Speaker: Deniz Genlik (University of Illinois, Urbana-Champaign) - https://www.denizgenlik.net/ When: Mon, September 28, 2026 - 2:00pm Where: Kirwan Hall 3206
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Abstract: The moduli space $\overline{M}_{0,n}$ parametrizes stable rational curves with $n$ marked points. Its boundary divisors generate the divisor class group, so every divisor class can be written (generally non-uniquely) as a linear combination of boundary divisor classes. For a fixed divisor class $[D]$, the collection of its effective boundary expressions forms a polytope. In this talk, I will describe these polytopes and for several natural divisor classes I will explain their connections with classical objects in graph theory and combinatorial optimization, including spanning trees and forests, Hamiltonian cycles, perfect matchings, and Turán graphs. These connections also produce new combinatorial formulas for these natural divisor classes on $\overline{M}_{0,n}$. This is joint work with Ian Cavey.
Abstract: Many problems in the physical sciences involve analysis of a large number of point clouds, either for classifying them based on their distributional properties or for tracking and predicting the behavior of the point clouds over time. This talk focuses on a framework called linearized optimal transport (LOT) that creates a featurization of point clouds to addresses two related challenges: applying off the shelf linear machine learning algorithms to classify and regress functions of these point clouds, and predicting how a point cloud evolves forward in time using standard numerical solvers. And most importantly, the featurization of the point clouds is provably both stable, meaning similar point clouds will be close in LOT space, and injective, meaning that the embedding does not discard any potentially important information about the point clouds. We will demonstrate potential applications of this framework in a number of settings, including classification of point clouds arising from single-cell data, generation of new point clouds arising from 3D mesh shapes, and forecasting of the temporal evolution of point clouds arising from bacterial chemotaxis and other stochastic particle systems.
Speaker: Dominik Gutwein (Universität Hamburg)-dominikgutwein.github.io/ When: Mon, September 28, 2026 - 3:00pm Where: Kirwan Hall 3206
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Abstract: Instantons over manifolds with special holonomy are a distinguished class of connections on principal bundles. In their seminal paper from 1998 Donaldson and Thomas envisioned invariants of special holonomy manifolds based on the moduli space of such instantons. However, a rigorous construction of these invariants faces formidable challenges arising from the possible non-compactness of this moduli space. One source of non-compactness comes from the formation of non-removable singularities, that is, a sequence of instantons might converge to an instanton that is singular along a subset of the underlying manifold. In this talk, I will focus on instantons over 6-manifolds with SU(3)-structures that have isolated singularities of conical type. In particular, I will discuss their moduli space, its structure, and its virtual dimension. This talk is based on joint work with Yuanqi Wang.
Speaker: Kevin Hu (UMD) - When: Mon, September 28, 2026 - 3:00pm Where: Kirwan Hall 1313
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Abstract: "It has been long perceived that resistive MHD evolution might be responsible for topology change, leading to magnetic reconnection events. Recently, a different type of magnetic reconnection mechanism was proposed, based on a modification of ideal MHD due to magnetohydrodynamic inertia. We prove magnetic reconnection without magnetic resistivity, for smooth solutions and for patch solutions. This is obtained by proving merger in corresponding systems of coupled active scalars. This is joint work with Peter Constantin."
Speaker: Jiaao Xu (Peking University and Stanford) - When: Tue, September 29, 2026 - 12:30pm Where: Kirwan Hall 1310
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Abstract: A function on a domain in C^n is usually called plurisubharmonic (psh) if it is upper semicontinuous (usc) and its restriction to every complex affine line is subharmonic (in particular, usc on that line). A folklore question is whether the global usc assumption is superfluous. A partial result is, proved by Lelong in 1945, that usc follows if the function is locally bounded from above.
In this talk, I will describe an affirmative answer to this question. More precisely, I will show that if the restriction of a function to every complex affine line is subharmonic, then the function is automatically locally bounded from above, so that Lelong's result applies. The proof is based on induction on the dimension, a psh analogue of the uniform boundedness principle, and the maximum principle for subharmonic functions. This is a joint work with Jianchun Chu and Zihang Hao.
Speaker: Dr. Sen Pei (Columbia University) - https://www.publichealth.columbia.edu/profile/sen-pei-phd When: Tue, September 29, 2026 - 12:30pm Where: Kirwan Hall 3206
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Abstract: Next-generation epidemic models need to incorporate human behaviors to
better support outbreak response. In this talk, I will introduce how to use cellphone-
based foot-traffic data to represent population mixing in different daily activities and
model the spread of respiratory outbreaks. We will discuss the predictability of reactive
mobility changes, behavioral mechanisms for decision-making, forecasting of
neighborhood-level outbreaks, and the use of AI in behavior modeling.
Speaker: Deep Ray (UMD) - https://deepray.github.io/ When: Tue, September 29, 2026 - 2:00pm Where: Kirwan Hall 3206
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Abstract: Bayesian inference provides a principled framework for learning unknown quantities from noisy and incomplete observations while quantifying the uncertainty associated with these predictions. It arises in numerous science and engineering applications, including medical imaging, weather forecasting, and predicting the spread of wildfires. However, Bayesian inference can be challenging to implement when the quantities being inferred are high-dimensional, the underlying models are computationally expensive, or the available prior information is complex.
In this talk, we will see how generative AI provides a powerful framework for learning and sampling from probability distributions arising in Bayesian inference. In particular, we will discuss how conditional generative models, such as conditional generative adversarial networks and conditional diffusion models, can be trained to generate samples from posterior distributions given available observations. Once trained, these models can rapidly generate posterior samples, potentially avoiding the computational expense associated with traditional sampling-based approaches.
Speaker: Brian Pierce (UMD/Cell Biology) - https://cbmg.umd.edu/people/brian-pierce When: Tue, September 29, 2026 - 2:30pm Where: Kirwan Hall 3206
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Abstract: Determining the structures of antibodies and T cell receptors (TCRs) in complex with their antigen targets can provide major insights into immune protection, immune-related diseases, and biotherapeutics. Accurate modeling of those complex structures has been a major challenge of computational biology, and if successful would enable characterization of vast numbers of complexes of interest not feasible for experimental structural methods. Recent deep learning structural modeling methods, including AlphaFold, have greatly advanced our ability to model protein structures from sequence, but their accuracy for modeling antibody and TCR recognition has received little systematic analysis. To address this gap, we benchmarked AlphaFold2, AlphaFold3, and related deep learning methods on sets of antibody and TCR complexes to assess and compare their accuracy. We found substantial differences in performance among methods and interface classes, with AlphaFold3 generally outperforming other methods, and antibody-peptide complexes representing the most challenging interfaces to model. Complementarity between methods indicates possible opportunities to pool models to increase success, while confidence scores were found to be a generally useful indicator of model accuracy. These results highlight remarkable advances enabled by deep learning protocols, while identifying shortcomings that can be addressed by future algorithm developments.
Speaker: Weilin Li (The City College of New York)-https://weilinlimath.github.io/ When: Tue, September 29, 2026 - 3:30pm Where: Kirwan Hall 3206
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Abstract: Spectral estimation is the problem of extracting the spectrum of a function from noisy samples. The celebrated MUSIC algorithm approximates the frequencies by creating a special function and finding its smallest local minima through a grid search. We introduce the Gradient-MUSIC algorithm, which instead finds local minima through local optimization with carefully chosen initialization, making it significantly more efficient and eliminates the need for discretization over a fine grid. Even though the optimization landscape is nonconvex, we prove a global convergence and optimality result: Gradient-MUSIC finds suitable initialization, converges at a linear rate, and estimates the unknown parameters at minimax optimal rates for several deterministic and random noise models. The mechanisms of Gradient-MUSIC are highly flexible, and our analysis identifies types of inverse problems for which it is possible to engineer nice optimization landscapes. Joint work with Albert Fannjiang and Wenjing Liao.
Speaker: Izumi Okada (The University of Tokyo) - https://sites.google.com/view/izumiokadamath When: Wed, September 30, 2026 - 2:00pm Where: Kirwan Hall 1311
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Abstract:We investigate fluctuation phenomena for the graph distance and the effective resistance associated with random media arising from the range of a random walk.
The behavior of such objects plays a central role in a variety of problems, including volume growth, metric scaling, and universality phenomena in random geometry.
Our results demonstrate a sequence of dimension-dependent phase transitions in the scaling behavior of these fluctuations, leading to qualitatively different regimes across dimensions lower than six, equal to six, and higher than six. This is joint work with Arka Adhikari and Daisuke Shiraishi.
Speaker: Partha Ghosh (IMJ - Paris)-Â sites.google.com/view/parthaghosh/home When: Wed, September 30, 2026 - 3:00pm Where: Kirwan Hall 3206
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Abstract: In this talk, I present an explicit formula for the ADM mass of asymptotically locally Euclidean (ALE) almost Kähler manifolds. The formula expresses the mass in terms of the total Hermitian scalar curvature and topological data associated with the underlying almost complex structure, extending a result of Hein and LeBrun in the Kähler ALE case. The proof is based on a spin-c adaptation of Witten’s proof of the positive mass conjecture in the spin case and is therefore distinct from previous complex-geometric methods. In dimension 4, I show that one can prove a positive mass theorem and a Penrose-type inequality for asymptotically Euclidean (AE) almost Kähler manifolds using this formula.
Speaker: Tim Kunisky (Johns Hopkins University) - https://www.kunisky.com/ When: Thu, October 1, 2026 - 3:30pm Where: Kirwan Hall 1311
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Abstract: Spiked matrix models describe noisy observations of low-rank signals. I will present results characterizing the fluctuations of the leading eigenvectors of such models around these hidden signals. In particular, for a rank-one signal and in the supercritical regime where the leading eigenvector of the noisy matrix is correlated with the signal vector, I will show that the fluctuations around this correlated part are universal and depend only on the first two moments of the noise entries, provided that the signal is sufficiently delocalized. In particular, these fluctuations are asymptotically Gaussian for Wigner-like noise matrices, resembling the case of noise drawn from the Gaussian orthogonal or unitary ensembles. A more general version of this analysis also applies to collections of several spiked matrices. In particular, even highly dependent collections of spiked matrices with uncorrelated Wigner-like noise can have leading eigenvectors with asymptotically independent Gaussian fluctuations, a phenomenon I will refer to as "pseudoindependence". Finally, I will describe the ramifications of pseudoindependence for spectral algorithms in statistical settings, showing that in some cases it can be advantageous to build spectral estimators from the leading eigenvectors of several deterministic transformations of an observed matrix rather than just from the leading eigenvector of the observed matrix itself.
Speaker: Baidehi Chattopadhyay (University of Maryland) - When: Thu, October 1, 2026 - 5:00pm Where: Kirwan Hall 1311
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Abstract: Markov numbers arise from a simple looking Diophantine equation first studied by Andrey Markov in the nineteenth century. In this talk, we will explore how Markov numbers are generated, why all solutions can be obtained from the simplest one, and some of their applications in arithmetic and geometry.
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