Abstract: This workshop aims to unite leading experts and emerging researchers in the fields of minimal dynamics, renormalization, and C∗-algebras to explore cutting-edge advancements and foster interdisciplinary collaboration. By bringing together these communities who rarely have the opportunity to engage directly, the workshop will provide a unique forum for the exchange of ideas and the cross-pollination of methods. Participants will showcase recent developments and establish connections between seemingly distinct areas, promoting a deeper understanding of shared mathematical structures.
The central focus of the workshop will be the study of topological invariants, such as cohomology and K-theory, and their roles in diverse contexts including dynamical systems, operator algebras, and mathematical physics. These invariants serve as powerful tools for capturing and classifying intricate properties of systems, and their study has profound implications across mathematics and physics. By highlighting these connections, the workshop will pave the way for new insights and collaborations, driving progress at the interface of these vibrant research areas.
Abstract: Kazhdan’s property (T) is a central concept in analytic group theory and is a strong rigidity property of unitary representations. In Kazhdan's original work, a relative version of property (T) for pairs of groups already appeared implicitly, and has since gained relevance. In this talk, I will discuss relative property (T) for unitary representations and more generally uniformly bounded representations; and some characterizations in terms of harmonic analysis involving suitable subspaces of Fourier multipliers.
Joint work with Ignacio Vergara.
Speaker: Gheehyun Nahm (Princeton University) - https://web.math.princeton.edu/~gn4470/ When: Mon, October 5, 2026 - 3:00pm Where: Kirwan Hall 3206
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Abstract: One challenge in studying knotted surfaces (surfaces embedded in 4-manifolds) is producing "genuinely new" examples. For example, until recently, every known knotted real projective plane in the 4-sphere could be expressed as the connected sum of a knotted 2-sphere and an unknotted real projective plane. Such knotted real projective planes are called reducible, or of Kinoshita type, and the Kinoshita conjecture stated that every knotted real projective plane in the 4-sphere is reducible.
I will begin by reviewing some constructions of knotted surfaces and surveying previous work on knotted real projective planes and irreducible knotted surfaces of other topological types. Then, I will present an irreducible real projective plane in the 4-sphere, which is joint work with Mark Hughes, Seungwon Kim, and Maggie Miller.
Speaker: Dr. Rafael Menezes (ICTP South American Institute for Fundamental Research) - https://rafaelmenezes.com/ When: Tue, October 6, 2026 - 12:30am Where: Kirwan Hall 3206
Speaker: Derek Paley ((UMD/Aerospace Engineering)) - https://aero.umd.edu/clark/faculty/58/Derek-A-Paley When: Tue, October 6, 2026 - 2:00pm Where: Kirwan Hall 3206
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Abstract: This talk will describe ongoing research in robotic triage at the University of Maryland under the DARPA Triage Challenge competition. UMD Team RoboScout aims to demonstrate a standoff sensing capability using COTS sensors placed on uncrewed air and ground mobile robotic platforms with AI-based casualty assessment algorithms that provide automated, real-time labeling of mass-casualty injuries in the field. The overall goal is to focus on assessing from a distance using non-contact, standoff signature acquisitions for the leading causes of preventable trauma death. The specific research objective is to apply tools from AI and perception, medical trauma and sensors, and robotics and autonomy to develop physiological signatures of severe injuries, data-driven models to detect them, and mobile platforms to collect the sensor data. UMD is a finalist in the upcoming competition in November 2026.
Bio: Derek A. Paley is the Willis H. Young Jr. Professor of Aerospace Engineering Education in the Department of Aerospace Engineering and the Institute for Systems Research at the University of Maryland, where he has been on the faculty since 2007. He served as Director of the Maryland Robotics Center (2019–2025) and the UMD Autonomous Micro Air Vehicle Team (2014–2024) and was a Sabbatical Fellow at The Johns Hopkins Applied Physics Laboratory in 2025-2026. Paley received the B.S. degree in Applied Physics from Yale University in 1997 and the Ph.D. degree in Mechanical and Aerospace Engineering from Princeton University in 2007. Paley’s research interests are in the area of dynamics and control, including AI and autonomy for national security and public safety. Paley is Fellow of the American Society of Mechanical Engineers, Associate Fellow of the American Institute of Aeronautics and Astronautics and Senior Member of the Institute of Electrical and Electronics Engineers. He served as an Associate Editor for AIAA Journal of Guidance, Control, and Dynamics, IEEE Transactions on Control of Network Systems, and IEEE Control Systems.
Speaker: Ramani Duraiswami (UMD/Computer Science) - https://users.umiacs.umd.edu/~ramanid/ When: Tue, October 6, 2026 - 2:30pm Where: Kirwan Hall 3206
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Abstract: My laboratory, the Physical Intelligence and Reality Lab, develops methods at the intersection of mathematical physics, sensing, scientific computing, and machine learning. In this seminar, I will describe two related research directions.
Differentiable physics through analytical gradients. Across science and engineering, forward models encode valuable domain knowledge. By making such models differentiable, we can integrate that knowledge directly into learning architectures and build more efficient pipelines for parameter estimation, inverse problems, and interpretable modeling in data-sparse settings. I will present examples spanning acoustics, signal processing, biology, and fluid mechanics.
Operator learning for partial differential equations. Numerical solvers for the operators governing physical systems have enabled the detailed exploration of individual problem instances. However, conventional solvers generally do not transfer computational effort from one solve to the next. Operator learning instead seeks to learn a surrogate for the underlying solution operator, enabling rapid inference for new inputs after training on a collection of solved instances. I will present our recent work on GAIA, a novel transformer-based architecture that addresses both forward and inverse problems in a single model.
Speaker: Artem Chernikov (UMD) - When: Tue, October 6, 2026 - 3:30pm Where: Kirwan Hall 1311
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Abstract: We survey the progress in the classification of theories without the strict order property, and present a proof that the classes of SOP2 and SOP3 first-order theories coincide (answering a question of Džamonja and Shelah). We also make some remarks on the use of AI in research in model theory.
Speaker: Juan R. Cebral (George Mason University) - When: Tue, October 6, 2026 - 3:30pm Where: Kirwan Hall 3206
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Abstract: Brain aneurysms are focalized pathological dilatations of cerebral arteries. Assessing their risk of rupture and hemorrhage is crucial for making personalized patient management decisions that minimize complications and optimize clinical outcomes. In addition to identifying and combining risk factors, detailed understanding of the mechanisms leading to vascular wall degeneration and weakening as well as healing after device deployment is extremely valuable for optimizing management strategies, designing novel therapeutic approaches, minimally invasive treatments and endovascular devices. In our previous work we have developed and used image-based patient-specific computational fluid dynamics models to identify hemodynamic rupture risk factors as well as flow conditions that favor healing after endovascular treatment. These (and others’) studies have highlighted several biological processes responsible for wall remodeling and degradation that drive the disease progression, including inflammation, cell proliferation, pathogen infiltration, hypoxia, collagen fiber remodeling and degradation, thrombus formation, device coverage and endothelizalization, to name a few. Motivated by these findings, our current efforts focus on the development of mathematical and computational models of cell behavior and interaction with their biomechanical environment. These models use a hybrid continuum-agent-based strategy where cells are modeled with a level set function that is convected with a local velocity field arising from a combination of forces including internal structural loads, contacts, chemotaxis, fluid drag, and tissue viscosity. Cell tracking and state variables are used to model processes such as cell activation, differentiation, phagocytosis, proliferation, damage, and death. Field equations are solved to update the biomechanics environment. This approach enables testing hypotheses about cell behavior and their effects and raises several intriguing mathematical questions.
Abstract: With any holomorphic vector bundle E over a compact base one can associate a certain line bundle L (often denoted O_{PE}(1)). According to a conjecture of Griffiths from the 1960s, if L admits a positively curved hermitian metric k, then E also admits a positively curved hermitian metric, h. In the talk I will discuss recent developments on this, in particular, a refutation of the conjecture.
Speaker: Emilio Dominguez (University of Maryland) - https://jedguez.github.io/ When: Wed, October 7, 2026 - 2:00pm Where: Kirwan Hall 3206
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Abstract: Given a 3-term perfect complex E over a variety X and a nonnegative integer r, we define a virtual cycle over the r-th degeneracy loci of E. This is done by modifying the complex E after pulling it back to certain blow ups of X.Â
We apply this construction to complexes over the Picard variety and the Hilbert schemes of non-singular complex projective surfaces. We recover, reprove and strengthen some of the known results involving the reduced cycles and the virtual cycles of the Hilbert schemes related to the curve counting theory and Vafa-Witten theory, respectively. This talk is based on joint work with Amin Gholampour.
Speaker: Sunder Sethuraman (University of Arizona) - https://sundersethuraman.github.io/ When: Wed, October 7, 2026 - 2:00pm Where: Kirwan Hall 1311
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Abstract: In a nutshell, we identify the fluctuation scaling limit of the bulk empirical mass in a system of particles (random walks) interacting by `gradient exclusion' on d-dimensional lattices as an SPDE, described as a generalized Ornstein-Uhlenbeck process. Although the hydrodynamic (LLN) limit has been shown in a variety of models, less is known about their fluctuations. A main difficulty is to perform a continuum homogenization of micro particle rates with respect to fluctuation scales. When starting in an invariant measure, so-called `Boltzmann-Gibbs' homogenizations have been successful. However, understanding the fluctuations, when starting from `non-equilibrium' initial conditions, has remained mostly an open question. In this talk, we describe progress on a general multi-scale procedure in d<4 to accomplish the needed homogenization. This is joint work with Claudio Landim.
Speaker: Perrin Ruth (University of Maryland, College Park) - When: Thu, October 8, 2026 - 5:00am Where: Kirwan Hall 1311
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Abstract: Ackermann's function is a function that exhibits extreme growth. Historically, it is an example of totally computable function that is not primitive recursive. Its inverse, on the other hand, grows extremely slowly. The inverse Ackermann function has been used to describe the efficiency of some algorithms, notably the union-find algorithm used for the online computation of connected components of graphs.
Speaker:Â Nam Le (Indiana) When: Thu, October 8, 2026 - 3:30pm Where: MTH3206
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Abstract: We present recent progress on the interior and global regularity of linearized Monge-Ampère equations. We also discuss several applications, including the semigeostrophic equations in meteorology, periodic homogenization, and the singular Abreu equation in complex geometry.
Speaker: Eliza O'Reilly (Johns Hopkins University) - https://sites.google.com/view/eliza-oreilly/home When: Thu, October 8, 2026 - 3:30pm Where: Kirwan Hall 1311
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Abstract: Random forests are a widely used class of prediction algorithms made of ensembles of randomized decision trees. The algorithms most commonly use only one covariate of the input data to partition the data in a given node of a tree. Oblique random forests are variants where splits are allowed to depend on linear combinations of the covariates. In this talk, we will discuss a class of efficiently generated random tree and forest estimators called oblique Mondrian trees and forests, as the trees are generated by first selecting a set of features from linear combinations of the covariates and then running a stochastic Mondrian process that hierarchically partitions the data along these features. Our theoretical analysis demonstrates that these estimators can adapt to dimension reduction models for which the output depends on a general low-dimensional relevant feature subspace and we quantify how robust the risk is with respect to error in the estimation of these relevant features. We will then discuss an approach for identifying the relevant feature subspace that uses a Mondrian forest to estimate the expected gradient outer product (EGOP). In addition, we introduce an iterative algorithm called Transformed Iterative Mondrian (TrIM) forest to improve the Mondrian forest estimator by using the EGOP estimate to update the set of features and weights used by the Mondrian partitioning mechanism.
Speaker: Alexander Volberg (Michigan State University) - When: Thu, October 8, 2026 - 3:45pm Where: Kirwan Hall 3206
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Abstract: Recent advances in classical and quantum learning required tools from harmonic analysis. We will mention tightness results for such quantum inequalities as 1) the comparison of operator norm and product norm of d-local hamiltonians, 2) Bohnenblust–Hille inequality for d-local hamiltonians and 3) for quantum Fourier entropy-influence conjecture. If time permits we also discuss the quantum Aaronson–Ambainis conjecture in a special case of anti-commuting Pauli strings. (Joint talk with the FFT2026 Conference)
Speaker: Mikhail Belkin (UCSD) - https://datascience.ucsd.edu/people/mikhail-belkin/ When: Fri, October 9, 2026 - 4:00pm Where: Kirwan Hall 3206
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Abstract: A trained Large Language Model (LLM) contains much of human knowledge. Yet, it is difficult to gauge the extent or accuracy of that knowledge, as LLMs do not always "know what they know'' and may even be unintentionally or actively misleading. In this talk I will discuss feature learning introducing Recursive Feature Machines—a powerful method originally designed for extracting relevant features from tabular data. I will show how this technique enables us to detect and guide LLM behaviors toward almost any desired concept by adding a multiple of fixed vectors in LLM activation spaces. I will give several examples including probing for whether LLM exhibits motivated reasoning. I will also comment on AI alignment, which is arguably the most important scientific problem of our time. (Part of the FFT 2026 Conference)
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