Inverse problems is a field of mathematics comprised of many areas including analysis, modeling, PDE's and scientific computation. Inverse problems arise in abundance in engineering, biology, physics, geophysics and more. This seminar addresses fundamental topics in inverse problems in a variety of applications.

Regular meeting times & location: Thursdays at 2 pm in Weber 223

Abstract: I will discuss several nonlinear PDEs that are integrable: the Korteweg - de Vries equation, the nonlinear Schroedinger equation, and the Davey-Stewartson equation. They are solved by methods referred to as inverse spectral / inverse scattering methods. I hope to explain this in a manner accessible to all. My interest is in understanding by rigorous analysis singular behaviors of the solutions of these equations. I seek to characterize phenomena such as the resolution into solitons, the formation of shocks, and the onset and propagation of wild oscillations. These phenomena are ubiquitous in nonlinear dynamical systems and PDEs, but analytical results are usually only possible in integrable examples. Open research directions will be discussed along the way.

Aug. 24 | Electrical impedance tomography imaging via the Radon transform | Samuli Siltanen, University of Helsinki |

Sept. 7 | no seminar - JM at IMA | |

Sept. 20 | The enclosure method for the anisotropic PDEs | Yi-Hsuan Lin, University of Washington |

Oct. 12 | Forward and inverse problems in geodynamic modelling: Part I -- Evolution of island chains in the South Atlantic and Indian Ocean | Rene Gassmoeller, CSU |

Oct. 26 | Forward and inverse problems in geodynamic modelling: Part II -- Thermochemical Convection | Juliane Dannberg, CSU |

Nov. 2 | no seminar - Math Day | |

Nov. 9 | Monte Carlo methods for radiative transfer with singular kernels | Olivier Pinaud, CSU |

Nov. 16 | Inverse problems and integrable PDEs | Kenneth McLaughlin, CSU |

[Spring 2015] [Fall 2014]