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The Second Annual Binghamton University Graduate Conference in Algebra and Topology (BUGCAT) will be held on Saturday and Sunday, November 14 and 15, 2009.

Keynotes

Louis Kauffman (UIC)

Title: From Knots to the Temperley-Lieb Algebra and Back

Abstract: We define the Jones polynomial via the bracket state sum model and show how this model leads directly, via the states of closed braids, to a diagrammatic form of the Temperley-Lieb algebra, and to representations of this algebra. We will discuss relationships of the Temperley-Lieb algebra to physics, combinatorics, quantum computing and to the original work of Vaughan Jones. And we will discuss open problems such as: Does the Jones polynomial detect knots? Time-permitting, we will discuss how all of the above leads to ideas about categorification and Khovanov homology. It is intended that this talk be self-contained.

Kim Ruane (TUFTS)

Kim Ruane received her Ph.D. from Florida State University in 1996. In her dissertation, she considered questions about the boundary of a CAT(0) space that admits a geometric group action. She then had a three year postdoc at Vanderbilt, followed by a one year position at the ETH in Zurich, and has been at Tufts since 2000.

Title: Boundaries and how to use them!

Abstract: If a group G acts geometrically on a Gromov hyperbolic space or a CAT(0) space, then G also admits an action by homeomorphisms on the boundary of that space. First I will give several important examples of boundaries to motivate the definition. I will then discuss how the topology of this boundary and the action of G on it can be useful for proving theorems about the group G. In particular, I will give examples of theorems where this approach has been useful. I would also like to prove at least one of these results during the talk.

Schedule

The most current schedule is available on our Schedule Page.

Talks

Graduate students and faculty talks of all levels will take place Saturday and Sunday. Titles and abstracts for this years 40 talks are available here.

Hotel Reservations

We are able to provide full funding for double occupancy rooms at the Comfort Suites on Vestal Parkway. Hotel registration is now closed. If you have any questions please contact us.

This conference is supported by National Science Foundation Grant No. DMS0946269 and several Binghamton University departments and organizations including the Mathematics Department, Office of the Vice President for Research, Convocations Committee, Harpur Dean's Office, and the Graduate School.