Speaker: Kobe Marshall-Stevens (Johns Hopkins University ) When: Tue, September 8, 2026 - 12:30pm Where: Kirwan Hall 1310
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Abstract: Isoperimetric boundaries minimise area for fixed enclosed volumes, with sharp regularity theory ensuring they are smooth away from a closed singular set of codimension seven. I will discuss recent work, with G. Niu, which constructs isoperimetric regions from hypersurfaces in closed manifolds. As a direct application, we show that a wide variety of topological types and singular sets arise in isoperimetric boundaries.
Speaker: Dr. Holly Moeller (UCSB) - https://www.igpms.ucsb.edu/people/affiliates/holly-moeller When: Tue, September 8, 2026 - 12:30pm Where: Kirwan Hall 3206
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Abstract: While biologists typically think of an organism's metabolism as hard-wired in its DNA, in reality a vast array of species gain access to additional forms of metabolism from other species. This “acquired metabolism” can be obtained through interactions ranging from mutualism to predation, creating opportunities for niche expansion and, ultimately, evolutionary diversification. I'll focus on two examples of acquired metabolism—chloroplast-stealing marine microbes and tree-fungal mutualisms—to illustrate how these metabolic exchanges create and maintain diversity on our planet. We'll explore these systems using a combination of field observations (and collections), laboratory experiments, and, especially, mathematical models, demonstrating how the synergy between these approaches can give us insight into the mechanisms underlying acquired metabolism.
Speaker: Jacob Stern (CUNY Graduate Center) - When: Tue, September 8, 2026 - 3:30pm Where: Kirwan Hall 1311
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Abstract: For expansions of linear orders many different notions of minimality may be considered. Among the most restrictive of these is weak o-minimality while among the least restrictive is dp-minimality, but there are also many other interrelated notions. We expand on machinery introduced by Guingona and Flenner to show that in the context of divisible ordered abelian groups many of these notions coincide. In particular we show that a locally convexly or- derable expansion of a divisible ordered abelian group is weakly o-minimal. This proves the equivalence of several intermediate minimality notions and gives several nice algebraic properties of such structures.
Speaker: Ling Liang (University of Tennessee, Knoxville) - When: Tue, September 8, 2026 - 3:30pm Where: Kirwan Hall 3206
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Abstract: The proximal augmented Lagrangian method (pALM) is a powerful framework for constrained convex optimization, but its practical performance often depends on absolute error criteria that require carefully tuned, summable tolerance sequences. In this talk, we introduce ripALM, a true relative-type inexact pALM that replaces these prescribed sequences with a single tolerance parameter tied to the progress of the algorithm. Unlike existing relative-type approaches, ripALM preserves the original pALM structure without an additional correction step and accommodates efficient first- and second-order subproblem solvers. We establish global convergence, ergodic and last-iterate convergence rates, and asymptotic superlinear convergence under a suitable error-bound condition. Numerical experiments on optimal transport and sparse-recovery problems demonstrate that ripALM is robust to parameter choices and can substantially reduce computational effort. We also discuss CompositeOT, an ongoing effort to build a unified, high-accuracy solver for a broad class of non-entropic composite optimal transport models.
Abstract: Mathematics of Dynamical Systems in Modern Machine Learning is a workshop that brings together mathematicians, computational scientists, and machine learning researchers to develop a unified dynamical-systems viewpoint for understanding and improving modern ML. The central premise is that training algorithms, model updates, and agent interactions can be viewed as dynamical processes shaped by iterative computation, feedback, and data–parameter coupling, and that tools from dynamical systems, numerical analysis, optimization, and control can provide principled insight into stability, robustness, efficiency, and interpretability. The program will feature invited talks, focused sessions, and panel discussions spanning broad themes such as learning dynamics under practical computational constraints, structure-aware and physically guided learning, optimization viewed through the lens of dynamical behavior, and the dynamics of adaptive or agent-based learning systems. The workshop also aims to catalyze new cross-disciplinary collaborations and produce community-facing outcomes.
Speaker: Yu Gu (UMD) - When: Wed, September 9, 2026 - 2:00pm Where: Kirwan Hall 1311
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Abstract: We study the open KPZ equation, a prototypical one-dimensional random growth model subject to boundary conditions. Using stochastic analytic tools, we show that a suitably resampled Brownian motion describes its long-time behavior. This is based on a joint work with Alex Dunlap and Tommaso Rosati.
Speaker: Alena Erchenko (University of Oregon ) - https://sites.google.com/view/aerchenko/home When: Thu, September 10, 2026 - 2:00pm Where: Kirwan Hall 3206
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Abstract: We introduce new normal forms for vector fields in a tubular neighborhood of hyperbolic periodic orbits for flows on 3-manifolds and normal forms for contact forms in the case of Reeb flows. These normal forms detect dynamical information of the flow, such as the Lyapunov exponents, the return time of the flow to the section, and the Anosov and Foulon-Hasselblatt classes around these periodic orbits. We will also discuss various rigidity and flexibility problems for smooth Anosov flows on 3-manifolds. This talk is based on joint work with Kurt Vinhage and Yun Yang.
Speaker: Jincheng Yang (Hopkins) When: Thu, September 10, 2026 - 3:30pm Where: MTH3206
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Abstract: We discuss the construction of a smooth solution to the kinetic Landau equation with "very hard" potential, that blows up in a self-similar fashion and exhibit implosion in macroscopic quantities. The solution is built around a local Maxwellian that corresponds to smooth imploding solution of compressible Euler. This is achieved by the stability analysis on macroscopic hydrodynamic quantities and the remaining microscopic kinetic quantities of the perturbation.
Speaker: Yuliang Xu (Johns Hopkins University) - https://sites.google.com/view/yuliang-xu/ When: Thu, September 10, 2026 - 3:30pm Where: Kirwan Hall 1311
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Abstract: We propose a function-valued evaluation metric for generative models based on the relative density ratio (RDR) designed to characterize distributional differences between real and generated samples. As an evaluation metric, the RDR function preserves ϕ-divergence between two distributions, enables sample-level evaluation that facilitates downstream investigations of feature-specific distributional differences, and has a bounded range that affords clear interpretability and numerical stability. Function estimation of the RDR is achieved efficiently through optimization on the variational form of ϕ-divergence. We provide theoretical convergence rate guarantees for general estimators based on M-estimator theory, as well as the convergence rate of neural network-based estimators when the true ratio is in the anisotropic Besov space. We demonstrate the power of the proposed RDR-based evaluation through numerical experiments on MNIST, CelebA64, and the American Gut project microbiome data. We show that the estimated RDR enables not only effective overall comparison of competing generative models, but also a convenient way to reveal the underlying nature of goodness-of-fit. This enables one to assess support overlap, coverage, and fidelity while pinpointing regions of the sample space where generators concentrate and revealing the features that drive the most salient distributional differences.
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