Applied Math

Organizers:  ryzhik [at] stanford.edu (Lenya Ryzhik) & lexing [at] stanford.edu (Lexing Ying)

For more information and access to abstracts, click here.

Upcoming Events

May
28
Date11:00 AM
Location
384H
Speaker
Wei Cai (SMU)

In this talk, we will present a martingale based neural network, SOC-MartNet, for solving high-dimensional Hamilton-Jacobi-Bellman (HJB) equations where no explicit expression is needed for the Hamiltonian $\inf_{u \in U} H(t,x,u, z,p)$, and stochastic optimal control problems (SOCP) with…

May
29
Date12:00 PM
Location
384H
Speaker
Gautam Iyer (Carnegie Mellon University)

In many situations, the combined effect of advection anddiffusion enhances dissipation. I will talk about this in two contexts: The first is for a randomly shifted alternating shear flows where we show that dissipation enhancement occurs on time scale O(\ln κ), where κ is the molecular…

Jun
05
Date12:00 PM
Location
384H
Speaker
Simona Diaconu (MYU)

Abstract

Past Events

May
15
Date12:00 PM
Location
384H
Speaker
Alexei Novikov (Penn State)

High-resolution imaging in complex media, such as turbulent air, underwater environments, or biological tissues, faces challenges due to wavefront distortion caused by scattering from inhomogeneities. I will describe an approach for imaging point-like sources in scattering media when large and…

May
08
Date12:00 PM
Location
384H
Speaker
Roman Vershynin (UC Irvine)

Perhaps the most elegant mathematical definition of privacy of data is called "differential privacy". I will describe a somewhat more general framework, which leads to some fun questions at the interface of probability and metric geometry. This talk is based on joint work with March Boedihardjo…

May
01
Date12:00 PM
Location
384H
Speaker
Andrea Montanari (Stanford)

I will discuss the problem of solving a system of equations F(x)=0,for x a d-dimensional unit vectors and D a non-linear map from R^d to R^n whose components are independent, rotationally invariant Gaussian processes. We studied this problem under the proportional asymptotics in which n and…

Apr
26
Date11:00 AM
Location
384H
Speaker
Leo Zepeda (Wisconsin-Madison and Google)

The advent of generative AI has turbocharged the development of a myriad of commercial applications, and it has slowly started to permeate to scientific computing. In this talk we discussed how recasting the formulation of old and new problems within a probabilistic approach opens the door to…

Apr
24
Date12:00 PM
Location
384H
Speaker
Elena Kosygina (Baruch College)

In this talk, we shall discuss our recent work which shows that in the periodic homogenization of viscous HJ equations in any spatial dimension the effective Hamiltonian does not necessarily inherit the quasiconvexity property (in the momentum variables) of the original Hamiltonian. Moreover,…

Apr
12
Date11:00 AM
Location
384H
Speaker
Molei Tao (Georgia Tech)

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…

Apr
10
Date12:00 PM
Location
384H
Speaker
Christophe Gomez (Université Aix-Marseille)

This presentation first discusses the derivation of radiative transfer equations for acoustic waves propagating in a randomly fluctuating half-space in the weak-scattering regime, and the study of boundary effects through an asymptotic analysis of the Wigner transform of the…

Apr
03
Date12:00 PM
Location
384H
Speaker
Ethan Epperly (Caltech)

Abstract

Mar
13
Date12:00 PM
Location
384H
Speaker
Lexing Ying (Stanford)

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…

Mar
06
Date12:30 PM
Location
384H
Speaker
Joseph Sloth (Caltech)

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…