# Colloquia/Fall18

## Contents

# 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 | TBA | 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)

Title: Harry Potter's Cloak via Transformation Optics

Abstract: 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)

Title: Journey to the Center of the Earth

Abstract: 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.