Mathematics Department

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 4Meeting with majors. No talk this week.
Sept 11The 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.

Sept 18Leadership Summit
Sept 25Jamie Pommersheim
Oct 2Aaron Abrams
Oct 9TBA
Oct 16TBA
Oct 23Fall break
Oct 30TBA
Nov 6TBA
Nov 13TBA
Nov 20TBA
Nov 27Thanksgiving. No talk this week.
Dec 4TBA

Spring

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

Jan 29TBA
Feb 5TBA
Feb 12TBA
Feb 19TBA
Feb 26TBA
Mar 5TBA
Mar 12TBA
Mar 19Spring Break
Mar 26TBA
Apr 2TBA
Apr 9TBA
Apr 16TBA
Apr 23TBA
Apr 30TBA