Abstract: Recent advances in experimental methods have provided unprecedented insight into biological systems at small scales. The proposed workshop will focus on new mathematical models that have been unlocked by these experimental advances. This includes models arising in neuroscience, ecology, cell motion, and physiology. One class of models that is of particular importance and will be at the heart of this workshop are structured PDEs, which can incorporate heterogeneity, spatial structure, and internal variables such as age or phenotype.
Our workshop will focus on new PDE models arising in biology and the development of methods to analyze them. It will highlight biological settings where PDE analysis have provided novel insights and where new PDE methods must be developed in the future.
Speaker: Lue Pan (Columbia University) - https://sites.google.com/view/luepan/home When: Mon, November 2, 2026 - 2:00pm Where: Kirwan Hall 3206
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Abstract: Let p be a prime. I will discuss my recent work with Matt Emerton, Toby Gee, and Xinwen Zhu concerning lifts of irreducible, totally odd, 2-dimensional mod p representations of the absolute Galois group of a totally real field.
Abstract: History-dependent constitutive models are central to material modeling because macroscopic material response often depends on loading history through memory effects emerging from microscale physics. Since these macroscopic constitutive laws are rarely available in closed form and their parameters are not directly measurable, they must be learned from data. This talk presents two complementary approaches to this learning problem, using data from microscopic and macroscopic scales.First, we consider operator learning of homogenized constitutive laws from microscopic unit-cell simulations, capturing dependence on both deformation history and microstructural properties. Here, we focus on characterizing the expressivity and complexity of a recurrent neural-operator architecture that uses internal variables to encode history.Second, we consider learning constitutive parameters from material testing, where parameter identifiability is often a major challenge. We show that a Bayesian optimal experimental design framework can be used to discover optimal designs of specimen geometries and loading paths that substantially reduce uncertainty in the identified parameters relative to randomly selected designs, especially for parameters associated with memory effects.
Speaker: Greg Chambers (Rice University) -Â https://math.rice.edu/~grc3/ When: Mon, November 2, 2026 - 3:00pm Where: Kirwan Hall 3206
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Abstract: In this talk, I will discuss the notion of monotone homotopies and sweepouts - what they are, when they exist, and why we care about them. In particular, we will show how they relate to the existence of minimal surfaces in certain noncompact settings, as well as recent work using them to find prescribed mean curvature surfaces. This talk will survey a number of articles with a variety of coauthors.
Speaker: Dana Dachman-Soled (UMD (ECE & UMIACS)) - https://user.eng.umd.edu/~danadach/ When: Mon, November 2, 2026 - 4:15pm Where: Kirwan Hall 3206
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Abstract: Modern cryptography and privacy-preserving technologies rely on mathematical tools to provide rigorous guarantees of security and privacy. In this talk, I will discuss two lines of research that illustrate how techniques from geometry, probability, and approximation theory can be used to address fundamental challenges in these areas.
First, I will discuss post-quantum cryptography, focusing on the Learning With Errors (LWE) problem, which underlies many leading cryptographic constructions designed to withstand attacks by quantum computers. I will describe our work developing mathematical frameworks and practical toolkits for estimating the concrete hardness of LWE in the presence of side information. These approaches use Gaussian approximations, convex geometry, and ellipsoidal optimization to incorporate information leaked to an adversary and quantify its impact on security.
Second, I will turn to privacy-preserving machine learning, focusing on training models using differentially private synthetic data. I will explain how polynomial approximation can be used to relate the preservation of low-dimensional marginals to guarantees on the excess risk of linear models trained on synthetic data.
Together, these results demonstrate how classical mathematical techniques can provide new insights and practical tools for modern problems in security and privacy.
Speaker: Aditya Kumar (UMD) - https://sites.google.com/view/adityakm When: Tue, November 3, 2026 - 12:30pm Where: Kirwan Hall 1310
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Abstract: We will discuss scalar curvature from the point of view of metric invariants. In particular, we will describe a new estimate for the codimension two width of circle bundles, and explain how it leads to counterexamples to the macroscopic version of Gromov’s Urysohn width conjecture, in dimensions four and higher. Based on joint work with B. Sen.
Speaker: Dr. James A. Yorke (University of Maryland, College Park) - https://ipst.umd.edu/people/james-a-yorke When: Tue, November 3, 2026 - 12:30pm Where: Kirwan Hall 3206
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Abstract: AI's present us with danger and opportunity. I will discuss some overdue changes we can make individually and as a community.
Speaker: Manuel Franco Sevilla (UMD/Physics) - http://flavor.physics.umd.edu/manuelf/ When: Tue, November 3, 2026 - 2:00pm Where: Kirwan Hall 3206
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Abstract: With the prospect of an unprecedented influx of data from the future Large Hadron Collider (LHC), in 1989 Tim Berners-Lee proposed the World Wide Web at CERN to help researchers share and navigate scientific information. Today, the enormous volumes of data produced by the LHC demand increasingly sophisticated tools to turn collisions into discoveries.
This talk explores how the LHCb experiment uses machine learning and AI to identify particles, select interesting events, and simulate detector responses. It then looks at emerging applications of large language models and AI agents to help particle physicists access knowledge, develop software, and support experiment operations, highlighting both their potential and the challenges of using them reliably in scientific research.
Speaker: Maria Cameron (UMD/Math) - https://www.math.umd.edu/~mariakc/ When: Tue, November 3, 2026 - 2:30pm Where: Kirwan Hall 3206
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Abstract: The advancement and availability of AI have had a major impact on mathematics research and education. I will share my thoughts on how we can reshape upper-division undergraduate and graduate applied math classes to take advantage of AI. I am thinking of courses that involve lecture and practice lab classes, a project-oriented agenda, mathematical, numerical, and applied components, and oral pass/not pass assessments and written exams.
Speaker: Shanyin Tong (University of Pennsylvania) - When: Tue, November 3, 2026 - 3:30pm Where: Kirwan Hall 3206
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Abstract: Mean-field games (MFGs) model non-cooperative games among large populations of agents and are widely applied in areas such as traffic flow, finance, and epidemic control. Inverse MFGs address the challenge of inferring environmental factors and interaction mechanisms from observed agent behavior. The coupled forward-backward structure of MFG equations makes solving these problems difficult and adds even greater complexity to their inverse problems. In this talk, I will discuss a policy iteration framework for solving inverse MFGs. This approach simplifies the problem by decoupling it into linear PDEs and linear inverse problems, leading to significant computational savings. The framework is flexible, accommodating numerical and machine learning methods for complex geometries and high-dimensional problems. I will also discuss how to combine this framework with operator learning to infer interaction terms. The talk will include convergence results for the policy iteration method, along with numerical examples demonstrating its accuracy and efficiency.
Speaker: Leonid Berlyand (Penn State University) - https://sites.psu.edu/leonidberlyand/ When: Wed, November 4, 2026 - 3:15pm Where: Kirwan Hall 3206
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Abstract:Â We begin with a brief overview of the rapidly developing research area of active matter (a.k.a. active materials). These materials are intrinsically out of equilibrium resulting in novel physical properties whose modeling and analysis requires the development of new mathematical tools. We focus on studying the onset of motion of a living cell (e.g., a keratocyte) driven by myosin contraction. We introduce a minimal two-dimensional free-boundary PDE model that captures the evolution of the cell shape and nonlinear diffusion of myosin.
We first consider a linear diffusion model with two sources of nonlinearity: Keller-Segel cross-diffusion term and the free boundary that models moving/deformable cell membranes. Here we establish asymptotic linear stability and derive the explicit formula for the stability-determining eigenvalue.
Next, we consider the effect of nonlinear myosin diffusion, which results in the change of the bifurcation type from super- to subcritical, and obtain an asymptotic representation of the bifurcation curve (for small velocities). This allows us to derive an explicit formula for the curvature at the bifurcation point that controls the bifurcation type. In the recent work in progress with the Heidelberg biophysics group, we study the relation between various types of nonlinear diffusion and bistability.
Finally, we discuss novel mathematical features of this free boundary model with a focus on non-self-adjointness, which plays a key role in the spectral stability analysis. Our mathematics reveals the physical origins of the non-self-adjoint of the operators in this free boundary  PDE model. We conclude by presenting an example when presence of a spectral gap does not guarantee stability and contrast this example with non linear stability in our minimal model.
Joint works with A. Safsten \& V. Rybalko (Transactions of AMS,2023, and Phys. Rev. E, 2022), with O. Krupchytskyi \& T. Laux (Journal of Nonlinear Scinence, 2026), and with A. Safsten \& L. Truskinovsky (ARMA, 2026), and with A. Safsten (2026-in progress). This work has been supported by NSF grants DMS-2404546, DMS-2005262, and DMS-2404546
Abstract: We consider one-space dimensional parabolic equations in nondivergence form with measurable coefficients. By using the convex integration method, we construct counterexamples to Sobolev estimates at $|p-2|\sim \kappa$, where $\kappa$ is the ellipticity constant. We show that estimates and unique solvability hold for $|p-2|
Abstract: Causal inference relies on human judgment to define questions, choose credible comparisons, and defend identifying assumptions, judgments that make analyses problem-specific. Modern AI has followed the opposite trajectory: general architectures that scale with data and compute, culminating in reusable foundation models, the pattern Sutton called the "bitter lesson." Can causal inference borrow from this lesson? We test it on panel data, where imputing untreated counterfactuals has produced a zoo of specialized estimators: synthetic controls, matrix completion, nearest neighbors, doubly robust procedures, etc.
The test unfolds in three acts. First, TabImpute repurposes a tabular foundation model for matrix completion via entry-wise featurization. Pre-trained once on synthetic matrices, it beats established imputation baselines zero-shot, but the featurization caps its scale. Second, MatrixFormer makes the architecture matrix-native: alternating row and column attention encodes the exchangeability and factor structure of matrix completion and scales to far larger matrices. With frozen weights — never trained on real data — it matches or beats specialized baselines across causal panels, tabular imputation, LLM benchmark-score prediction, and recommender systems. Third, an auto-research agent, given only a validation metric, searches the loss and synthetic-data mixture and improves the recipe beyond our manual tuning.
Together, these results suggest that synthetic pre-training plus compute can amortize estimator design, a concrete test of the bitter lesson in causal inference.
Bio: Raaz Dwivedi is an Assistant Professor of Operations Research and Information Engineering at Cornell University and Cornell Tech, and CTO and co-founder of Traversal. His research develops statistical and computational methods for reliable decision-making with incomplete data and limited computation, spanning causal inference, matrix completion, distribution compression, and efficient AI systems. He was previously a FODSI postdoctoral fellow at Harvard and MIT and earned his Ph.D. in EECS from UC Berkeley and B.Tech. in Electrical Engineering from IIT Bombay. His honors include the Blackwell–Rosenbluth Award, an ASA Best Student Paper Award, teaching awards at Harvard and Berkeley, and IIT Bombay’s President of India Gold Medal.
Speaker: Jefferson Baudin (Stockholm University and Northwestern University) - https://sites.google.com/view/jeffersonbaudin/home When: Fri, November 6, 2026 - 2:00pm Where: Kirwan Hall 3206
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Abstract: Our objective is to study smooth families of varieties admitting a nowhere vanishing top form (also known as K-trivial varieties), such as abelian varieties or K3 surfaces. Over the complex numbers, it is known that any smooth family of K-trivial varieties over a simply connected and projective base must be isotrivial. One of the key steps in this case is that the underlying variations of Hodge structures must be constant, together with semipositivity theorems.
In positive characteristic however, there exist non-isotrivial families of abelian surfaces over P^1, due to Moret-Bailly. Nonetheless, these abelian surfaces are all supersingular, meaning in a way that "their cohomology does not lift well to characteristic zero". In this talk, we will show that a smooth family of K-trivial varieties over a projective simply connected basis must be constant, as long as at least one fiber is not supersingular in the sense above. One of the crucial inputs come from a positive characteristic analogue of variation of Hodge structures, which we will explain. This is joint work with Zsolt Patakfalvi and Yang Zhang.
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