In this “something for everyone” talk, we will place the matrix decompositions that are so valuable in all fields of computation in a historical abstract context. It is well known that the singular value decomposition was discussed as far back as the 19th century by Beltrami and Jordan. Lesser known is that Cartan had a blueprint…
In this talk, I'll survey recent progress on problems in additive combinatorics, harmonic analysis, and ergodic theory related to Bergelson and Leibman's polynomial generalization of Szemer\'edi's theorem. Zoom ID: 980 3116 7550 Passcode: last 4 digits of the Zoom ID in reverse order
Counterexamples to some old-standing optimization problems in the smooth convex coercive setting are provided. Block-coordinate, steepest descent with exact search or Bregman descent methods do not generally converge. Other failures of various desirable features are established: directional convergence of Cauchy’s gradient curves, convergence of Newton’s flow, finite length of Tikhonov path, convergence of central paths,…
Congratulations, you are graduating with a PhD! You have done fantastic work in your thesis and are ready to take on the world. What is going to happen now? Should you go to industry or academia? You probably heard a lot about both job choices. In this lecture, the speakers, Andrea Klaiber-Langen and Vakhtang Putkaradze,…
Consider the geometric inverse problem: There is a set of delta-sources in spacetime that emit waves travelling at unit speed. If we know all the arrival times at the boundary cylinder of the spacetime, can we reconstruct the space, a Riemannian manifold with boundary? With a finite set of sources we can only hope to…
Chair: Seth Sullivant (smsulli2@ncsu.edu, contact for Zoom access)
In 1955, Serre conjectured that every row vector with entries in a commutative polynomial ring R=k over a field k, admitting a right inverse over R, could be completed into a square matrix whose determinant is 1. That conjecture was independently proved by Quillen and Suslin in 1976 and is nowadays called the Quillen-Suslin theorem.…
We introduce the notion of p-ellipticity of a complex matrix function and discuss basic examples where it plays a major role, as well as the techniques that led to the introduction of the notion. In the second part of the talk we focus on a so-called trilinear embedding theorem for complex elliptic operators and its…
Stein and Wainger introduced an interesting class of maximal oscillatory integral operators related to Carleson's theorem. The talk will be about joint work with Ben Krause on discrete analogues of some of these operators. These discrete analogues feature a number of substantial difficulties that are absent in the real-variable setting and involve themes from number theory and analysis. Zoom…
Broadly speaking, an energy landscape is the graph of a loss function over a parameter space. Some examples include the potential energy landscape of a chemical reaction, measuring the fitness of a mechanism to perform many tasks, and a loss function arising from a training set in machine learning. This talk will discuss some successes…
It's time for the last installment in our "Milestones" Series: The Qualifying Exams Presentation and Panel. This event will consist of a short presentation giving an overview of qualifying exams, followed by a panel of four students who cumulatively have taken nearly every qualifying exam. Where: https://ncsu.zoom.us/j/92018165412
Chair: Cynthia Vinzant (clvinzan@ncsu.edu, contact for Zoom access)
Chair: Patrick L. Combettes (plc@math.ncsu.edu, contact for Zoom access)
Chair: Irina Kogan (Contact Eric at edgeiger@ncsu.edu for Zoom access)
Chair: Hien Tran (tran@ncsu.edu) and Kevin Flores (kbflores@ncsu.edu) - contact for Zoom access
Chair: Agnes Szanto (aszanto@ncsu.edu, contact for Zoom access)
Chair: Bojko Bakalov (bnbakalo@ncsu.edu, contact for Zoom access)
Chair: Tim Kelley (tim_kelley@ncsu.edu, contact for Zoom access)
In order to explain the bi-concave shape of red blood cells, Helfrich proposed to study the minimisation of a bending energy amongst closed surfaces with given fixed area and volume. In the homogeneous case, the Helfrich functional simplifies to the scaling invariant Willmore functional. Thus, for the minimisation, the two constraints on area and volume…