Applied Math Seminar
The Applied Math Seminar hosts a wide range of talks in fields such as applied analysis, mathematical biology, fluid dynamics and electromagnetics, numerical computation, etc.
The seminar usually meets at 2:30pm on Fridays in room 1302 of Warren Weaver Hall.
Please email oneil@cims.nyu.edu with suggestions for speakers. If you would like to be added to the mailing list, please send an email to cims-ams+subscribe@nyu.edu from the address at which you wish to receive announcements.
Seminar Organizer(s): Mike O'Neil
Upcoming Events
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Friday, January 24, 20252:30PM, Warren Weaver Hall 1302
Sailing as momentum transport
David Hogg, NYUSynopsis:
Sailboats represent an ancient (but newly relevant) sustainable form of transportation. They work off the relative velocity between the air and the water. Sailboats can sail upwind (by tacking), they can sail downwind faster than the wind (also by tacking), and they can sail crosswind much faster than the wind. I present the simplest possible momentum transport model of a sailboat, and explain all of these capabilities. In this model, the sailboat is defined by three dimensionless numbers: The sail-to-keel area ratio, a lift ratio for the sail, and a lift ratio for the keel. The model makes a number of amusing "predictions" that explain the properties of commercial and competitive sailboats. There are many connections to sustainable energy. (For the mathematicians: I will ask an open question, and point out an error made by Terence Tao.) -
Friday, February 14, 20252:30PM, Warren Weaver Hall 1302
Data driven reduced order modeling for first order hyperbolic systems with application to waveform inversion
Liliana Borcea, Columbia UniversitySynopsis:
Waveform inversion seeks to estimate an inaccessible heterogeneous medium by using sensors to probe the medium with signals and measure the generated waves. It is an inverse problem for a hyperbolic system of equations, with the sensor excitation modeled as a forcing term and the heterogeneous medium described by unknown, variable coefficients. The traditional formulation of the inverse problem, called full waveform inversion (FWI), estimates the unknown coefficients via nonlinear least squares data fitting. For typical band limited and high frequency data, the data fitting objective function has spurious local minima near and far from the true coefficients. This is why FWI implemented with gradient based optimization can fail, even for good initial guesses. We propose a different approach to waveform inversion: First, use the data to "learn" a good algebraic model, called a reduced order model (ROM), of how the waves propagate in the unknown medium. Second, use the ROM to obtain a good approximation of the wave field inside the medium. Third, use this approximation to solve the inverse problem. I will give a derivation of such a ROM for a general first order hyperbolic system satisfied by all linear waves in lossless media (sound, electromagnetic or elastic). I will describe the properties of the ROM and will use it to solve the inverse problem for sound waves.
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Friday, March 14, 20252:30PM, Warren Weaver Hall 1302
TBA
Manas Rachh, Center for Computational Mathematics, Flatiron Institute -
Friday, April 4, 20252:30PM, Warren Weaver Hall 1302
TBD
Emily Palmer, Cooper Union