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?

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.