Applied Mathematics

Researchers and practitioners will discuss mathematical foundations of data science, including high-dimensional geometry, dimensionality reduction, scalable algorithms, uncertainty and machine learning. The conference takes place in person at the Salt Palace Convention Center on 16–20 November 2026. Registration is open, with early rates through 19 October; abstract and travel-support deadlines have passed. Registration also covers the co-located SIAM Imaging Science and Data Mining conferences.

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.

Eirik Valseth discusses mathematical models of weather and storm surges and the computations used to make forecasts. Conversation in Norwegian.

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.

Mikaela Iacobelli introduces kinetic theory and the mathematical description of charged particles in plasmas through Vlasov-type equations. The colloquium examines stability and instability, well-posedness, and how solutions behave in singular limits. It also presents a new family of Wasserstein-type distances that offers tools for studying the stability of kinetic equations. The exposition is intended for a broad mathematical audience.

Nearest-neighbor indexes usually rely on a single distance function, but accurate comparisons can be expensive. This talk proposes a bi-metric framework: a cheap proxy metric builds the index, while the query procedure uses a limited number of evaluations of both the proxy and an expensive ground-truth metric. The theory applies to DiskANN and Cover Tree. When the proxy approximates the ground-truth metric within a bounded factor, the resulting structure can achieve arbitrarily good approximation guarantees under the accurate metric. Experiments on text retrieval using models with very different computational costs show improved accuracy-efficiency tradeoffs on almost all MTEB datasets compared with alternatives such as reranking. Joint work with Haike Xu and Sandeep Silwal.

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.