Applied Math
Organizers: ryzhik [at] stanford.edu (Lenya Ryzhik) & lexing [at] stanford.edu (Lexing Ying)
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Upcoming Events
In recent years, researchers have developed a number of fast, randomized algorithms for linear algebra problems. But for widespread deployment of these methods, speed is not enough. To safely incorporate randomized algorithms into general-purpose linear algebra software, we need algorithms which…
This talk will discuss some nontrivial but often pleasant effects of large learning rates, which are commonly used in machine learning practice for improved empirical performances, but defy traditional theoretical analyses. I will first quantify how large learning rates can help gradient descent…
Abstract
Past Events
This talk discusses the unstructured sparse recovery problems of a general form. The task is to recover the spike locations and weights of an unknown sparse signal from a collection of its unstructured observations. Examples include rational approximation, spectral function estimation, Fourier…
Degree-d multivariate polynomials over small finite fields are of central importance in theoretical computer science. And yet they retain many mysteries; for example, their Fourier spectra are very poorly understood. We will discuss the so-called "Fourier growth" of such functions…
I will present fast practical algorithms for approximate semidefinite programming (SDP) based on regularization by the von Neumann entropy. These approaches are based on a dual formulation of the regularized problem, and dual updates are computed using randomized trace estimators.…
The singularity formation problem is a central question in fluid dynamics, and it is still widely open for several fundamental models, including the 3d incompressible Euler equations. In this talk, I will first review the singularity formation problem, describing how particle transport poses the…
The large-scale rheology of random suspensions aims at describing how suspensions of small but many objects influence (sometimes drastically) a fluid flow. In physics this is the realm of complex fluids, with well-established phenomenological models. The derivation of such models from the…
Placing a two-dimensional lattice on another with a small rotation gives rise to periodic “moiré” patterns on a superlattice scale much larger than the original lattice. The Bistritzer-MacDonald (BM) model attempts to capture the electronic properties of twisted bilayer graphene (TBG) by…
Nonlinear resonance is a mechanism by which energy is continuously exchanged between a small number of wave modes, and is common to many nonlinear dispersive wave systems. In the context of free-surface gravity waves, nonlinear resonances have been studied extensively over the…
In this talk, I will introduce a new quantum algorithm for the quantum ground state preparation problem. Different from previous algorithms, our method is based on the simulation of a specific Lindblad dynamics that contains only one jump operator and fixes the ground state as an equilibrium.…
The stochastic heat equation is a fundamental model in statistical physics featuring noise scaled by the solution itself. In this talk, I will discuss the pointwise statistics of a family of nonlinear stochastic heat equations in the critical dimension two. Curiously, these statistics evoke a "…
Abstract: Classical algorithms are often not effective for solving nonconvex optimization problems where local minima are separated by high barriers. In this talk, we introduce optimization algorithms based on quantum dynamical systems. On the one hand, we leverage the global effect of…