Princeton University

David Persson presents Polar Express, a method for polar decomposition and the matrix sign function motivated by the Muon neural-network optimizer. It uses matrix multiplications suited to GPUs and adapts each polynomial update through a minimax problem to reduce worst-case error. The talk covers convergence, finite-precision implementation in bfloat16 and validation-loss improvements when training GPT-2 on FineWeb data. This is an in-person PACM IDeAS seminar at Princeton.

Lawrence Cheuk presents experiments using laser-cooled polar molecules held in optical-tweezer arrays. Molecular internal states and electric-dipole interactions provide resources for quantum computation, simulation and precision measurement. The talk covers preparation, control and detection of individual molecules; two-qubit operations and deterministic molecular entanglement; and one-dimensional spin simulations. Those experiments examine how spin excitations move, form bound pairs and undergo coherent pair creation and removal. A second set of experiments generates molecular spin-squeezed states and uses spatially resolved measurements to investigate reduced measurement noise, bipartite entanglement and Einstein-Podolsky-Rosen steering. Preliminary progress toward larger arrays may also be discussed. The Donald R. Hamilton Colloquium takes place in Jadwin Hall A-10 at Princeton University.

Leonid Berlyand discusses mathematical models for the onset of cell motion driven by myosin contraction. A two-dimensional free-boundary PDE model links cell-shape evolution to diffusion and Keller–Segel-type transport. The talk examines linear stability, a stability-determining eigenvalue and the way nonlinear diffusion changes the bifurcation from supercritical to subcritical. It also considers the curvature of the bifurcation curve, connections to bistability, and the role of non-self-adjoint operators. An example illustrates why a spectral gap alone need not guarantee stability. This is an in-person Analysis of Fluids and Related Topics seminar at Princeton.