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Mathematics

CBB Algebra-Topology Colloquium Series

The Colby-Bates-Bowdoin Algebra-Topology Colloquium Series will consist of six lectures by preeminent mathematicians working in the fields of algebra and topology. Additionally, a number of local seminar participants will contribute lectures based on their own research.

This research seminar will bring together members of the mathematics departments of Bates, Bowdoin and Colby Colleges with research interests related to algebra and topology. The seminar has two main goals:

  • to provide a forum in which participants can discuss recent developments in these fields of mathematics, and
  • to stimulate interaction and research between members of these three mathematics departments.

This last goal is based on an emerging trend in research mathematics: solutions to intricate problems in mathematics, and especially in topology, require techniques from a wide variety of mathematical subfields. This seminar will facilitate the exchange of ideas among local participants and with visiting lecturers.

Calendar

Friday, February 2, 2008
David Vogan, MITSpeaker: David Vogan
Massachusetts Institute of Technology
4:30 in Searles 217. Reception at 4:00.
Title: The Character Table for E8, or How we wrote down a 453,060 by 453,060 matrix and found happiness.

Abstract:
This is a story about what happens when pure mathematicians, proud of their inability to add, try to do a really large computation. I'll explain something about what character tables for Lie groups look like, what interesting information is inside them, and how "we" (that is, Jeff Adams and Fokko du Cloux) went about this computation.

Sponsored by the Mellon Foundation and Bowdoin, Bates and Colby Colleges

Tuesday, February 19
David Fisher, Indiana University-Bloomington, speaking at Bowdoin College

Friday, March 7
Ross Geoghegan, Binghamton University, speaking at Bates College

Tuesday, March 18
Joseph Silverman, Brown University, speaking at Bates College

Monday, April 21
Kiran Kedlaya, Massachusetts Institute of Technology, speaking at Bowdoin College

Previously

Friday, Oct. 26, 2007
Prof. Michael Hopkins of Harvard 

October 12, 2007
Speaker: James Cannon, BYUSpeaker: James Cannon, BYU
4:30 in Searles 217. Reception at 4:00.
Title: Random 3-Manifolds

Abstract:
Every 3-manifold can be obtained by identifying faces in pairs on the boundary of a 3-cell with cellulated boundary. However, the probability of obtaining a closed 3-manifold by such a face-pairing, chosen randomly, is 0, according to a theorem of Dunfield and Thurston. Typically, one obtains instead a 3-dimensional pseudo-manifold having at least one vertex whose link is a closed 2-manifold that is not a 2-sphere.

I will outline a proof of the Dunfield and Thurston theorem, then describe the simple bitwist operation which starts with a random face-pairing and mechanically yields a parametrized, infinite collection of closed 3-manifolds. (The construction generalizes our earlier twisted-face-pairing construction.)

The advantages of the bitwist operation are these: (1) One obtains every closed, orientable 3-manifold in this manner. (2) If the original face-pairing is simple, even trivial, the resultant face-pairings are also relatively simple. (3) The bitwist face-pairings yield elegant presentations for the fundamental groups involved. (4) The parametrized fundamental groups yield beautiful families for study by the methods of geometric group theory.

Colloquium Organizers

Jennifer Taback, Bowdoin College
Peter Wong, Bates College
Alex Ghitza, Colby College

Funding for the project was provided by The Andrew W. Mellon Foundation