Ivan Ventura's Abstract

 

Claremont Mathematics Weekend

 

Sponsored by Claremont Colleges

 

January 30 - 31, 2016

 

Speaker: Ivan Ventura
Title: Can you "hear" the shape of a radial Schrödinger operator?
Abstract:

Inverse problems are a large class of both theoretical and applied problems that have captivated the mathematical community for over half a century.  During this time numerous applications have arisen in in a variety of fields, such as medical imaging and cloaking. In the first half of this talk  I will discuss, by example, general inverse problems and how they arise in the real world. In the second half I will focus specifically on spectral inverse problems, starting with the classic "Can you hear the shape of a drum?" problem in the case of the sphere. Finally I will present an analogous result for semiclassical Schr\"odinger operators.