## Colloquium

#### Upcoming Seminar

September 11,
4:10 PM
in
Physics 123*The Combinatorics of CAT(0) Cubical Complexes and Robotic Motion Planning*

Federico Ardila, Department of Mathematics, San Francisco State University

A cubical complex is CAT(0) if it has global non-positive curvature; informally, "all its triangles are thin". These complexes play an important role in pure mathematics (group theory) and in applications (phylogenetics, robot motion planning, etc.). In particular, as Abrams and Ghrist observed, when one studies the possible states of a discrete robot, one often finds that they naturally form a CAT(0) cube complex.

Gromov gave a remarkable topological/combinatorial characterization of CAT(0) cube complexes. We give an alternative, purely combinatorial description of them, allowing a number of applications. In particular, for many robots, we can use these tools to find the fastest way to move from one position to another one.

The talk will describe joint work with Tia Baker, Megan Owen, Seth Sullivant, and Rika Yatchak. It will require no previous knowledge of the subject, and be accessible to undergraduate students.

Most Thursday afternoons during the academic year, the Reed College Department of Mathematics hosts a math talk. The talks are directed to our mathematics majors but are usually accessible on a variety of levels. Refreshments are served before the talks. For more information, please email davidp at reed.edu.

### 2014-15 Schedule

#### Fall

**4:10-5:00** in **Physics 123** (unless marked otherwise). Directions to Reed.

Sept 4 | Meeting with majors. No talk this week. |
---|---|

Sept 11 | The Combinatorics of CAT(0) Cubical Complexes and Robotic Motion PlanningFederico Ardila, Department of Mathematics, San Francisco State University A cubical complex is CAT(0) if it has global non-positive curvature; informally, "all its triangles are thin". These complexes play an important role in pure mathematics (group theory) and in applications (phylogenetics, robot motion planning, etc.). In particular, as Abrams and Ghrist observed, when one studies the possible states of a discrete robot, one often finds that they naturally form a CAT(0) cube complex. Gromov gave a remarkable topological/combinatorial characterization of CAT(0) cube complexes. We give an alternative, purely combinatorial description of them, allowing a number of applications. In particular, for many robots, we can use these tools to find the fastest way to move from one position to another one. The talk will describe joint work with Tia Baker, Megan Owen, Seth Sullivant, and Rika Yatchak. It will require no previous knowledge of the subject, and be accessible to undergraduate students. |

Sept 18 | Leadership Summit |

Sept 25 | Jamie Pommersheim |

Oct 2 | Aaron Abrams |

Oct 9 | TBA |

Oct 16 | TBA |

Oct 23 | Fall break |

Oct 30 | TBA |

Nov 6 | TBA |

Nov 13 | TBA |

Nov 20 | TBA |

Nov 27 | Thanksgiving. No talk this week. |

Dec 4 | TBA |

#### Spring

**4:10-5:00** in **Physics 123** (unless marked otherwise). Directions to Reed.

Jan 29 | TBA |
---|---|

Feb 5 | TBA |

Feb 12 | TBA |

Feb 19 | TBA |

Feb 26 | TBA |

Mar 5 | TBA |

Mar 12 | TBA |

Mar 19 | Spring Break |

Mar 26 | TBA |

Apr 2 | TBA |

Apr 9 | TBA |

Apr 16 | TBA |

Apr 23 | TBA |

Apr 30 | TBA |