CIMS Weekly Bulletin | About this seminar | Contact Info |

Speaker: | Daniel L. Stein | |
---|---|---|

Title: | Order, Disorder, Symmetry and Complexity | |

Date and time: | April 25, 1:00 p.m. (light refreshments at 12:45 p.m.) | |

Venue: | WWH 1302 |

One of the deepest scientific questions we can ask is, How might complexity arise? That is, starting from simple, undirected processes subject to physical and chemical laws, how could structures with complex shapes and patterns arise, and even more perplexing, what processes could give rise to living cells, and how might they then organize themselves into complex organisms, leading ultimately to such things as brains, consciousness, and societies? We are far from answering these questions at almost any level, but they have attracted increasing attention in the scientific community, and some initial headway has been made. The basic problem can be reframed as one involving the self-organization of microscopic constituents into larger assemblies, in such a way that the process leads to an increase of information, the creation of new patterns, and eventually increasing hierarchical levels of complex structure. The key to understanding these processes cannot be found in any single (natural or social) scientific field but rather in collaborations that cross many disciplinary boundaries.Although we are still at the initial stages of inquiry, new and interesting approaches and points of view have arisen. In this talk I present one that arises from the point of view of physics. We start by describing the (well-understood) phenomenon of matter organizing itself into simple ordered structures, like crystals and magnets, and then explore how our ideas are affected when we consider the effects of randomness and disorder, pervasive in the physical world. We will see that randomness and disorder are, paradoxically, essential for more ordered, complex structures to arise. Using these ideas, we provide some hints (but only hints) as to how we can gain a handle on issues related to the increase of complexity. Underlying all of our considerations is the notion of symmetry in physics: where it comes from and how matter "breaks" its inherent symmetry to create new information and ever-increasing complexity.

It aims to accomplish the following:

- provide a venue for talks that young mathematicians will
*understand* - expose students to
*areas of research*at the Courant Institute

Speaker: | Miles Crosskey, Duke University | |
---|---|---|

Title: | Learning and Fast Simulation of Intrinsically Low-Dimensional Stochastic Dynamical Systems in High Dimensions | |

Abstract |

Speaker: | Michael L. Overton | |
---|---|---|

Title: | Investigation of Crouzeix's Conjecture via Optimization | |

Abstract |

Speaker: | Pierre Germain | |
---|---|---|

Title: | The Mathematics and Physics of weak turbulence | |

Abstract |

Speaker: | Katherine Newhall | |
---|---|---|

Title: | Dynamics of ferromagnets: averaging methods, bifurcation diagrams, and thermal noise effects | |

Abstract |

Speaker: | Mehryar Mohri | |
---|---|---|

Title: | Multiple-Source Adaptation Problem | |

Abstract |

Speaker: | Zahra Sinaei | |
---|---|---|

Title: | Convergence of harmonic maps | |

Abstract |

Speaker: | Daniel L. Stein | |
---|---|---|

Title: | Order, Disorder, Symmetry and Complexity | |

Abstract |

Speaker: | Leslie Greengard | |
---|---|---|

Title: | TBA | |

Abstract |

Aukosh Jagannath | aukosh [at] cims [dot] nyu [dot] edu | |

Irena Vankova | vankova [at] cims [dot] nyu [dot] edu | |

Klaus Widmayer | klaus [at] cims [dot] nyu [dot] edu |

Department of Mathematics

Courant Institute of Mathematical Sciences

New York University

251 Mercer St.

New York, NY 10012