Applied Mathematics Colloquium - Fall 2017

Colloquium Schedule

Colloquia are held on Fridays at 11:30 a.m. in Cullimore Lecture Hall II, unless noted otherwise. Refreshments are served at 11:30 am. For questions about the seminar schedule, please contact David Shirokoff.

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Date Speaker, Affiliation, and Title Host
September 8 Allison Bishop, Columbia University
In Pursuit of Obfuscation

We will survey developments in cryptographic research on program obfuscation: the quest to make working code that can keep secrets.
Christina Frederick
September 15 Maxence Cassier, Columbia University
On the limiting Amplitude Principle for Maxwell’s Equations at the Interface of a Metamaterial

In this talk, we are interested in a transmission problem between a dielectric and a metamaterial. The question we consider is the following: does the limiting amplitude principle hold in such a medium? This principle defines the stationary regime as the large time asymptotic behavior of a system subject to a periodic excitation. An answer is proposed here in the case of a two-layered medium composed of a dielectric and a particular metamaterial (Drude model). In this context, we reformulate the time-dependent Maxwell’s equations as a Schrödinger equation and perform its complete spectral analysis. This permits a quasi-explicit representation of the solution via the ”generalized diagonalization” of the associated unbounded self-adjoint operator. As an application of this study, we show finally that the limiting amplitude principle holds except for a particular frequency, called the critical frequency, characterized by a ratio of permittivities and permeabilities equal to -1 across the interface. This frequency is a resonance of the system and the response to this excitation blows up linearly in time.
Roy Goodman
September 22 Robert Pego, Carnegie Mellon
Microdroplet Instablity in a Least-Action Principle for Incompressible Fluids

The least-action problem for geodesic distance on the `manifold' of fluid-blob shapes exhibits an instability due to microdroplet formation. This reflects a striking connection between Arnold's least-action principle for incompressible Euler flows and geodesic paths for Wasserstein distance. A connection with fluid mixture models via a variant of Brenier's relaxed least-action principle for generalized Euler flows will be outlined also. This is joint work with Jian-Guo Liu and Dejan Slepcev.
David Shirokoff
September 29 Alex Townsend, Cornell University
Why are There so Many Matrices of Low Rank in Computational Math?

Matrices that appear in computational mathematics are so often of low rank. Since random ("average") matrices are almost surely of full rank, mathematics needs to explain the abundance of low rank structures. We will give a characterization of certain low rank matrices using Sylvester matrix equations and show that the decay of singular values can be understood via an extremal rational problem. We will give another characterization involving the Johnson-Lindenstrauss Lemma that partially explains the abundance of low rank structures in big data.
Michael Booty
October 6 Aleksandar Donev, New York University
Lou Kondic
October 13 TBD TBD
October 20 Daniel Szyld, Temple University
Yassine Boubendir
October 27 Peter Monk, University of Delaware
Yassine Boubendir
November 3 Johannes Tausch, Southern Methodist University
Michael Siegel
November 10 Javier Diez, Rutgers University
Lou Kondic
November 17 Mike O'Neil, New York University
Shidong Jiang
December 1 Michael Shelley, New York University / Flatiron Institute
Michael Siegel
December 8 Mette Olufsen, North Carolina State University
Casey Diekman

Updated: September 12, 2017