# Difference between revisions of "PDE Geometric Analysis seminar"

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== Abstracts == | == Abstracts == | ||

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+ | ===Jun Kitagawa (Toronto)=== | ||

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+ | Regularity theory for generated Jacobian equations: from optimal transport to geometric optics | ||

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+ | Equations of Monge-Ampere type arise in numerous contexts, and solutions often exhibit very subtle qualitative and quantitative properties; this is owing to the highly nonlinear nature of the equation, and its degeneracy (in the sense of ellipticity). Motivated by an example from geometric optics, I will talk about the class of Generated Jacobian Equations; recently introduced by Trudinger, this class also encompasses, for example, optimal transport, the Minkowski problem, and the classical Monge-Ampere equation. I will present a new regularity result for weak solutions of these equations, which is new even in the case of equations arising from near-field reflector problems (of interest from a physical and practical point of view). This talk is based on joint works with N. Guillen. |

## Revision as of 10:19, 18 January 2015

The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.

## Contents

### Previous PDE/GA seminars

### Tentative schedule for Fall 2015

# Seminar Schedule Spring 2015

date | speaker | title | host(s) |
---|---|---|---|

January 21 (Departmental Colloquium: 4PM, B239) | Jun Kitagawa (Toronto) | Regularity theory for generated Jacobian equations: from optimal transport to geometric optics | Feldman |

January 26 | |||

February 2 | Jessica Lin (Madison) | TBA | Kim |

February 9 | |||

February 16 | |||

February 23 | Jennifer Beichman (Madison) | TBA | Kim |

March 2 | Benoit Pausader (Princeton) | TBA | Kim |

March 9 | |||

March 16 | |||

March 23 | |||

March 30 | Spring recess Mar 28-Apr 5 (S-N) | ||

April 6 | |||

April 13 | |||

April 20 | Yuan Lou (Ohio State) | TBA | Zlatos |

April 27 | |||

May 4 |

## Abstracts

### Jun Kitagawa (Toronto)

Regularity theory for generated Jacobian equations: from optimal transport to geometric optics

Equations of Monge-Ampere type arise in numerous contexts, and solutions often exhibit very subtle qualitative and quantitative properties; this is owing to the highly nonlinear nature of the equation, and its degeneracy (in the sense of ellipticity). Motivated by an example from geometric optics, I will talk about the class of Generated Jacobian Equations; recently introduced by Trudinger, this class also encompasses, for example, optimal transport, the Minkowski problem, and the classical Monge-Ampere equation. I will present a new regularity result for weak solutions of these equations, which is new even in the case of equations arising from near-field reflector problems (of interest from a physical and practical point of view). This talk is based on joint works with N. Guillen.