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Today

Barbara Kaltenbacher, University of Klagenfurt, Some Asymptotics of Equations in Nonlinear Acoustics

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High 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

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One 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

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Machine 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…

Jérôme Bolte, Université Toulouse 1 Capitole, A Bestiary of Counterexamples in Smooth Convex Optimization

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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,…

Andrea Klaiber-Langen and Vakhtang Putkaradze from ATCO

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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,…

Alban Quadrat, Sorbonne University, Paris, France, An introduction to the Quillen-Suslin theorem: algorithms and applications

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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.…

Oliver Dragičević, University of Ljubljana, Slovenia, Trilinear embedding theorem for elliptic partial differential operators in divergence form with complex coefficients

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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…

‪Joris Roos, University of Massachusetts Lowell, Discrete analogues of maximally modulated singular integrals of Stein-Wainger type

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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…

Jonathan Hauenstein, University of Notre Dame, Energy landscapes and algebraic geometry

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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…

Qualifying Exams Presentation and Panel

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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