Events
Vishesh Jain, Stanford University, On the real Davies’ conjecture
ZoomWe show that every $n \times n$ real matrix $A$ is within distance $\delta \|A\|$ in the operator norm of an $n\times n$ real matrix $A'$ whose eigenvectors have condition number $\tilde{O}(\text{poly}(n)/\delta)$. In fact, we show that with high probability, an additive i.i.d. sub-Gaussian perturbation of $A$ has this property. Up to log factors, this…
GaYee Park, University of Massachusetts Amherst, Naruse hook formula for linear extensions of mobile posets
ZoomLinear extensions of posets are important objects in enumerative and algebraic combinatorics that are difficult to count in general. Families of posets like straight shapes and $d$-complete posets have hook-length product formulas to count linear extensions, whereas families like skew shapes have determinant or positive sum formulas like the Naruse hook length formula from 2014.…
Barbara Kaltenbacher, University of Klagenfurt, Some Asymptotics of Equations in Nonlinear Acoustics
ZoomHigh intensity (focused) ultrasound HIFU is used in numerous medical and industrial applications ranging from lithotripsy and thermotherapy via ultrasound cleaning and welding to sonochemistry. The relatively high amplitudes arising in these applications necessitate modeling of sound propagation via nonlinear wave equations and in this talk we will first of all dwell on this modeling aspect. Then…
Orsola Capovilla-Searle, Duke, Infinitely many Lagrangian Tori in Milnor fibers constructed via Lagrangian Fillings of Legendrian links
ZoomOne approach to studying symplectic manifolds with contact boundary is to consider Lagrangian submanifolds with Legendrian boundary; in particular, one can study exact Lagrangian fillings of Legendrian links. There are still many open questions on the spaces of exact Lagrangian fillings of Legendrian links in the standard contact 3-sphere, and one can use Floer theoretic…
Dylan Bates, NC State, Machine Learning: My First Neural Networks
ZoomMachine learning has blown up in popularity in the past decade, with applications from healthcare to self-driving cars, being used to create art, play video games, and act as customer service representatives. One of the most common and useful tools for these applications are neural networks: universal function approximators. This interactive workshop is meant for…
Alan Edelman, Massachusetts Institute of Technology, 53 Matrix Factorizations and Random Matrix Theory
ZoomIn 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…
Sarah Peluse, Princeton University/IAS, On the polynomial Szemer\’edi theorem and related results
ZoomIn 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
Jérôme Bolte, Université Toulouse 1 Capitole, A Bestiary of Counterexamples in Smooth Convex Optimization
ZoomCounterexamples 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,…
Andrea Klaiber-Langen and Vakhtang Putkaradze from ATCO
ZoomCongratulations, 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,…
Teemu Saksala, NC State, Stable reconstruction of simple Riemannian manifolds from unknown interior sources
ZoomConsider 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…
Pratik Misra, NC State, Combinatorial problems on trees and graphical models
ZoomChair: Seth Sullivant (smsulli2@ncsu.edu, contact for Zoom access)
Alban Quadrat, Sorbonne University, Paris, France, An introduction to the Quillen-Suslin theorem: algorithms and applications
ZoomIn 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.…
Oliver Dragičević, University of Ljubljana, Slovenia, Trilinear embedding theorem for elliptic partial differential operators in divergence form with complex coefficients
ZoomWe 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…
Joris Roos, University of Massachusetts Lowell, Discrete analogues of maximally modulated singular integrals of Stein-Wainger type
ZoomStein 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…
Jonathan Hauenstein, University of Notre Dame, Energy landscapes and algebraic geometry
ZoomBroadly 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…
Qualifying Exams Presentation and Panel
ZoomIt'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
Georgy Scholten, NC State, Combinatorial and real algebraic structures in statistics and optimization
ZoomChair: Cynthia Vinzant (clvinzan@ncsu.edu, contact for Zoom access)
Zev Woodstock, NC State, Recovery of functions from nonlinear observations
ZoomChair: Patrick L. Combettes (plc@math.ncsu.edu, contact for Zoom access)