Speaker: Andy Senger (UMD)Â When: Mon, November 9, 2026 - 2:00pm Where: Kirwan Hall 3206
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Abstract: In this preparatory talk, I will give the background
necessary to understand the chromatic splitting conjecture. I will
describe the category of spectra, discuss how chromatic homotopy
theory organizes this category, and explain how the chromatic
splitting conjecture fits into this picture.
Abstract: Modern decision-making in complex physical and engineered systems increasingly requires quantifying high-dimensional uncertainty and solving risk-averse optimization problems under uncertainty, often in near real time. Operator learning has emerged as a promising framework for constructing scalable surrogate models in this setting. Yet approximation errors in learned operators can significantly degrade the quality of downstream decisions arising from inverse problems and optimization tasks.
In this talk, we present a framework that formulates operator learning through the lens of downstream optimization objectives. By deriving a priori error bounds for inverse problems and optimization under uncertainty, we motivate learning formulations that explicitly penalize errors in the derivatives of input–output maps. We illustrate the effectiveness of these ideas on applications including structural health monitoring, shape optimization, and fluid flow control. The resulting methods yield improved accuracy in surrogate-based optimization and consistently stronger empirical performance in related statistical learning tasks.
Speaker: Jonathan Weitsman (Northeastern University) -Â https://cos.northeastern.edu/people/jonathan-weitsman/ When: Mon, November 9, 2026 - 3:00pm Where: Kirwan hall 3206
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Abstract: Alan Weinstein proposed a geometric understanding of the nature of symplectic geometry in terms of a symplectic "category".In Weinstein's symplectic "category", objects are symplectic manifolds and morphisms are canonical relations, which may not be composable; it is therefore only morally a category. We construct a true differential graded category which is morally dual to Weinstein's "category". The objects in this category are prequantum systems, associated to integral symplectic manifolds. The morphisms are a complex of differential forms twisted by a prequantum line bundle. We also consider the cohomology category, which turns out to be an (ordinary) linear category. In each case, Weinstein's morphisms are associated with currents dual to the forms. For the differential graded category, these are isotropic, or if preferred Lagrangian, currents, twisted by a section of the prequantum line bundle; in the case of cohomology, these currents are supported on {\em integral} Lagrangian submanifolds, equipped with a global covariant constant section of the prequantum line bundle. We then apply our methods to quantization, and show that for Kahler manifolds, a quantization in this category is related to holomorphic quantization. Along the way we show that in the case of prequantum systems, the Lefschetz action of ${\mathfrak {sl}}(2,\R)$ on differential forms, studied by Brylinski, Mathieu, Guillemin, and Tseng-Yau in the symplectic case, is promoted to an action of the superalgebra osp(1|2) on twisted differential forms, with ${\mathfrak {sl}}(2,\R)$ as the even subalgebra. A first application of this superalgebra action is the vanishing theorem which shows the cohomology category is supported in middle dimension.
Speaker: Seyed Abdolhamid Banihashemi (UMD) - When: Mon, November 9, 2026 - 3:00pm Where: Kirwan Hall 1313
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Abstract: For any initial datum \theta_0 \in L^{4/3}_x it is proved the existence of a global-in-time weak solution \theta \in L^\infty_t L^{4/3}_x to the surface quasi-geostrophic equation whose Hamiltonian, i.e. the \dot H^{-1/2}_x norm, is constant in time. The solution is obtained as a vanishing viscosity limit. The main idea is to propagate in time the non-concentration of the L^{4/3}_x norm of the initial data, from which the strong compactness in the Hamiltonian norm is deduced. Minimal Onsager supercritical conditions preventing anomalous dissipation are given.
Speaker: Abhinav Bhatele (UMD (CS & UMIACS)) - https://www.cs.umd.edu/~bhatele/ When: Mon, November 9, 2026 - 4:15pm Where: Kirwan Hall 3206
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Abstract: Significant advances in computer architecture (development of extremely powerful server-class GPUs) and parallel computing (scalable libraries for dense and sparse linear algebra) have contributed to the on-going AI revolution. In particular, distributed training of deep neural networks (DNNs) relies on scalable matrix multiplication algorithms and efficient communication on high-speed interconnects. Pre-training and fine-tuning large language models (LLMs) with hundreds of billions to trillions of parameters and graph neural networks (GNNs) on extremely large graphs requires hundreds to tens of thousands of GPUs. However, such training often suffers from significant scaling bottlenecks such as high communication overheads and load imbalance.
In this talk, I will present several systems research directions that directly impact AI model training. First, I will describe my group's work in using a three-dimensional parallel algorithm for matrix multiplication in large-scale LLM training. Second, I will demonstrate the application of the same algorithm to full-graph and mini-batch GNN training when working with extremely large graphs. Finally, I will also discuss the need for scalable collective communication routines for large-scale DNN training.
Speaker: Dr. Jana Gevertz (The College of New Jersey) - https://science.tcnj.edu/science_faculty/jana-gevertz-fiorelli/ When: Tue, November 10, 2026 - 12:30pm Where: Kirwan Hall 3206
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Abstract: Mathematical models are powerful tools that can vastly improve our understanding of cancer dynamics and treatment response. However, to be useful, experimental or clinical data are necessary to both train and validate such predictive models, and not all data are created equal. Here I present two methodologies that improve upon model-informed experimental design and model-based predictions. First, I will introduce a multi-objective optimization algorithm to identify combination protocols that maximize synergy from the perspective of both efficacy and potency (toxicity), while simultaneously reconciling sometimes contradictory assessments made by different synergy metrics. Second, using the notion of parameter identifiability, I will address the question of how to determine the minimal amount of experimental data to collect, and when to collect it, to have confidence in a model's predictions. Real-world applications of both methodologies will be presented.
Speaker: Perrin Ruth (UMD) - https://perrineruth.github.io/ When: Tue, November 10, 2026 - 2:00pm Where: Kirwan Hall 3206
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Abstract: This talk is largely motivated by the recent advances in AI towards proving mathematical theorems. As an experiment, I handed Claude a small conjecture with reasonable but unproven confidence that it is true. The conjecture is in graph theory. Consider a basis of the cycle space of a graph. From this basis construct a higher order dual graph whose nodes are basis cycles and edges are pairs of cycles that share nodes. The claim is that the cycles (of cycles) in this dual graph are generated by triangles. We use this to inform the structure of ring clusters in chemical data. In this talk, I will briefly motivate this problem, then I will summarize my rocky but overall successful experience proving this result with Claude.
Speaker: Sean Cox (VCU) - When: Tue, November 10, 2026 - 3:30pm Where: Kirwan Hall 1311
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Abstract: Soon after the proof of the Flat Cover Conjecture (every module has a flat cover) around the year 2000 by Bican, El Bashir, and Enochs, two related concepts were isolated for classes of modules: deconstructible classes, and the strictly weaker Kaplansky classes. All commonly-studied Kaplansky classes, such as the class $\mathcal{FM}$ of Flat Mittag-Leffler modules in $R$-Mod and the class $\mathcal{D}$ of Drinfeld vector bundles in Qcoh($X$), satisfy a stronger property I introduced in https://arxiv.org/abs/2608.00905: they are \textbf{Uniformly Stationary Kaplansky (USK)} classes, a set-theoretic property involving elementary submodels of (fragments of) the universe of sets. While USK classes generally lack the key feature (existence of precovers) that make deconstructible classes so central to modern relative homological algebra, they are always Galois stable (assuming the class is closed under pure extensions). This is true even in the absence of the Amalgamation Property, with various restricted classes of morphisms, and in some non-additive settings. For example, the AEC of $\mathcal{FM}$ with pure embeddings, and $\mathcal{D}$ with (either categorical or geometric) pure embeddings, are stable in all sufficiently closed cardinals. These results were inspired by, and strengthen, the results of Mazari-Armida and Trlifaj "Deconstructible classes of modules and stability" (https://arxiv.org/abs/2512.17799).
Speaker: Anna Yesypenko (The Ohio State University) - When: Tue, November 10, 2026 - 3:30pm Where: Kirwan Hall 3206
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Abstract: Nonlocal operators are ubiquitous in scientific computing, and their dense discretizations pose a major obstacle to scalable numerical algorithms. They arise in a wide range of settings, including numerical PDEs, boundary integral equations, domain decomposition methods, and kernel-based computations. Yet the interactions they encode often exhibit compressible structure: in particular, interactions between well-separated regions frequently admit low-rank approximations, enabling efficient matrix representations and factorizations.
In this talk, I will present randomized algorithms that exploit this structure using only matrix–vector products with an operator and its adjoint. These methods recover hierarchical low-rank representations and construct approximate factorizations that can serve as efficient solvers and preconditioners. A central focus will be on the theoretical guarantees for randomized recovery and how they compare with those of deterministic methods. Applications include compressing dense PDE operators with over a million unknowns and constructing fast preconditioners for wave-scattering problems.
Speaker: Andy Senger (UMD) When: Wed, November 11, 2026 - 2:00pm Where: Kirwan Hall 3206
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Abstract: I will explain what is known about the chromatic splitting
conjecture, with an emphasis on the "coheight 1" variant of the
conjecture. A prominent role is played by a generalization of
Faltings' two-towers isomorphism between the infinite height
Lubin--Tate and Drinfeld symmetric spaces. Much of this talk will
describe joint work with Barthel, Mann, Ray, Schlank, Weinstein and
Zhou.
Speaker: Ofer Zeitouni (Weizmann Institute of Science and New York University) - https://www.wisdom.weizmann.ac.il/~zeitouni/ When: Wed, November 11, 2026 - 2:00pm Where: Kirwan Hall 1311
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Abstract:Â Does there exist a non-zero band-limited function (i.e., belonging to the Paley-Wiener space) that vanishes on all points of a sine-beta process? if not, how many points do we need to remove in order to see such function? I will discuss this question and report on work in progress with Paul Bourgade and Misha Sodin, where logarithmically correlated fields (with a twist) make their appearance.
Abstract: I will discuss recent progress on the quantitative homogenization of first-order Hamilton–Jacobi equations. In the periodic setting, I will present optimal convergence rates and sketch some main ideas of our program.
Speaker: Jonathan Stewart (Florida State University) - https://jrstewart.ac/ When: Thu, November 12, 2026 - 3:30pm Where: Kirwan Hall 1311
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Abstract: Over the last several decades, latent space models have become central tools for analyzing networks. The standard statistical theory supporting these models and associated spectral methods for inference from a single observed network, however, is built on the assumption that edges are conditionally independent given the latent structure. This assumption is often unrealistic in practice because observed networks are cross-sectional snapshots of complex stochastic processes whose underlying forces can produce dependence beyond that explained by latent structure. For example, a mutual collaborator may introduce two researchers, directly influencing whether they form a collaboration. Despite this, these models and methods have been applied with considerable success to real-world networks, yielding scientifically meaningful insights into academic collaboration networks, organizational and communication networks, biological networks, and more. This contrast between empirical success and restrictive theoretical assumptions motivates the development of guarantees that accommodate the dependence present in real-world networks.
We help close this gap between theory and practice by establishing spectral norm concentration for random graphs with controlled edge dependence. Such concentration is a key ingredient in theoretical guarantees for spectral methods, which provide computationally efficient procedures for community detection, graph embedding, and low-rank network estimation. Dependence is quantified through an influence matrix $\mathbf{T}$ and an associated dependence coefficient $\mathcal{D}$, while $\gamma p_{\max}$ provides a global sparsity envelope for the conditional edge probabilities. Under suitable sparsity and regularity conditions, we show that, with high probability,
\[
\|\mathbf{A}-\mathbf{P}\|_2
\leq C\,\mathcal{D}\,\sqrt{\gamma n p_{\max}}.
\]
When the edges are independent, $\mathcal{D}=1$ and $\gamma=1$, recovering the classical spectral concentration scale $\sqrt{n p_{\max}}$. Simulation studies examine finite-sample spectral community recovery under local edge dependence. We then apply our concentration result to obtain consistency guarantees for spectral methods in stochastic block models and random dot product graphs with dependent edges.