We survey the known results concerning the minimal Riesz energy on sufficiently smooth sets, and present some new results on fractal sets, which are the key examples of non-rectifiable sets. In particular, we will talk about the connection of these problems to ergodic theory and probability theory: the key step in our proofs is applying…
The Ricci curvature Ric(g) is a symmetric 2-tensor on a Riemannian manifold (M,g) that encodes curvature information. It features in several interesting geometric PDEs such as the Ricci flow and the Einstein equation. The nature of Ric(g) as a differential operator -- nonlinear and degenerate elliptic -- make these equations particularly challenging. Host: Peter McGrath Instructions to join: Zoom…
Zoom link: https://ncsu.zoom.us/j/96495890729?pwd=VUhKZWFKbXBGLy9LVjlJalRsL2RBdz09 Passcode: SIAM Abstract: Join Tracie Ellis, Vice President Business Analytics at Bandwidth, for an informal discussion about her team’s role in creating a data-driven culture at Bandwidth, a software/telecommunications company on Centennial Campus. Tracie will share a bit of background about the company, their data evolution and the qualifications and experience of the Analytics…
Organizer: smsulli2@ncsu.edu
In this talk we discuss two ways in which dyadic analysis and number theory share a rich interaction. The first involves a complete classification of "distinct dyadic systems". These are sets of grids which allow one to compare any Euclidean ball nicely with any dyadic cube, and allow for showing that a large number of…
Chair: Seth Sullivant (smsulli2@ncsu.edu, contact for Zoom access)
Inverse problems are ubiquitous in many areas of Science and Engineering and, once discretized, they lead to ill-conditioned linear systems, often of huge dimensions: regularization consists in replacing the original system by a nearby problem with better numerical properties, in order to find a meaningful approximation of its solution. After briefly surveying some standard regularization…
When is a function in the spacetime uniquely determined by its integrals over all light rays? I will introduce the problem, discuss why we might care about it, and how one might go about proving such uniqueness results. Depending on time and audience interest, I can also discuss proofs and tensor tomography. Organizer: T.…
Chair: Arvind Saibaba (asaibab@ncsu.edu, contact for Zoom access)
Chair: Alina Chertock (chertock@math.ncsu.edu, contact for Zoom access)
Chair: Alen Alexanderian (alexanderian@ncsu.edu, contact for Zoom access)
In 2001, Lasserre introduced a nowadays famous hierarchy of relaxations, called the moment-sums of squares hierarchy, allowing one to obtain a converging sequence of lower bounds for the minimum of a polynomial over a compact semialgebraic set. Each lower bound is computed by solving a semidefinite program (SDP). There are two common drawbacks related to…
If you take a simple finite-dimensional Lie algebra g and tensor it with the Laurent polynomials in one variable, then you will get an infinite-dimensional Lie algebra known as a loop algebra. Affine Lie algebras are the central extensions of such loop algebras and their representations have been of interest to several mathematicians. What happens if we tensor g with…
Chair: Mette Olufsen (msolufse@ncsu.edu, contact for Zoom access)
Chair: Kevin Flores (kbflores@ncsu.edu, contact for Zoom access)
The resurging interest in deep learning is commonly attributed to advances in hardware and growing data sizes and less so to new algorithmic improvements. However, cutting-edge numerical methods are needed to tackle ever larger and more complex learning problems. In this talk, I will illustrate numerical analysis tools for improving the effectiveness of deep learning…
A popular method to approximate a fixed point of a non-expansive map is C is the Krasnoselskii-Mann iteration. This covers a wide range of iterative methods in convex minimization, equilibria, and beyond. In the Euclidean setting, a flexible method to obtain convergence rates for this iteration is the PEP methodology introduced by Drori and Teboulle…
Chair: Tien Khai Nguyen, contact for Zoom access.