Vishesh Jain, Stanford University, On the real Davies’ conjecture

We 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,…

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GaYee Park, University of Massachusetts Amherst, Naruse hook formula for linear extensions of mobile posets

Linear 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…

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

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…

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Orsola Capovilla-Searle, Duke, Infinitely many Lagrangian Tori in Milnor fibers constructed via Lagrangian Fillings of Legendrian links

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…

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Dylan Bates, NC State, Machine Learning: My First Neural Networks

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…

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Alan Edelman, Massachusetts Institute of Technology, 53 Matrix Factorizations and Random Matrix Theory

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…

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Sarah Peluse, Princeton University/IAS, On the polynomial Szemer\’edi theorem and related results

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…

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

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…

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Andrea Klaiber-Langen and Vakhtang Putkaradze from ATCO

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…

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Teemu Saksala, NC State, Stable reconstruction of simple Riemannian manifolds from unknown interior sources

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…

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Pratik Misra, NC State, Combinatorial problems on trees and graphical models

Chair: Seth Sullivant (smsulli2@ncsu.edu, contact for Zoom access)

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

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…

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

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…

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

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…

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

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…

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Qualifying Exams Presentation and Panel

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…

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Georgy Scholten, NC State, Combinatorial and real algebraic structures in statistics and optimization

Chair: Cynthia Vinzant (clvinzan@ncsu.edu, contact for Zoom access)

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Zev Woodstock, NC State, Recovery of functions from nonlinear observations

Chair: Patrick L. Combettes (plc@math.ncsu.edu, contact for Zoom access)

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