Abstract: Recently, there has been great progress in understanding rank-one rigidity phenomena in dynamics. “Rank-one” rigidity refers the rigidity of a single diffeomorphism or flow rather than the rigidity of a bigger group action. Rank one rigidity in dynamics has close ties to geometric rigidity problems in negative and non-positive curvature such as marked length spectrum rigidity and boundary rigidity and makes use of a variety of methods, such as microlocal analysis, coarse geometry, and KAM theory. This workshop will bring together researchers working on rank-one problems from a variety of points of view to discuss recent work and the future directions and challenges in the field.
This workshop will also feature a 2-day special session in honor of Keith Burns’ 70th birthday.
Speaker: Avik Das (UMD) - When: Mon, October 19, 2026 - 2:00pm Where: Phys1219
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Abstract: We provide an example of Banach spaces $X$ and $E$ such that $X$ coarsely embeds into $E$, but $X$ does not uniformly embed into $E$, resolving an open problem in the nonlinear theory of Banach spaces. We then investigate the converse question whether the existence of a uniform embedding $X \to E$ implies the existence of a coarse embedding $X \to E$. We strengthen a theorem of Rosendal, showing it holds under coarse, rather than linear, embeddability of $E \oplus E$ into $E$. We then construct an example of a Banach space $E$ such that $E \oplus E$ does not coarsely embed into $E$.
Speaker: Sotiria Chatzimarkou (University of Patras) - https://www.sotiriachatzimarkou.com When: Mon, October 19, 2026 - 3:00pm Where: Kirwan Hall 3206
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Abstract: Nakajima quiver varieties are a large class of hyperk\"ahler manifolds sharing many properties with the moduli spaces of Higgs bundles. Inspired by this connection and by the proof of existence of the conformal limit for Higgs bundles, in this talk we will present a conformal limit construction for Nakajima quiver varieties.
Speaker: Jiwoong Jang (UMD) - When: Mon, October 19, 2026 - 3:00pm Where: Kirwan Hall 1313
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Abstract: In this talk, we look at cell-cell adhesion through a large-scale limit of the Patlak-Keller-Segel system. Our primary motivation is the celebrated Differential Adhesion Hypothesis (DAH), a central belief in the study of cell-cell adhesion proposed by Malcolm Steinberg in 1962, which posits that cell populations self-organize by minimizing adhesion energy in a manner analogous to fluids minimizing surface tension. We provide an energy converge result in the large-scale limit, which then governs the macroscopic evolution and equilibria. Furthermore, we recover the regimes predicted by the DAH, and lastly, we identify the evolution law of cells as the multiphase Hele-Shaw flow with surface tension.
Speaker: Madeleine Youngs (UMD (AOSC)) - https://mkyoungs.github.io/ When: Mon, October 19, 2026 - 4:15pm Where: Kirwan Hall 3206
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Abstract: Baroclinic and barotropic instabilities are major dynamical features of the atmosphere and ocean. They can be characterized by an instability with a linear growth rate, and the instability can be identified by a necessary condition in the sign change of the potential vorticity gradient. However, there are still open questions about their dynamics, primarily how baroclinic (growing on vertical shear) and barotropic (horizontal shear) interact with each other through their potential vorticity. In this seminar I present several examples of these questions and how I attempt to address them. First, I investigate mixed instability and determine that the 1-dimensional conditions for instability are not sufficient in the mixed case. Then, I show an application of this to the Southern Ocean. Finally, I present work where I investigate a fundamental oscillation present in atmospheric baroclinic instability with a dynamical mode decomposition. Moving forward, my group will use these dynamical systems techniques to investigate cross-scale turbulence and larger climate-scale problems such as the Atlantic Meridional Overturning Collapse or Antarctic Ice Shelf tipping points.
Abstract: This talk explores recent research on rigidity phenomena in non-linear infinite-dimensional geometries, focusing on two key examples: Ebin's space of Riemannian metrics and the Wasserstein space of probability measures. Both are infinite-dimensional spaces built over a finite-dimensional base. I will show that these spaces do not gain exotic new symmetries; nearly every isometry arises directly from symmetries of the base, with a single exception for the Wasserstein space over the real line. Furthermore, these spaces faithfully preserve their structural origins: Ebin's space determines the underlying smooth manifold up to diffeomorphism, and the Wasserstein space determines the Riemannian manifold up to isometry.
Speaker: Kyle Hall (UMD/Atmosphere) - https://aosc.umd.edu/people/kyle-hall When: Tue, October 20, 2026 - 2:00pm Where: Kirwan Hall 3206
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Abstract: Climate simulations can take supercomputers months to run. Could an AI trained on just 41 years of data learn to imitate them? We test a new ocean-atmosphere emulator built on the same technology as AI image generators, asking whether it can reproduce El Niño and respond realistically to rising CO2.
Emulating internal variability and CO2-associated change in the ocean-atmosphere system at monthly scales using coupled latent diffusion models
Artificial Intelligence (AI)-based emulators of the coupled ocean-atmosphere system build on recent successes in AI-based weather prediction. It is crucial that these coupled emulators simultaneously characterize coupled modes of internal variability like the El Niño-Southern Oscillation (ENSO) and respond to external forcings appropriately. Training them to do so remains challenging due to the limited climate record and entanglements between slow ocean variability and forced changes. In this seminar, we explore the extent to which Monthly Diffusion (MDv1), a coupled ocean-atmosphere climate emulator based on latent diffusion, learns to represent internal variability and CO2-associated changes in the U.S. Department of Energy's Energy Exascale Earth System Model version two (E3SMv2). We train MDv1 on a 41-year segment of a single E3SMv2 historical realization, and compare its learned ensemble behavior under a prescribed SSP3-7.0 CO2-pathway to that of a reference ensemble composed of held-out E3SMv2 ensemble members. We show that MDv1 captures aspects of spatiotemporal ENSO variability, while displaying variable-specific biases in CO2-associated change.
Speaker: Doron Levy (UMD) - https://www.math.umd.edu/~dlevy/ When: Tue, October 20, 2026 - 2:30pm Where: Kirwan Hall 3206
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Abstract: How many ways can six 2×4 LEGO bricks be combined? For thirty years LEGO quoted 102,981,500, until Søren Eilers showed that this counted only towers; the true number is 915,103,765. This talk presents two extensions of the problem, both developed in collaboration with AI. First, we color the bricks. Burnside’s lemma reduces every colored count to the distribution of shapes by how a 180° rotation permutes their bricks. A new decomposition method computes this distribution exactly through nine bricks, yielding the first exact colored counts beyond five. It also shows that symmetric shapes become exponentially rare, with a striking odd–even alternation. Second, we add gravity: towers that may only grow upward. A mean-field approximation reduces counting to the equation G = zΦ(G), which gives a growth rate of 92.31 per brick and the full asymptotic formula in closed form. Rigorous bounds then place the true directed growth rate between 36.93 and 92.31.
Speaker: Turbo Ho (Towson University) - When: Tue, October 20, 2026 - 3:30pm Where: Kirwan Hall 1311
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Abstract: A major theme in mathematics is the classification problem: given a class of objects and a notion of equivalence, classify the objects up to the equivalence. In algebra, this often takes the form of isomorphism problems. There are multiple ways to formalize the complexity of isomorphism problems. A particularly fruitful way of doing this is comparing them via Borel reduction defined by Friedman and Stanley.
In this talk, we study an effective analogue of the Borel complexity of isomorphism problems. Instead of Borel reductions, we consider computable reductions, where the reduction function must be computable. Furthermore, instead of considering the atomic diagram of the structure, we consider (algebraic) finitely generated, computably enumerated presentations instead. In this setting, we consider the isomorphism problems of various classes of algebraic structures, and compare them to well-studied benchmark equivalence relations. We also obtain some general results connecting the algebraic properties of varieties and the complexity of their isomorphism problems.
Speaker: Ruth Chapman (London School of Economics, UK) - When: Tue, October 20, 2026 - 3:30pm Where: Kirwan Hall 3206
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Abstract: A non-autonomous system can undergo a rapid change of state inresponse to a small or slow change in forcing, due to the presence of nonlinear
processes that give rise to critical transitions or tipping points. Such transitions are
thought possible in various subsystems (tipping elements) of the Earth’s climate
system. The Atlantic Meridional Overturning Circulation (AMOC) is considered one
such tipping element where models of varying complexity have shown the potential
for bi-stability and tipping. I will present a conceptual model of the AMOC which can
be used to investigate tipping mechanisms. We utilise an Ordered Line Integral
Method (OLIM, Cameron et al 2012) to approximate the Quasipotential of this low-
order system and explore noise tipping paths. We are working to extend this method
for 3 dimensional systems with anisotropic noise to investigate the role of additional
ocean basins in the tipping of this circulation. This work is supported by a SIAM
postdoctoral support grant.
Speaker: Francesco Gaffi ( University of Bergamo) - https://francescogaffi.github.io/ When: Tue, October 20, 2026 - 3:30pm Where: PHY 2106
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Abstract: Slice sampling is a standard Monte Carlo technique for Dirichlet process (DP)--based models, widely used in posterior simulation. However, formal assessments of the scalability of posterior slice samplers have remained largely unexplored, primarily because the computational cost of a slice-sampling iteration is random and potentially unbounded. In this work, we obtain high-probability bounds on the computational complexity of DP slice samplers. Our main results show that, uniformly across posterior cluster-growth regimes, the overhead induced by slice variables, relative to the number of clusters supported by the posterior, is $O_{\mathbb P}(\log n)$. As a consequence, even in worst-case configurations, super-linear blow-ups in per-iteration computational cost occur with vanishing probability. Our analysis applies broadly to DP--based models without any likelihood-specific assumptions, still providing complexity guarantees for posterior sampling on arbitrary datasets. These results establish a theoretical foundation for assessing the practical scalability of slice sampling in DP-based models.
Speaker: Rémy Mahfouf (École Polytechnique Fédérale de Lausanne) - http://remymahfouf.com/ When: Wed, October 21, 2026 - 2:00pm Where: Kirwan Hall 1311
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Abstract: We identify the scaling limit of full-plane Kadanoff–Ceva fermions
on generic, non-degenerate s-embeddings. In this broad setting, the scaling
limits are described in terms of solutions to conjugate Beltrami equations with
prescribed singularities. For the underlying Ising model, this leads to the
scaling limit of the energy–energy correlations connecting the scaling limits of
(near-)critical planar Ising models to Green kernels of uniformly elliptic operators
and quasiconformal mappings. For grids approximating bounded domains
in the complex plane, we establish, in the scaling regime, the conformal covariance
of the energy density on critical doubly periodic graphs. Moreover, we prove a connection between the planar Ising energy field in smooth limiting strict and (massive)-holomorphic fermions defined on surfaces of the Minkowski space R^{(2,1)}. These results highlight that the scaling limits of generic (near-)critical Ising models naturally live on a substantially richer conformal structure than the classical Euclidean one.
Speaker: Eric Nalisnick (Johns Hopkins University) - https://enalisnick.github.io/ When: Thu, October 22, 2026 - 3:30pm Where: Kirwan Hall 1311
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Abstract: In safety-critical domains such as healthcare, AI will not replace human experts for the foreseeable future: models often lack nuanced contextual information and accountability will require that humans provide oversight. It is better to think not in terms of isolated AI systems but rather human-AI teams. In this talk, I will present a statistical framing of human-AI collaboration, first discussing when three distinct workflows---assistance, combination, and delegation---preserve the calibration of the underlying human and AI. I will then discuss learning in the delegation setting, including how to extend the optimization objective to multiple, perhaps never-before-seen humans.