Mathematics Graduate Students Organization

Seminar:

Date: February 24

P. Tretkoff: "An introduction to transcendental number theory old-modern and newer-old-modern"

Abstract: We give some history of the beginnings of modern transcendence from the 1800's. We then view these same results in 20th century terms and highlight some open problems of the 21st century.

G. Petrova: "Convergence rates for greedy algorithms in reduced basis methods."

Abstract: The reduced basis method is used for the accurate online evaluation of solutions to a parameter dependent family of elliptic partial differential equations. It can be viewed as determining a “good” n dimensional space to be used in approximating the elements of a compact set in a Hilbert space. A popular computational approach is to find this space through a greedy strategy. We quantify the performance of this greedy strategy by relating it to the performance of the best n-dimensional subspace that would minimize the projection error for the whole compact set over all n-dimensional subspaces (the so-called Kolmogorov width).