Mathematics Colloquium

All colloquia are on Fridays at 4:00 pm in Van Vleck B239, unless otherwise indicated. The calendar for spring 2019 can be found here.

Fall 2018

date	speaker	title	host(s)
Sep 12	Gunther Uhlmann (Univ. of Washington) Distinguished Lecture series	Harry Potter's Cloak via Transformation Optics	Li
Sep 14	Gunther Uhlmann (Univ. of Washington) Distinguished Lecture series	Journey to the Center of the Earth	Li
Sep 21	Andrew Stuart (Caltech) LAA lecture	The Legacy of Rudolph Kalman	Jin
Sep 28	Gautam Iyer (CMU)	TBA	Thiffeault
Oct 5	Eyal Subag (Penn State)	TBA	Gurevich
Oct 12	Arie Levit (Yale)	TBA	Gurevich
Oct 19	Jeremy Teitelbaum (U Connecticut)	TBA	Boston
Oct 26	Douglas Ulmer (Arizona)	TBA	Yang
Nov 2	Reserved for job talk	TBA	hosting faculty
Nov 9	Reserved for job talk	TBA	hosting faculty
Nov 16	Reserved for job talk	TBA	hosting faculty
Nov 30	Reserved for job talk	TBA	hosting faculty
Dec 7	Reserved for job talk	TBA	hosting faculty

Abstracts

Sep 12: Gunther Uhlmann (Univ. of Washington)

Harry Potter's Cloak via Transformation Optics

Can we make objects invisible? This has been a subject of human fascination for millennia in Greek mythology, movies, science fiction, etc. including the legend of Perseus versus Medusa and the more recent Star Trek and Harry Potter. In the last fifteen years or so there have been several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion one of them, the so-called "traansformation optics" in a non-technical fashion n the so-called that has received the most attention in the scientific literature.

Sep 14: Gunther Uhlmann (Univ. of Washington)

Journey to the Center of the Earth

We will consider the inverse problem of determining the sound speed or index of refraction of a medium by measuring the travel times of waves going through the medium. This problem arises in global seismology in an attempt to determine the inner structure of the Earth by measuring travel times of earthquakes. It has also several applications in optics and medical imaging among others.

The problem can be recast as a geometric problem: Can one determine the Riemannian metric of a Riemannian manifold with boundary by measuring the distance function between boundary points? This is the boundary rigidity problem. We will also consider the problem of determining the metric from the scattering relation, the so-called lens rigidity problem. The linearization of these problems involve the integration of a tensor along geodesics, similar to the X-ray transform.

We will also describe some recent results, join with Plamen Stefanov and Andras Vasy, on the partial data case, where you are making measurements on a subset of the boundary. No previous knowledge of Riemannian geometry will be assumed.

Sep 21: Andrew Stuart (Caltech)

The Legacy of Rudolph Kalman

In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.