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.
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: 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: 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.