CCMS Colloquium: Anna Ma (UCI)
2025-10-31 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 Anna Ma (UCI)

Title: Stochastic iterative methods for solving tensor linear systems

Abstract: Solving linear systems is a crucial subroutine and challenge in data science and scientific computing. Classical approaches for solving linear systems assume that data is readily available and small enough to be stored in memory. However, in the large-scale data setting, data may be so large that only partitions (e.g., single rows/columns of the matrix/tensor) can be utilized at a time. In this presentation, we discuss the advantages and role of randomization in iterative methods for approximating the solution to large-scale linear systems. Time permitting, we will also discuss our recent work on applications to solving systems involving higher-dimensional arrays, or tensors. Unlike previously proposed randomized iterative strategies, such as the tensor randomized Kaczmarz method (row slice method) or the tensor Gauss-Seidel method (column slice method), which are natural extensions of their matrix counterparts, our approach delves into a distinct scenario utilizing frontal slice sketching.

Bio: Dr. Anna Ma is an Assistant Professor at UC Irvine in the Department of Mathematics. Prior to her position at UCI, she was a Visiting Assistant Professor at UCI and a UC Chancellor’s Postdoctoral Fellow at UC San Diego in the Department of Mathematics. Her research interests are in randomized algorithms, numerical linear algebra, and the mathematics of data science. She is also interested in data visualization and unsupervised machine learning. Anna earned her BS in Mathematics at UC Los Angeles. She received her PhD in Computational Science from Claremont Graduate University and the Computational Science Research Center at San Diego State University, where she studied the design and analysis of algorithms that solve problems involving large-scale data.

GEMS November 1st Session
2025-11-01 10:00 - 11:55 | Shanahan B450, Harvey Mudd College, 301 Platt Blvd., Claremont, 91711, United States
This GEMS session will be facilitated by Grace Akinwande from the Claremont Graduate University.

Title: From Pizza to Calculus: Understanding Area Through Approximation

Abstract: How much more pizza do you really get from a larger size? In this presentation, we explore the concept of area starting from an everyday question—the pizza dilemma! We’ll review basic geometric areas and extend the idea to regions bounded by curves. Using simple rectangular approximations, we’ll discover how increasing the number of rectangles improves accuracy and leads us naturally to the concept of limits. By connecting geometry, algebra, and reasoning, this session illustrates how real-world problems can introduce fundamental ideas of calculus in a fun and intuitive way.

Convergence analysis of the Alternating Anderson-Picard method for nonlinear fixed-point problems (Xue Feng, UCLA)
2025-11-03 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Abstract: Anderson Acceleration (AA) has been widely used to solve nonlinear fixed-point problems due to its rapid convergence. This talk focuses on a variant of AA in which multiple Picard iterations are performed between each AA step, referred to as the Alternating Anderson-Picard (AAP) method. Despite introducing more `slow’ Picard iterations, this method has been demonstrated to be efficient and even more robust in both linear and nonlinear cases. However, there is a lack of theoretical analysis for AAP in the nonlinear context. In this work, we address this gap by establishing the equivalence between AAP and a multisecant-GMRES method that employs GMRES to solve a multisecant linear system at each iteration. From this perspective, we show that AAP actually “converges” the well-known Newton-GMRES method. These connections also help us understand the convergence behavior of AAP, especially the asymptotic convergence rate.

Classifying possible density degree sets of hyperelliptic curves (Jasmine Camero, Emory University)
2025-11-04 12:15 - 13:10 | Estella 2099
Let $C$ be a nice (smooth, projective, geometrically integral) curve over a number field $k$. The single most important geometric invariant of a curve is the genus, which can control various arithmetic properties of a curve. A celebrated result of Faltings implies that all points on $C$ come in families of bounded degree, with finitely many exceptions. This result symbolized an advancement in the study of arithmetic information about curves and serves as the guiding philosophy of arithmetic geometry by highlighting the idea that “geometry governs arithmetic.” We explore the behavior of parameterized points and deduce consequences for the arithmetic of hyperelliptic curves, specifically focusing on classifying the density degree sets of such curves.

Claremont Topology Seminar: Robert Cass (Claremont McKenna College)
2025-11-04 16:00 - 17:00 | Fletcher 104, Pitzer College, 1050 N Mills Ave, Claremont, 91711, United States
We welcome all undergraduate/graduate students and faculty to attend topology seminar!
Speaker: Robert Cass (Claremont McKenna College)
Title: Schubert varieties are splinters
Abstract: Schubert varieties are among the most well-studied singular algebraic varieties, and they have numerous applications in combinatorics and representation theory. In positive characteristic, Schubert varieties are known to be Frobenius split by the work of Mehta and Ramanathan. More recently, Bhatt showed that the full flag variety for GL_n is a derived splinter by entirely different methods. In this talk, we explain these concepts, and we show how to generalize Bhatt’s result to all Schubert varieties. Our methods apply equally well to affine Schubert varieties, which are of interest in number theory. This is joint work with João Lourenço.

CCMS Colloquium: Jemma Lorenat (Pitzer)
2025-11-07 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 Jemma Lorenat (Pitzer)

Title: Recognizing data: statistical literacies around 1900

Abstract: This talk centers on the first (and perhaps only) doctorate in the theory of correlations, granted by University College London in 1899 to Alice Lee. The production and reception of Lee’s research sheds light on the varieties of statistical literacies around 1900.

Bio: Jemma Lorenat is a historian of mathematics at Pitzer College. She spends a great deal of time thinking about the history and future of statistical literacies. She also loves conic sections and (some) other algebraic curves.

To Wait or Not to Wait? A Trade-off Between Population Externality and Signal Quality (Lan-Yi Liu, National Taiwan University)
2025-11-10 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Abstract: Transparency is vital for efficiency in social systems, yet individuals with critical information often strategically postpone disclosure, even when required, to benefit themselves.
To study this behavior, we introduce a multi-stage Chinese restaurant game with incomplete information that features system-recommended action rules and varying levels of player foresight. In our model, players initially receive a suggestion to join a queueing group based on their private signal, but can choose to switch groups. Following this, players sequentially select a final resource, balancing the desire to avoid congested externalities with the need to acquire more information.
We prove a closed-form solution for the players’ pure-strategy Nash equilibrium. Our key finding is that players with high-quality signals have no incentive to reveal their information to those with low-quality signals. This suggests that allowing players to strategically determine their decision timing, without further system design, leads to an inefficient equilibrium allocation.
Our results on congested externalities and system suggestions help explain the inherent trade-off between information quality and decision timing in various real-world scenarios, such as the challenges of vaccine distribution during a pandemic, the strategic crowding of factory location selection, and the decision-making faced by political candidates positioning themselves on the spectrum.

Elementary probability via bundles (Wai Yan Pong, Cal State Dominguez Hills)
2025-11-11 12:15 - 13:10 | Estella 2099
This talk explores elementary probability and statistics through the language of category theory. We introduce a category of Bundles and use it to reinterpret several results typically covered in an introductory course on probability and statistics. This approach naturally reveals the underlying geometric structures common to these results. The talk is accessible to anyone familiar with linear algebra, and we hope teachers of probability will find this perspective fresh and interesting.

The 16th Atul Vyas Memorial Lecture in Mathematics (Teal Witter, CMC)
2025-11-12 16:15 - 17:15 | Freeberg Forum, LC 62, Kravis Center, CMC
Atul Vyas was an outstanding CMC student who was majoring in Mathematics and Physics. He tragically lost his life in a train crash that occurred on September 12, 2008 in Chatsworth, California. The Mathematical Sciences Department at CMC fondly remembers Atul as someone who was equally excited by the power of mathematical abstraction and the possibilities for its applications.
In memory of Atul, the CMC Mathematical Sciences Department hosts a yearly lecture series, aimed at a general audience, on the Creative Application of Abstract Mathematical Ideas.
A brief reception will take place prior to the talk at 4:00 PM
For more details, please see the attached Flyer
Speaker: R. Teal Witter, Assistant Professor of Mathematical and Computer Science, CMC
Title: Estimating Shapley Values for Explainable AI via Richer Model Approximations
Abstract: Gradient descent is at the heart of modern machine learning: We iteratively update the weights of machine learning models to minimize a problem-specific loss. When it works well, we deploy the model in human-facing domains like healthcare, finance, or the justice system. But even though we know how models are trained, we don’t understand why they make the decisions they do. A particularly compelling approach to explaining AI predictions is the Shapley value, a game-theoretic quantity that measures how each input to the model affects its output. Mathematically, the i-th Shapley value is the average change in the i-th dimension of a particular function defined on the d-dimensional hypercube. Because the hypercube has 2^d points, exactly computing Shapley values is infeasible. In this talk, we will instead leverage algorithmic insights to develop state-of-the-art approximation methods.

CCMS Colloquium: Robert Sanchez (HMC)
2025-11-14 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 Robert Sanchez (HMC)

Title: Tides: Under the Sea and Under the Ice

Abstract: Physical oceanography is the study of ocean fluid dynamics (e.g., waves, currents, plumes, turbulence). This talk will introduce physical oceanography and the methods used to analyze ocean data such as time-series analysis and numerical solutions to differential equations. We will use these methods to investigate the tidally driven waves in a glacial fjord. Data analysis and numerical modeling of the system suggest a surprising origin for the waves with potential consequences for the melting of glaciers.

Bio: Robert Sanchez is a new Assistant Professor at Harvey Mudd College with a joint appointment between the Mathematics Department and the Hixon Center for the Climate and Environment. Prior to Harvey Mudd, he was an NSF Postdoc Scholar at the University of Florida and he received his PhD in Physical Oceanography from the Scripps Institution of Oceanography.

A Signal Separation View of Classification (Ryan O'Dowd, CGU)
2025-11-17 16:15 - 17:15 | Estella 1021 (Emmy Noether Room), Pomona College, Claremont, CA, 91711, United States
Abstract: The problem of classification in machine learning has often been approached in terms of function approximation. In this talk, we propose an alternative approach for classification in arbitrary compact metric spaces which, in theory, yields both the number of classes, and a perfect classification using a minimal number of queried labels. Our approach uses localized trigonometric polynomial kernels initially developed for the point source signal separation problem in signal processing. Rather than point sources, we examine a convex combination of probability distributions representing the various classes from the machine learning classification problem. The localized kernel technique developed for separating point sources is then shown to separate the supports of these distributions. This is done in a hierarchical manner in our MASC algorithm to accommodate touching/overlapping class boundaries. The algorithm works in an active learning paradigm, deciding on points to query for their true class label and extending those labels to nearby points. We illustrate our theory on several simulated and real life data sets, including the Salinas and Indian Pines hyperspectral data sets and a document data set.

Non-vanishing of L-functions over function fields (Alexandra Florea, UC Irvine)
2025-11-18 12:15 - 13:10 | Estella 2099
I will talk about some results concerning the non-vanishing of $L$-functions associated to fixed order characters $ell$ at the central point over functions fields. Quadratic characters have been studied a lot over the years, and very good non-vanishing results are available in this case, due to work of Soundararajan. When focusing on cubic and higher order characters, much less is known. In this talk, I will explain how one can obtain a positive proportion of non-vanishing for any fixed order $ell$ characters, which goes to $0$ as $ell$ goes to infinity. This is based on joint work with C. David and M. Lalin.

Claremont Topology Seminar: Chris Grossack (UC Riverside)
2025-11-18 16:00 - 17:00 | Fletcher 104, Pitzer College, 1050 N Mills Ave, Claremont, 91711, United States
We welcome all undergraduate/graduate students and faculty to attend topology seminar!
Speaker: Chris Grossack (UC Riverside)
Title: Explicitly Computing Fukaya Categories of Surfaces
Abstract: Fukaya categories are rich and interesting invariants of symplectic manifolds that are often difficult to compute in practice. In the case of surfaces, however, the computation becomes pleasantly combinatorial, and can be carried out explicitly. In this expository talk we’ll explain why one might care about Fukaya categories and how one can compute them explicitly enough for computer implementation using tools from “Noncommutative Mirror Symmetry”. With any remaining time, we’ll explain the ideas behind the speaker’s PhD thesis, which relies heavily on this machinery.

CCMS Colloquium: Shriya Nagpal (Pitzer)
2025-11-21 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 Shriya Nagpal (Pitzer)

Title: Synchronization in Erdős–Rényi Graphs with Kuramoto Dynamics: A Graphon Approach

Abstract: Networks of coupled Kuramoto oscillators have been used to model a wide array of phenomena, including circadian rhythms, flashing fireflies, and high-voltage electric grids. In many such applications, synchronization is an emergent behavior of interest. Recent work has focused on understanding synchronization in random networks of Kuramoto oscillators. We contribute to this literature, by considering interaction networks generated by a graphon model known as a $W$-random network, and examine the dynamics of an infinite number of identical ​ Kuramoto oscillators. We show that with sufficient regularity on $W$, the solution to the dynamical system over a $W$-random network of size $n$ converges to the solution of the infinite graphon system, with high probability as $nrightarrowinfty$. We leverage this convergence result to study synchronization for identical Kuramoto oscillators on ErdH{o}s-R’enyi random graphs.

Bio: Shriya V. Nagpal is an Assistant Professor of Mathematics at Pitzer College. In 2024, she completed her Ph.D. in Applied Mathematics at Cornell University, where she was co-advised by Francesca Parise and Lindsay Anderson. Prior to joining Cornell in 2018, she received her bachelor’s degree in Mathematics from Trinity College. Her research leverages tools from network theory and dynamical systems to study emergent behavior in interconnected systems.

NO CCMS Colloquium this Friday!
2025-11-28 11:00 - 12:15 | Davidson Lecture Hall, CMC, 340 E 9th St, Claremont, CA, 91711, United States
We’ll be back next week!
Happy Thanksgiving!

Structure-Aware Adaptive Nonconvex Optimization for Deep Learning and Scientific Computing (Minxin Zhang, UCLA)
2025-12-01 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Abstract: Modern machine learning and scientific computing pose optimization challenges of unprecedented scale and complexity, demanding fundamental advances in both theory and algorithmic design for nonconvex optimization. This talk presents recent advances that address these challenges by exploiting matrix and tensor structures, integrating adaptivity, and leveraging sampling techniques. In the first part, I introduce AdaGO, a new optimizer that combines orthogonalized momentum updates with adaptive learning rates. Building on the recent success of the Muon optimizer in large language model training, AdaGO incorporates an AdaGrad-type stepsize that scales orthogonalized update directions by accumulated past gradient norms. This design preserves the structural advantage of orthogonalized updates while adapting stepsizes to noise and the optimization landscape. We establish optimal convergence rates for smooth nonconvex functions and demonstrate improved performance over Muon and Adam on classification and regression tasks. The second part focuses on zeroth-order global optimization. We develop a theoretical framework for inexact proximal point (IPP) methods for global optimization, establishing convergence guarantees when proximal operators are estimated either deterministically or stochastically. The quadratic regularization in the proximal operator induces a concentrated Gibbs measure landscape that facilitates effective sampling. We propose two sampling-based algorithms: TT-IPP, which constructs a low-rank tensor-train (TT) approximation using a randomized TT-cross algorithm, and MC-IPP, which employs Monte Carlo integration. Both IPP algorithms adaptively balance efficiency and accuracy in proximal operator estimation, achieving strong performance across diverse benchmark functions and applications. Together, these works advance structure-aware adaptive first-order optimization for deep learning and zeroth-order global optimization in scientific computing.

Positivity aspects of complete homogeneous symmetric polynomials (Stephan Garcia, Pomona)
2025-12-02 12:15 - 13:10 | Estella 2099
Hunter’s theorem ensures that the complete homogeneous symmetric (CHS) polynomials of even degree are positive definite functions. We provide new proofs of Hunter’s theorem, applications to operator theory, and a noncommutative (NC) generalization that sheds light even on the commutative case. Surprisingly, this work emerged from a problem in analytic combinatorics.

Claremont Topology Seminar: Indraneel Tambe (UCLA)
2025-12-02 16:00 - 17:00 | Fletcher 104, Pitzer College, 1050 N Mills Ave, Claremont, 91711, United States
We welcome all undergraduate/graduate students and faculty to attend topology seminar!
Speaker: Indraneel Tambe (UCLA)
Title: Steinberg skein relations at roots of unity
Abstract: This talk discusses some of the relationships between skein theory and the representation theory of quantum sl2 when q is a root of unity. Specifically, I focus on the Frobenius pullback functor on Uq sl2 representations and see how this relates to Bonahon-Wong’s Frobenius skein homomorphism between Kauffman bracket skein modules. I’ll describe results from my joint work with Vijay Higgins in which we proved what we called Steinberg skein identities and used these in a new proof of the well-definition of the Frobenius skein homomorphism.

CCMS Colloquium: Konstantin Zuev (Caltech)
2025-12-05 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 Konstantin Zuev (Caltech)

Title: Course-Prerequisite Networks

Abstract: An academic curriculum is a complex system of courses and their interactions that lies at the heart of an academic institution and underlies its educational mission. Understanding these systems is essential for providing high-quality education. Course-prerequisite networks (CPNs) are directed acyclic graphs that model academic curricula by representing courses as nodes and prerequisite relationships between them as directed links. In this talk, we will show how CPNs can be used to visualize, analyze, and optimize curricula; identify key courses; allocate teaching resources; quantify the strength of knowledge flow between departments; and uncover the most influential and interdisciplinary areas of study. The proposed methodology applies to any CPN and is illustrated using a network of courses taught at the California Institute of Technology. If time permits, we will also discuss three new global CPN measures, breadth, depth, and flux, which enable macro-scale comparisons of different curricula. We illustrate these measures numerically using three real and synthetic CPNs from the Cyprus University of Technology, the California Institute of Technology, and Johns Hopkins University.

Bio: Dr. Konstantin Zuev is a Teaching Professor of Computing and Mathematical Sciences at the California Institute of Technology, where he teaches a variety of courses in mathematics and statistics and conducts research on network science with undergraduate students. He is the author of about 30 papers and a forthcoming book, Fundamentals of Statistical Inference: Foundations of Data Analysis. His teaching and research have been recognized with several awards: the ASCIT Teaching Award (2018 & 2023), the Carver Mead Seed Fund Grant (2023), the Graduate Student Council Teaching Award (2023), the Humboldt Research Fellowship for Experienced Researchers (2021), and the Northrop Grumman Prize for Excellence in Teaching (2019). For more information about his background, please visit http://www.its.caltech.edu/~zuev/index.html

GEMS December 6th Session
2025-12-06 10:00 - 11:55 | Shanahan B450, Harvey Mudd College, 301 Platt Blvd., Claremont, 91711, United States
This GEMS session will be facilitated by Professor Ryan Aschoff from the Claremont Graduate University.

Title: Randomness: Creating Order from Chaos

Abstract:
From the hiss of white noise to the gentle hum of ocean waves, randomness surrounds us — yet hidden within that chaos lies remarkable order. In this talk, we’ll explore how unpredictable events, when viewed collectively, give rise to smooth and universal patterns. We’ll listen to and visualize the “colors” of noise — white, pink, and brown — to see how sound encodes randomness across different frequencies. We’ll discover how unrelated random events, like coin flips or marble drops, merge into beautifully predictable bell-shaped distributions. And we’ll watch how diffusion and blurring transform disorder into structure, revealing the same mathematics behind sound, heat, and motion.

Along the way, we’ll take part in hands-on activities: generating and analyzing noise spectra, building simple low-pass “smoothing” filters, and experimenting with diffusion and random walks to watch chaos become order before our eyes. No advanced math required — just curiosity and a willingness to play with randomness!

Fractional Brownian Motion: Small Increments and First Exit Time from One-sided Barrier (Qidi Peng, CGU)
2026-01-26 16:00 - 17:00 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Abstract: The talk introduces a conjecture on the first exit time of fractional Brownian motion: the upper-tail probability for a fractional Brownian motion to first exit a positive-valued barrier over time T has the exact asymptotic rate T^(H-1), where H is the Hurst parameter of the fractional Brownian motion. The talk tries to understand this conjecture by providing several equivalent statements. We then introduce the best effort made in the current literature towards solving this conjecture.

The forbidden quiver of a link (Sam Nelson, CMC)
2026-01-27 12:15 - 13:10 | Estella 2099
Virtual links can be represented as equivalence classes of Gauss diagrams under Reidemeister moves. The Forbidden Moves are moves which look plausible but change the virtual isotopy class of the knot or link — indeed, virtual knots are all trivial if we allow forbidden moves. However, virtual links remain non-trivial. In this talk we show how to think of these links as quivers and in the process, define several polynomial invariants of link homotopy. This is joint work with Stella Shah (Scripps College).

Sampling from the proper colorings of a graph using a number of colors linear in the maximum degree in expected linear time (Mark Huber, CMC)
2026-01-29 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Abstract: A proper coloring of a graph is an assignment of colors from ( {1, 2, ldots, k} ) to each node of a graph such that no two nodes connected by an edge receive the same color. Let ( Delta ) denote the maximum degree of the graph. If ( k geq Delta + 1 ) then at least one proper coloring always exists. However, counting the number of proper colorings of an arbitrary graph is a #P-complete problem, even when ( Delta = 3 ). This means finding a polynomial time exact algorithm is unlikely to be found. On the other hand, if a user can sample uniformly at random from the proper colorings of a graph, then it becomes possible to approximately count the number of proper colorings to arbitrary precision in polynomial time. This work presents the first algorithm that has an expected running time that is linear in the size of the graph under the condition that ( k > 3.637 Delta ). Joint work with Kritika Bhandari.

CCMS Colloquium: John Baez (UCR)
2026-01-30 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 John Baez (UCR)

Title: The mathematics of tuning systems

Abstract: Leibniz said “Music is the pleasure the human mind experiences from counting without being aware that it is counting.” The first step is choosing a tuning system — the frequency ratios between pitches in a scale. Different kinds of music sound best in different tuning systems! In music from the Middle Ages until today, new musical styles have gone hand in hand with mathematical innovations in tuning systems. Here I will focus on a few of the most important and beautiful Western systems, from Pythagorean tuning to today’s reigning champion: equal temperament. Can you hear the difference? What will come next?

Bio:
John Baez is a mathematical physicist, formerly at U. C. Riverside and currently the Maxwell Fellow at the University of Edinburgh. He is known for the Cobordism Hypothesis connecting manifolds to higher categories. In 1993 he began writing This Week’s Finds in Mathematical Physics, which has been called the world’s first blog. Since then he has helped start two well-known blogs: The n-Category Caf e, a group blog on math and physics, and Azimuth, on mathematics and ecological issues. He also writes a regular column in Notices of the American Mathematical Society.

Relationships between skein algebras (Helen Wong, CMC)
2026-02-03 12:15 - 13:10 | Estella 2099
We will examine the multiplicative structure of two skein algebras— the usual Kauffman bracket skein algebra of a surface (generated by loops) and a generalization of it due to Roger-Yang (generated by loops and arcs). In joint work with Chloe Marple, we found a homomorphism between the usual skein algebra for a closed torus and the Roger-Yang skein algebra for a twice-punctured annulus. In this talk, I’ll present some ways we used that homomorphism to do computations, and whether there might be similar relationships between skein algebras of other surfaces.

CCMS Colloquium: Teal Witter (CMC)
2026-02-06 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 Teal Witter (CMC)

Title: Exactly Computing do-Shapley Values

Abstract:
Causal questions lie at the heart of scientific inquiry, from evaluating economic policies to determining medical treatments. Yet, observational data alone is often insufficient due to the fundamental problem of causal inference: we cannot observe the counterfactual world where a specific intervention did not occur. Structural Causal Models (SCMs) offer a powerful solution by explicitly modeling the underlying mechanisms of a system. By formalizing data generation, SCMs allow us to use the do-operator to rigorously simulate interventions, answering questions like, “If a patient were administered prednisone and made to stop smoking, what would be their expected pain level?”

However, characterizing a system through individual queries is computationally daunting. As the number of features d grows, the landscape of possible interventions scales exponentially (2^d). To extract interpretable insights from this combinatorial complexity, we utilize the do-Shapley value, a game-theoretic framework that attributes the complicated dynamics of an SCM to individual features.

In this talk, I will present a new algorithmic approach that makes computing these values more tractable. We show that the causal landscape is structured into “irreducible sets”, a building block where multiple interventions yield identical effects. By leveraging this structure, we introduce an algorithm that computes do-Shapley values exactly, with runtime that depends on the graph’s complexity rather than 2^d. We further propose an estimator that targets these sets directly, producing more accurate estimates than prior work by several orders of magnitude or more.

Joint work with Álvaro Parafita, Tomas Garriga, Maximilian Muschalik, Fabian Fumagalli, Axel Brando, and Lucas Rosenblatt.

Bio: Teal is an Assistant Professor of Mathematics and Computer Science at Claremont McKenna College. His recent research explores randomized algorithms for problems in explainable AI and generative AI. More broadly, he is interested in leveraging ideas from theoretical computer science and machine learning to design provably accurate algorithms. Before joining the consortium, Teal completed his Ph.D. in Computer Science at New York University, where he was supported by an NSF Graduate Research Fellowship. Prior to graduate school, Teal attended Middlebury College.

GEMS February 7th Session
2026-02-07 10:00 - 11:55 | Shanahan B450, Harvey Mudd College, 301 Platt Blvd., Claremont, 91711, United States
This GEMS session will be facilitated by Professor Teal Witter from Claremont McKenna College.

Title: Who Can Write Down the Bigger Number?

Abstract:
If you had fifteen seconds to write the largest distinct whole number possible on an index card, what would you write? While most would look to the physical world for inspiration—counting the grains of sand in the Sahara or the atoms in the observable universe—we will explore much larger numbers. Our journey will take us beyond the limits of scientific notation, moving from “power towers” and the mind-bending Ackermann function to the very edge of computer science. Ultimately, we will arrive at the “Busy Beaver” sequence: numbers so unfathomably vast that they are theoretically uncomputable. Join us to explore the boundaries of language, logic, and the truly gargantuan.

A BKM-type criterion for the 3D incompressible Euler equations (Mustafa Aydin, USC)
2026-02-09 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Abstract: The three-dimensional incompressible Euler equations describe the motion of an ideal fluid, yet the mechanisms that govern the possible loss of regularity of smooth solutions remain only partially understood. A classical result of Beale, Kato, and Majda shows that if a smooth solution breaks down in finite time, then the time integral of the vorticity’s supremum norm must diverge, providing a sharp conditional criterion for regularity.
In this talk, I will present a new blow-up criterion in the spirit of the Beale–Kato–Majda theorem that emphasizes a different form of control. Instead of requiring bounds on the full vorticity, the criterion involves tangential derivatives of the velocity field, and shows that smooth solutions persist as long as these derivatives remain appropriately bounded in time. The result holds in a variety of settings, including the whole space, periodic domains, and domains with boundaries.

Analysis Seminar: Generalized Elmendorf’s Theorem in Context (Sofía Martínez Alberga, Bryn Mawr College)
2026-02-12 16:15 - 17:15 | Estella 2099, Pomona College, 610 N. College Ave., Claremont, CA, United States
Abstract: In general, the objective of algebraic topology is to classify spaces using some algebraic invariants or up to some notion of equivalence. In the area of equivariant homotopy theory, the goal is the same but now spaces equipped with a group action are considered and algebraic invariants of choice are homotopy groups. It turns out there is an analogous version of Whitehead’s theorem in the equivariant setting which in some sense motivates studying weak homotopy equivalences over homotopy equivalences. This talk will review some of these homotopical notions and introduce Elmendorf’s theorem. Proved in the eighties, this theorem sheds some light on how one can better understand equivariant homotopical notions as functors from the orbit category of the group to the category of topological spaces. Also, in this talk we will address how this perspective is used more modernly to understand better equivariant notions of other categories and to expand nonequivariant notions to equivariant ones.

CCMS Colloquium: Sofia Martinez Alberga (Bryn Mawr College)
2026-02-13 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 Sofia Martinez Alberga (Bryn Mawr College)

Title: Stay in the Loop and Fun Group

Abstract: In this talk, we will discuss the goal of algebraic topology. After we will discuss a topological space that can be associated with any topological space, say $X$, and base point, $b in X$: the based loop space denoted $Omega(X, b)$. The loop space has some interesting algebraic structure that allows us to define an invariant for spaces. We will see how this invariant can be used more generally and when the action of a group is present on the space.

Bio: Dr. Sofía Martínez Alberga is a Research Associate at Bryn Mawr College working in algebraic topology. Originally born and raised in southern California, she earned her Bachelor’s of Science in mathematics from the University of California, Riverside in 2019 and that same year she won the NSF Graduate Research Fellowship and the Math Alliance Fellowship. Dr. Martínez Alberga earned her PhD from Purdue University and during graduate school, she held roles like MSRI-Undergraduate Program graduate research assistant, Enhancing Diversity Graduate Education summer program graduate mentor, and Women In Science Programs (WISP) Liaison. Furthermore Dr. Martínez Alberga has been invited to attend and speak at conferences and seminars internationally and has organized and secured grants for sessions at major conferences such as JMM.
