and ‘judgements about sensations’ on the physical side, and the description of logic as acts, performances and processes of symbol manipulation. After a careful look at the dissertation I will bring out the surprisingly strong resemblances (as well as the important differences) between Newman’s treatment of mathematical activities and Turing’s analysis of the human “computor”.

Extremal Eigenvalues of Weighted Steklov Problems (Chiu-Yen Kao, CMC)
2026-04-13 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Abstract: We study the optimization of Steklov eigenvalues with respect to a boundary density function ρ on a bounded Lipschitz domain. We investigate the minimization and maximization of a Steklov eigenvalue over admissible densities satisfying pointwise bounds and a fixed integral constraint. We establish the existence of optimal solutions and provide structural characterizations: minimizers are bang-bang functions and may have disconnected support, while maximizers are not necessarily bang-bang. On circular domains, the minimization problem admits infinitely many minimizers generated by rotational symmetry, while the maximization problem has infinitely many distinct maximizers that are not symmetry-induced. We also show that an eigenvalue is generally neither convex nor concave with respect to the density function, limiting the use of classical convex optimization tools. To address these challenges, we analyze the objective functional and introduce a Fréchet differentiable surrogate that enables the derivation of optimality conditions. We further design an efficient numerical algorithm, with experiments illustrating the difficulty of recovering optimal densities when they lack smoothness or exhibit oscillations.

Knot complements, series invariants and Lie superalgebra (John Yoonseok Chae)
2026-04-14 12:15 - 13:10 | Estella 2099
Inspired by the categorification program for a numerical invariant of three-manifolds, series invariants for closed manifolds and for knot complements were introduced. This in turn motivated an extension of the series invariant of the former case to Lie superalgebras. It was recently generalized to knot complements. In this talk, we review the original series invariants and introduce the recent generalization and explore its properties and examples.

CCMS Colloquium: Ryan Moruzzi (CSU Northridge)
2026-04-17 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 Ryan Moruzzi (CSU Northridge)

Title: Exploring Leaky Forcing Through Hopi Rectangle graphs

Abstract: Leaky forcing, introduced in 2019, is a graph-coloring process motivated by questions of network monitoring, in which the loss of information can hinder propagation through a graph. As a variant of standard zero forcing, leaky forcing has opened new directions in the study of zero forcing and related graph parameters. In this talk, based on joint work with students, we will collaboratively investigate the leaky forcing number for several graphs before focusing on a family of graphs called Hopi Rectangles. By viewing these graphs as induced subgraphs of d-dimensional grid graphs, we classify their leaky forcing numbers. Time permitting, we will conclude by discussing the maximum nullity of this graph family and its connection to standard zero forcing.

Bio: I am a husband, father, sports enthusiast, and mathematician who enjoys spending time with my family and the energy of sports. I earned my B.S. in Mathematics from Cal Poly Pomona and my Ph.D. in Mathematics from the University of California, Riverside, where I specialized in representation theory. My research interests lie in combinatorics, discrete mathematics, and linear algebra, with particular emphasis on the inverse eigenvalue problem of a graph, zero forcing and its variations, throttling, and propagation time on graphs. I also care deeply about teaching and mentorship, and as an educator I am committed to fostering equity and inclusion by working intentionally to remove barriers that limit student success.

The Secret Life of Turbulent Fluids (Vincent Martinez, Caltech)
2026-04-20 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Abstract: Turbulence influences our lives in a multitude of ways, ranging from the mundane (when we stir milk into our coffee) to the spectacular (the formation of galaxies). It is a great achievement of the human intellect that we are able to locate fundamental mechanisms shared by phenomenon with such a dramatic difference in scale and subsequently study them abstractly through mathematics. This talk will present some of the ways for how fluids and turbulent motion can be studied mathematically and introduce a few interesting problems, both theoretical and practical, of ongoing scientific relevance.

Diophantine avoidance, primitive elements, and normal basis theorem (Sehun Jeong, CMC)
2026-04-21 12:15 - 13:10 | Estella 2099
Diophantine avoidance has been studied by several authors in recent years. This refers to effective results on existence of points of bounded size in a given algebraic set avoiding some specified subsets. The famous primitive element theorem states that every number field K is of the form Q(a) for some element a in K. From the proof of this theorem, it is clear that not only there are infinitely many such primitive elements in K, but in fact most elements in K are primitive. One natural question to ask is about finding a primitive element of small “size”, where we use a height function to measure size. We discuss the conjecture of Ruppert and known results in this direction, as well as our recent work on this problem. In addition, we provide the standard and effective version of normal basis theorem, obtaining an explicit bound in terms of the degree and discriminant of K, where K/Q is a Galois extension. At the end, we discuss a particularly good bound in the case of prime degree. This is joint work with Lenny Fukshansky.

CCMS Colloquium: Manuel Reyes (UCI)
2026-04-24 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 Manuel Reyes (UCI)

Title: When XY is not equal to YX

Abstract: The commutative property of algebra states that the order of multiplication makes no difference: XY = YX. This property is so ingrained in our experience that it becomes difficult to imagine how algebra would function without it! If the commutative property fails, we step into the territory of noncommutative algebra. Where and why does noncommutative algebra occur? How different is it from our ordinary commutative algebra? This talk will be an introduction to noncommutative algebra, with several examples and a glimpse into current research problems.

Bio: Manny Reyes is an Associate Professor of Mathematics at UC Irvine. His research lies at the intersection of several topics including ring theory, noncommutative geometry, category theory, and quantum foundations. After studying at Westmont College and UC Berkeley, he was a postdoctoral fellow at UC San Diego and a faculty member for several years at Bowdoin College before returning to California. He strives to teach in a way that invites anyone to discover a passion for mathematics, regardless of their past experiences.

From ICON to GenICON: In-Context Operator Learning with Uncertainty Quantification (Siting Liu, UCR)
2026-04-27 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Abstract: I will introduce In-Context Operator Networks (ICON), a framework in which a single neural network learns solution operators for differential equations directly from a few prompted input-output examples at inference time, without any weight updates. ICON acts as a few-shot learner across forward and inverse problems for ODEs, PDEs, and mean-field control. I will then present a probabilistic interpretation: under a random differential equation data model, ICON implicitly computes the posterior predictive mean given the context, linking operator learning to Bayesian inference. This motivates GenICON, a generative variant that samples from the posterior predictive for principled uncertainty quantification, yielding a unified Bayesian view of in-context operator learning.

Coordinate ring of the universal centralizer via Demazure operators (Tom Gannon, UCR)
2026-04-28 12:15 - 13:10 | Estella 2099
One of the key objects used in Ngo’s proof of the fundamental lemma is the group scheme of universal centralizers associated to a split reductive group G. In this talk, we’ll discuss forthcoming work, joint with Victor Ginzburg, which describes the coordinate ring of the group scheme of universal centralizers in terms of the root datum of G using Demazure (or divided difference) operators. We will then discuss how our result follows from a more general computation on Weil restriction and, time permitting, we will discuss a potential generalization of our result to Coulomb branches.
