Welcome to the home page of the Graduate Analysis Seminar. This page will list the past and upcoming talks for the seminar. For the Fall 2016 Semester, the seminar is being organized by Érik De Amorim, and will run at Mondays at 5pm in the Graduate Student Lounge (Hill 701).
Speaker: Matt Charnley
Date: October 17, 2016
Abstract: The inverse scattering problem, trying to locate an obstacle from either the far-field or near-field scattering data, is a highly non-linear problem. If the wavelength of the source is similar to the dimensions of the obstacle, the problem is inherently non-linear, and neither the high- or low-frequency approximations work. In this talk, I will discuss the so-called ``linear sampling method'' for solving this inverse problem. It reduces the problem to solving a linear integral equation at each point, and using the result to determine whether or not that point is contained in the obstacle. At the end, we will discuss the potential for applying this method in physical situations.
Speaker: Katie McKeon
Date: October 10, 2016
Abstract: I'll discuss a new technique (due to Professors Falk and Nussbaum) for efficiently estimating Hausdorff dimension of certain sets.
Speaker: Érik Amorim
Date: October 3, 2016
Abstract: I will talk about the things in the title, assuming no prior knowledge, and show how they can all be used together to prove the Elliptic Regularity Theorem. This theorem basically says that an elliptic PDE has the property that its solutions are as regular as you can expect, given the order of the equation, for an appropriate meaning of "regular".