For more information about this meeting, contact Nigel Higson, Stephanie Zerby.

Title: | Geometry and physics in high-dimensional Euclidean spaces |

Seminar: | Department of Mathematics Colloquium |

Speaker: | Sal Torquato, Princeton University |

Abstract: |

I will discuss five different problems that arise in discrete geometry, physics and materials science in d-dimensional Euclidean space: sphere packings, density fluctuations via the number variance (closely related to a problem in number theory), coverings, quantizers, and continuum percolation. Four of these problems can be posed as energy minimization problems, i.e., ground states of many particles interacting with various potential functions. The connections between all of these problems are discussed. Strong theoretical evidence for the remarkable possibility that disordered (rather than ordered) sphere packings are the densest for sufficiently large dimensions is provided. Indeed, disordered point patterns may provide the optimal solutions for the density-fluctuation, covering and quantizer problems in high enough dimensions. |

### Room Reservation Information

Room Number: | MB114 |

Date: | 10 / 31 / 2013 |

Time: | 03:35pm - 04:25pm |