Applied Mathematics seminars

This seminar investigates Anderson localization in subwavelength elastic periodic systems with random perturbations. For the unperturbed structure, layer-potential methods recast the eigenvalue problem as boundary integral equations, yielding asymptotic expressions for subwavelength eigenvalues and establishing a band gap above the subwavelength band. A Floquet transform then brings the perturbed problem into a periodic formulation and produces equations for resonant frequencies under general perturbations. Numerical experiments on monomer and dimer structures test agreement with the analysis. Increasing the strength and number of random perturbations demonstrates localization, providing a mathematical basis for elastic metamaterial design.

Marcos Petrúcio Cavalcante connects geometric stability to physical examples involving soap films, bubbles and vibrating membranes. He first describes his route through differential geometry and the development of a research group and graduate programme in Maceió, Brazil. The scientific discussion concerns shapes that are critical points of a functional. Its second variation defines stability, while the Morse index counts independent directions of improvement. Through examples and pictures, the talk explains why stable configurations tend to have simple geometry and topology. Two results make this principle precise: a genus-dependent lower bound on the Morse index of compact constant-mean-curvature surfaces in Euclidean space, and a rigidity theorem for stable extremal domains of the first Dirichlet eigenvalue on the round sphere.

Ivo D. Dinov examines augmented intelligence as a partnership between people and computational systems. The talk traces the technical and philosophical development of neural networks, then introduces complex-time, or kime, representations and the inference methods they support. Applications include medical imaging, healthcare and economic forecasting. It also considers the academic mission, societal consequences of AI and tensions between rapid technical development and human values, framing mathematical AI methods as extensions of human reasoning. Free hybrid seminar hosted by Wayne State University's Institute for AI and Data Science, AIDaS: CAD Seminar Series. Wednesday 30 September 2026, 14:30–15:30 EDT (America/Detroit; UTC−4). Attend in Room 1146, Faculty/Administration Building, 656 W. Kirby, Detroit, MI 48202, USA, or use the Zoom link on the official event page. Researchers, practitioners, students and faculty are welcome; the organizer encourages in-person attendance.

Two-lecture series by Mohammed Abouzaid (Stanford): 'Framed bordism and nearby Lagrangians' (September 16) and 'Complex bordism and Hamiltonian fibrations' (September 17), on bordism-theoretic approaches to Lagrangian embeddings in symplectic manifolds and Arnold's nearby Lagrangian conjecture.

Kirk Public Lecture at the Isaac Newton Institute by Yoshiko Ogata (Kyoto University) on how macroscopic properties of matter emerge from quantum particle interactions and the classification of topological order from an operator-algebraic perspective in mathematical physics.

Robert E. Gompf (University of Texas, Austin) lectures on 'On classifying smoothings of R^4 - from the beginning to the present', tracing how 4-manifold topology emerged from the breakthroughs of Freedman and Donaldson and how Euclidean 4-space admits exotic smoothings that resist classification by countable numerical invariants.

Isaac Newton Institute seminar in the 'Mathematics of many-body entanglement' (MMB) programme: Ignacio Cirac of the Max-Planck-Institut für Quantenoptik speaks on the preparation of tensor network states.

Yousef Saad examines relaxed gradient descent for large-scale optimization. Relaxing the optimal step length in Cauchy's steepest descent avoids its characteristic zigzag behavior and can bring the search direction close to an eigenvector of the Hessian. Once that alignment is sufficiently accurate, properties of the Lanczos method can accelerate convergence. The talk analyzes several such strategies and illustrates them in global minimization of strictly convex functions, retaining the simplicity and low memory requirements that make gradient methods attractive for machine learning.

Daniel Szyld extends randomized point and block Gauss-Seidel and Gauss-Southwell convergence results from Hermitian positive-definite matrices to certain non-Hermitian classes, including overlapping variables in domain decomposition. The analysis treats a range of sampling probabilities and greedy selection strategies and identifies choices that optimize the bounds. The best expected convergence bounds for randomized methods match those of more expensive deterministic Gauss-Southwell algorithms. These results establish a convergence rate for asynchronous iterations. Joint work with Andreas Frommer.

Erik Boman discusses preconditioning for asynchronous linear solvers. Inner products create synchronization requirements in Krylov methods, while preconditioners can also improve iterations such as Richardson's method. The talk focuses on asynchronous incomplete factorizations and introduces ATS-ILU, an iterative incomplete LU method with synchronous and asynchronous versions that performs competitively with ParILU.

Edmond Chow examines how asynchronous updates improve parallel iterative computation. The first part covers asynchronous versions of classical first- and second-order linear iterations, Chebyshev methods, and multigrid, with attention to efficiency and fault tolerance. The second introduces reinforcement learning and asynchronous state-value estimation for finding optimal policies. When the state space is too large to enumerate, these updates focus computational effort on frequently visited regions.

Optimal transport is a mathematical method to define a distance between probability distributions. This is particularly useful in various domains, including physics, biology, machine learning, and economics, among others. After introducing the Optimal Transport (OT) problem at finite temperature, we show how it can be formulated as a statistical physics problem. This approach allows us to derive very efficient algorithms to effectively compute the distance between two probability distributions. The a priori unrelated Schrödinger bridge (SB) problem is presented, and it is shown to be a dynamical version of the optimal transport problem. Indeed, the Schrodinger bridge looks for the most probable path in probability distribution space, which connects two given probabilities. The Schrodinger bridge problem, originally devised for freely diffusing particles, can be generalized to the case of interacting particles. It can be formulated in terms of functional integrals over bosonic fields, which allows us to derive partial differential equations that characterize the most probable paths in probability space. CARL VAN VREESWIJK MEMORIAL LECTURE 2026. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2026-04-15. Recording duration: 00:55:05.

Davide Palitta introduces the S^T S-SVD, a decomposition of A derived from the SVD of its sketch SA. It is exact with high probability, preserves singular values probabilistically, and makes left singular vectors orthonormal in the sketch-induced seminorm, with lower computational cost. The talk relates this perspective to subspace embeddings and least-squares residuals, assesses sketch quality, and bounds departures from ordinary orthogonality in randomized QR. A further application extends the nearest-orthogonal-matrix problem to S^T S-orthogonality. The work builds on Gilbert, Park, and Wakin and is joint with Valeria Simoncini.

Joel Tropp studies structured dimension reduction through the injectivity of random maps, motivated by fast low-rank approximation and least-squares regression. This viewpoint sharpens guarantees for sparse maps and gives exponential improvements for tensor-product dimension reduction. Experiments assess the resulting structured random matrices on synthetic problems and scientific applications. Joint work with Chris Camaño, Ethan Epperly, and Raphael Meyer, available as arXiv:2508.21189.

Sherry Xiaoye Li surveys randomized construction of hierarchically low-rank matrices, including H/H2, HODLR, HSS, and butterfly formats with different off-diagonal structures. Applications include integral equations, boundary elements, discretized PDEs, and statistical or machine-learning kernel matrices, using either iterative matrix-vector products or direct factorization and solves. Constructing these representations from an implicit dense operator is often the main cost. The talk offers a unified view of sketch distributions, sketch sizes, approximation error bounds, high-performance implementation, applications, and open questions.

Optical imaging is a major research tool in the basic sciences, and is the only imaging modality that routinely enables non-ionized imaging with subcellular spatial resolutions and high imaging speeds. In biological imaging applications, however, optical imaging is limited by tissue scattering to short imaging depths. This prevents large-scale bio-imaging by allowing visualization of only the outer superficial layers of an organism, or specific components isolated from within the organism and prepared in-vitro.

Matrix multiplication underpins scientific computing and artificial intelligence, yet practical numerical libraries and hardware accelerators commonly retain the classical cubic-time algorithm despite decades of subcubic theoretical advances. This talk reviews the effort to make faster multiplication algorithms useful in practice. It examines why arithmetic complexity alone does not determine performance: some algorithms require enormous matrices or incur large hidden constants, while communication costs, numerical stability and the match between software and hardware create additional obstacles. The historical perspective connects asymptotic algorithm design to actual performance and power consumption.

Pharmacokinetics in the eye is an important factor for the success of ocular drug delivery and treatment. Pharmacokinetic features determine the feasible routes of drug administration, dosing levels and intervals, and it has impact on eventual drug responses. Several physical, biochemical, and flow-related barriers limit drug exposure of anterior and posterior ocular target tissues during treatment during local (topical, subconjunctival, intravitreal) and systemic administration (intravenous, per oral). Mathematical models integrate joint impact of various barriers on ocular pharmacokinetics (PKs) thereby helping drug development. The models are useful in describing (top-down) and predicting (bottom-up) pharmacokinetics of ocular drugs. This is useful also in the design and development of new drug molecules and drug delivery systems. Furthermore, the models can be used for interspecies translation and probing of disease effects on pharmacokinetics. In this lecture, ocular pharmacokinetics and current modelling methods (noncompartmental analyses, compartmental, physiologically based, and finite element models) are introduced. Future challenges are also highlighted (e.g. intra-tissue distribution, prediction of drug responses, active transport).

Tom Crawford explores how mathematical models turn questions about the world into equations that can be investigated. Examples range from relativity and infectious-disease modelling to his research on the spread of pollution in the ocean. The lecture also applies modelling to video games, sport and partner selection, illustrating how the same mathematical tools can clarify problems across very different settings.