Speaker: Christian Rosendal (UMD) - When: Mon, October 26, 2026 - 2:00pm Where: Phys1219
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Abstract: Let $\mathcal H=\ell^2(\Z;\R)$ and let $\Z$ act on $\mathcal H$ by bilateral shifts. We prove that the quotient $\mathcal H/\Z$ does not bilIpschitz embed into $\mathcal H$ itself. The proof represents finite subsets of high-distortion flat tori, with arbitrarily small bilipschitz error, inside $\mathcal H/\Z$ and uses an earlier bound on the Hilbert distortion of these flat tori due to Khot and Naor. This solves a problem of Cahill, Iverson and Mixon. The proof was found using AI and is joint work with A. Das.
Speaker: Lars Hesselholt (University of Copenhagen) - https://web.math.ku.dk/~larsh/ When: Mon, October 26, 2026 - 2:00pm Where: Kirwan Hall 3206
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Abstract: Using their theory of Gestalten, Scholze and Stefanich has found a very general form of Cartier duality and the Fourier transform. My purpose with this talk is to make some propaganda for this theory and to explain the Cartier duality statement in the simple case of (the transmutation of) the additive formal group (along the six-functor formalism of coherent cohomology).
Abstract: Recent advances in Weak form Scientific Machine Learning (WSciML) allows for the creation and inference of interpretable models directly from data via advanced numerical functional analysis, computational statistics, and numerical linear algebra techniques. This class of methods completely bypasses the need for forward-solve numerical discretizations and yields both parsimonious mathematical models and efficient parameter estimates. These methods can be orders of magnitude faster and more accurate than traditional approaches and far more robust to the high noise levels. The combination of these features in a single framework provides a compelling alternative to both traditional modeling approaches as well as modern black-box neural networks.
A central question in these methods concerns the choice of test functions. In this talk, I will discuss several strategies proposed by our group including spectral matching, multi-scale orthonormalization, and single-scale local algorithms. I will also present a unified framework for understanding how the bias/variance trade-off is manifested when choosing test function in using a weak form method for computing derivatives from noisy data. Time permitting, I will discuss a novel strategy for optimal test function design.
Speaker: George Domat (University of Michigan) - https://sites.google.com/view/georgedomat/home When: Mon, October 26, 2026 - 3:00pm Where: Kirwan Hall 3206
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Abstract: Given a Riemann surface X one can define two natural groups of transformations: the mapping class group MCG(X), consisting of equivalence classes of homeomorphisms of X, and the Teichmuller modular group Mod(X), consisting of equivalence classes of only quasiconformal homeomorphisms of X. When X is of finite type these groups coincide, however, when X is of infinite type, MCG(X) is an infinite index subgroup of MCG(X). In this talk we will see how by prescribing the "behavior at infinity" of elements of MCG(X) and Mod(X), in a suitable sense in each case (combinatorially and analytically), we often obtain commensurable subgroups. All of this is joint work with Javier Aramayona and Chris Leininger.
Speaker: Hong-Zhou Ye (UMD (Chemistry & Biochemistry)) - https://sites.google.com/view/yegroup When: Mon, October 26, 2026 - 4:15pm Where: Kirwan Hall 3206
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Abstract: A central task of computational materials science is to accurately solve the many-electron Schrödinger equation for condensed-phase materials, which are commonly modeled as infinite systems under periodic boundary conditions. Materials quantum chemistry is an emerging field in which computational tools developed in the quantum chemistry community——historically focused on finite molecular systems——are being adapted and applied to periodic solids. The promise lies in the systematic improvability of quantum chemistry methods, but extending these methods to infinite systems presents new numerical challenges.
In this talk, I will describe our recent work on tackling two such challenges: controlling errors associated with finite system sizes and finite basis sets. The first is to accelerate convergence to the infinite-system limit when evaluating the Hartree–Fock exchange energy, an important component of hybrid density functional theory (DFT) calculations. The second is to optimize atom-centered Gaussian basis functions for accurate and numerically stable electronic-structure calculations in periodic solids. I will conclude with examples of applications in computational materials science enabled by these new tools.
Speaker: Jared Marx-Kuo (U Chicago) - When: Tue, October 27, 2026 - 12:30pm Where: Kirwan Hall 1310
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Abstract: For a closed manifold (M,g) with isometry group, G, we will discuss the construction of G-invariant minimal hypersurfaces. Pitts-Rubinstein initiated the program to construct such hypersurfaces via min-max methods. The community has made significant progress when the cohomogeneity of the manifold is at least 3 (i.e. the quotient M/G "looks" 3 dimensional). However, serious complications arise when the cohomogeneity is 2, as min-max on closed surfaces produce geodesic networks. Using the Allen-Cahn regularization of the area functional, we provide a general method for constructing minimal hypersurfaces in cohomogeneity 2 when there are no exceptional orbits of the group action, and any cohomogeneity greater than 2 for any action. This is joint work with Pedro Gaspar and Rayssa Caju.
Speaker: Dr. Bruce Pell (Lawrence Technological University) - https://ltu.edu/faculty/pell-bruce/ When: Tue, October 27, 2026 - 12:30pm Where: Kirwan Hall 3206
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Abstract: The efficacy of Immune Checkpoint Inhibitors (ICIs) is frequently limited by adaptive immune resistance via the PD-1/PD-L1 pathway. While pairing ICIs with potent immunostimulants (such as NHS-muIL12) offers a strategy to overcome this, foundational mathematical models often struggle to capture complex preclinical behaviors, specifically non-monotonic tumor responses. In this talk, we introduce a refined deterministic model that addresses this limitation by incorporating PD-L1 expression as a fully dynamic variable rather than a static parameter. We demonstrate that this model, using a single parameter set, successfully reproduces experimental data across six distinct treatment arms, including monotherapies and combinations. This framework provides a robust mechanistic explanation for dose-dependent treatment failure driven by adaptive PD-L1 upregulation, while also elucidating the drivers of therapeutic synergy. We will present the systematic development of the model, simulation results, and a mathematical analysis of the system's stability and dynamics.
Speaker: Tao Tao (UMD/Physics) - When: Tue, October 27, 2026 - 2:00pm Where: Kirwan Hall 3206
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Abstract: Pseudorandom number generators are deterministic algorithms designed to produce sequences that appear random, making them a useful setting for studying what Transformers can learn from seemingly unpredictable data. In this talk, I will present our work on training Transformers to predict several families of PRNGs. I will discuss when Transformers can learn these algorithms, how curriculum learning enables generalization to more challenging generators, and what these results reveal about the computational mechanisms learned by Transformers.
Speaker: Todd Rowland (UMD(Math)) - When: Tue, October 27, 2026 - 2:30pm Where: Kirwan Hall 3206
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Abstract: How can a human and an AI collaborate in a meaningful way on an open mathematical problem? This talk follows one such journey, by a nonexpert in number theory working with Claude, an AI assistant, on Gauss’s class number one problem for real quadratic fields. Numbers of the form a + b√d can fail to have unique factorization into primes, and the class number measures the failure, with class number 1 meaning it holds. Gauss conjectured that this happens for infinitely many square-free d > 0. Over two hundred years later the question is still open, in contrast with negative d, where exactly nine values work.
The journey includes human experiments, AI explanations, mistakes from both, misunderstandings between us, and the checks that caught them. I will describe what worked, what did not, and what this suggests for how humans and AI can do mathematics together, including how a nonexpert can test an AI’s claims.
Speaker: Egbert Rijke (Johns Hopkins University) - https://egbertrijke.github.io When: Tue, October 27, 2026 - 3:30pm Where: Kirwan Hall 1311
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Abstract: Homotopy Type Theory is a language for mathematics in which the most basic objects are homotopy types, as opposed to more traditional languages for mathematics in which the most basic objects are sets. The homotopical nature of homotopy type theory originates from the rules of the identity type. The innocent-looking elimination principle for the identity type endows all types with the structure of a higher groupoid. Homotopy Type theory is therefore the study of types, using ideas from homotopy theory. By adding rules for higher inductive types, it becomes possible to construct many types that are analogous to familiar topological spaces, such as the spheres. In this talk, I will show how the univalence axiom can be used, along with the type-theoretic reasoning principles for higher inductive types, to construct the complex and quaternionic Hopf fibrations on the 1-sphere and the 3-sphere. If time permits, I will say a bit more about the complications that arise when attempting the same construction on the 7-sphere.
Speaker: Charles Parker (U.S Naval Research Laboratory) - https://sites.google.com/view/charlieparker2 When: Tue, October 27, 2026 - 3:30pm Where: Kirwan Hall 3206
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Abstract: Constructing finite element spaces and developing preconditioners for problems discretized with the elements is typically viewed as a disjoint process as the same finite element space may be used for many different problems. However, some typical applications, like incompressible flow, are solved so frequently in practice that designing finite element spaces in conjunction with specific solvers becomes a worthwhile investment. In this talk, we consider divergence-conforming finite element discretizations of the incompressible Navier-Stokes equations. We show how one can design high-order H1-conforming velocity spaces that (i) pair with the standard discontinuous piecewise polynomial pressure space, (ii) share many properties with high-order H(div)-conforming elements, and (iii) lead to subspace decompositions for augmented Lagrangian preconditioners with better scalability with respect to the polynomial degree for both transient and steady flow.
Speaker: Dmitry Kaledin ( Steklov Institute/University of Chicago) - https://homepage.mi-ras.ru/~kaledin/ When: Wed, October 28, 2026 - 2:00pm Where: Kirwan Hall 3206
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Abstract: In non-commutative algebraic geometry, an algebraic variety isreplaced by a DG algebra A, and the role of de Rham cohomology is played
by periodic cyclic homology HP(A). It is a standard expectation that all
the additional motivic-type structure on de Rham cohomology should also
exist in non-commutative generality. There has been a lot of progress on
this in the p-adic situation, but the archimedian case is much more
problematic. The missing ingredient is complex conjugation. While a
Hodge filtration on periodic cyclic homology exists by definition, we
also expect that HP(A) for a good A over C carries a functorial
R-structure, and it is not clear at all where it might come from. I am
going to present a proposal towards this based on L^2-completed version
of HP. This is still work-in-progress, but the proposal looks viable, so
hopefully, this won't be a complete waste of audience's time.
Speaker: Sayan Das (Vanderbilt University) - https://sayan-pq.github.io/ When: Wed, October 28, 2026 - 2:00pm Where: Kirwan Hall 1311
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Abstract: The KPZ universality class consists of random growth models that share common scaling exponents and random matrix-type scaling limits. These models are typically defined on the real line; however, interesting new phenomena arise in their half-space counterparts, where the models are studied on the half-line in the presence of boundary conditions.
The study of invariant measures is an important problem in the half-space setting. It dates back to the work of Liggett in 1975, who introduced a family of invariant measures for half-space asymmetric exclusion processes, a model in the KPZ universality class. However, to the best of our knowledge, a complete classification of all invariant measures in half-space models remains open. In this talk, I will discuss recent results on the complete classification of invariant measures for the half-space geometric last passage percolation (geo LPP) model, which is closely related to exclusion processes. This is based on joint work with Evan Sorensen and Zongrui Yang.
Speaker: Massimiliano Berti (IAS/SISSA, Trieste) - https://sites.google.com/view/prof-massimiliano-berti/home When: Thu, October 29, 2026 - 2:00pm Where: Kirwan Hall 3206
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Abstract: The spectral instability of traveling periodic water waves has been investigated for more than sixty years, since the seminal discovery of Benjamin and Feir. We establish the first rigorous description of the 3d unstable spectrum of small-amplitude gravity Stokes waves in deep water in a full neighborhood of the McLean resonant curves for arbitrary three-dimensional -- longitudinal and transverse — wave perturbations. Our results reveal that the Benjamin-Feir instability and the first longitudinal high-frequency isola originate from the same resonant interaction, hidden in the purely longitudinal setting. This is a joint work with A. Maspero and A. Radakovic.
Abstract: The abelian Yang-Mills-Higgs equations in two space dimensions admit topological vortex solutions. I will discuss the asymptotic stability of the degree-one vortex at self-dual coupling, for small equivariant perturbations. An important feature of the problem is the presence of an internal mode in the spectral gap of the linearized operator. The interaction between this discrete mode and the continuous spectrum leads to a damping mechanism, quantified by a nonlinear Fermi Golden rule. The main difficulties in the proof of stability are 1) The slow decay of the internal mode. 2) Proving decay for the projection of the perturbation onto the continuous spectrum, which satisfies a Klein-Gordon equation with a matrix potential. The latter is achieved by combining the spacetime resonance method for the flat Klein-Gordon equation with local energy decay for the linearized operator.
Speaker: Nan Xu (University of Maryland, College Park) - https://www.inspirelab.site/team/ When: Thu, October 29, 2026 - 3:30pm Where: Kirwan Hall 1311
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Abstract: Understanding how information flows through the brain requires statistical methods that go beyond conventional correlation-based measures and restrictive distributional assumptions. In this talk, I will present our recent methodological developments integrating statistical modeling, information theory, and game-theoretic optimization to characterize directed interactions in complex neural dynamics.
I will begin with a predictive modeling approach for characterizing time-varying directed interactions, motivating the need for more general measures of information transmission. I will then focus on a distribution-aware, information-theoretic framework that extends classical Gaussian channel capacity to non-Gaussian settings. By combining a dual-flow min-max formulation with flexible normalizing-flow models, this approach enables the estimation of directed information transmission under complex statistical dependencies. Through theoretical analysis, simulations, and neuroimaging applications, I will illustrate how these advances provide new perspectives on information processing in brain networks.
Speaker: Joshua Culver () - When: Thu, October 29, 2026 - 5:00pm Where: Kirwan Hall 1311
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Abstract: One aspect of Hilbert’s Program in the early 1900’s attempted to provide positive answers to three different problems in number theory:
1) Does every statement true in the natural numbers have finite proof in first order logic, say, by the Peano Axioms?
2) Subquestion: Does every statement provably true in the natural numbers using set theory have a finite proof in first order logic?
3) Subsubquestion: Can an axiomatization of the natural numbers in first order logic prove its own consistency, which set theory does prove?
In the 1930s, Gödel answered no to all of these questions. This talk will give a brief introduction into first order logic, primitive recursive functions, and Gödel’s chief insights which enabled him to prove these results. Precise details will be provided as time allows, and those wishing to learn more are invited to take Math 713 in Spring 2027 or peruse David Marker’s An Invitation to Mathematical Logic, from which the talk was derived.
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