# 2014-2015 Baylor Lecture Series in Mathematics

## Gunther Uhlmann

Professor Gunther Uhlmann, the Walker Family Professor of Mathematics at the University of Washington, was the speaker in the eighth annual Baylor Lecture Series in Mathematics. Dr. Uhlmann visited Baylor University from October 14-17, 2014.

Dr. Uhlmann has earned several honors and won several awards for his research during his career. In 2001, he was elected a Corresponding Member of the Chilean Academy of Sciences. He is a Fellow of the Institute of Physics (2004), the American Academy of Arts and Sciences (2009), a SIAM Fellow (2010), and an AMS Fellow (2012). He was an invited speaker at the International Congress of Mathematicians in Berlin in 1998 as well as a plenary speaker at the International Congress on Industrial and Applied Mathematics in Zurich in 2007. Professor Uhlmann was named a Clay Senior Scholar at the Mathematics Research Institute at UC Berkeley. He received a Sloan Fellowship in 1984 and a Guggenheim Fellowship in 2001. He won both the Bôcher Memorial Prize and the Kleinman Prize in 2011, the same year that he was the Rothschild Distinguished Visiting Professor at the Isaac Newton Institute at Cambridge. Dr. Uhlmann delivered the American Mathematical Society’s Einstein Lecture in 2012. In 2013, Dr. Uhlmann was elected Foreign Member of the Finnish Academy of Science and Letters. In 2015, he will give a plenary lecture at the International Congress of Mathematical Physics.

Dr. Uhlmann studied mathematics as an undergraduate student at the Universidad de Chile in Santiago, gaining his Licenciatura degree in 1973. He continued his studies at MIT, where he earned his Ph.D degree in 1976. He has held postdoctoral positions at MIT, Harvard, and NYU, including a Courant Instructorship at the Courant Institute in 1977-1978. In 1980, he became an Assistant Professor at MIT and then moved, in 1985, to the University of Washington. In 2010-2012, he was on leave at the University of California, Irvine, as the Excellence in Teaching Chair.

Professor Uhlmann’s research in microlocal analysis and its applications is well known. For the past several years, he has been interested in the physics and mathematics of cloaking and invisibility and transformation optics.

The titles, and abstracts, for his two lectures are:

*Wednesday, October 15, 2014 at 4:00 pm - MMSci 101*

### PUBLIC LECTURE: Harry Potter's Cloak

**Abstract**: Invisibility has been a subject of human fascination for millennia, from the Greek legend of Perseus versus Medusa to the more recent The Invisible Man, The Invisible Woman, Star Trek and Harry Potter, among many others.

Over the years, there have been occasional scientific prescriptions for invisibility in various settings but the route to cloaking that has received the most attention has been transformation optics. To achieve invisibility one can design materials that would steer light around a hidden region, returning it to its original path on the far side. Not only would observers be unaware of the contents of the hidden region, they would not even be aware that something was being hidden.

As Science Magazine stated in 2006 in naming cloaking one of the 10 breakthroughs of the year: "...no matter how you look at it the ideas behind invisibility are likely to cast a long shadow".

*Thursday, October 16, 2014 at 4:00 pm - MMSci 301*

### Inverse Problems: Seeing the Unseen

**Abstract**: Inverse problems arise in all fields of sciences and technology where causes for a desired or observed effect are to be determined. By solving an inverse problem is in fact is how we obtain a large part of our information about the world. An example is human vision: from the measurements of scattered light that reaches our retinas, our brains construct a detailed three-dimensional map of the world around us. We know about the interior structure of the Earth by using the information provided by earthquakes, the structure of DNA from solving inverse X-ray diffraction problems, and the structure of the atom and its constituents from studying the scattering when materials are bombarded with particles. Medical imaging is also a fertile area of application of inverse problems including CT scans, ultrasound, MRI, and several other imaging methods.

We will describe several inverse problems and concentrate in more detail on the mathematics of the inverse problem proposed by Calder\'on, also called Electrical Impedance Tomography: Can one determine the conductivity inside a medium by making voltage and current measurements at the boundary? This problems arises, for instance, in early breast cancer detection and oil exploration.