Principal Investigator: Thang Le, Jozef H. Przytycki

This proposal supports US participation at the conference Swiss Knots 2011: Knot Theory and Algebra, to be held in Lake Thun, Switzerland in May 2011. The goal of the conference is to bring together experts and junior researchers to discuss recent advances and perspectives for future developments in Knot Theory and its interaction with Algebra. Specific topics include planar algebras, categorification and link homology, virtual knots, quantization, and various invariants of links and 3-manifolds.

The conference Swiss Knots 2011 will create a forum for the exchange of ideas between the experts in knot theory and algebra. Junior mathematicians will have a chance to learn about new developments in the fields and will be able to present their own research accomplishments. The participants will come from all over the world. The US researchers and graduate students will interact with mathematicians from other countries. Organizers hope this opportunity will yield future collaborations. More information about the conference can be found at the website

Project Report

conference was held during May 23-27, 2011 at Lake Thun, Switzerland and was supported under DMS-1105703. The purpose of the conference was to disseminate and exchange the latest ideas and developments in the area of knot theory and 3-manifold topology including the Jones polynomial, topological quantum field theories, the Kontsevich integral, gauge theory type invariants in 4-dimensional topology, etc. Knot theory has long been an active branch of topology. NSF funding was used to support travel expenses for 2 organizers and for 18 participants. Funding priority was given to graduate students, post-docs, young researchers and faculty with little or no support. Intellectual merit: There have been exciting new developments in the last 25 years. The new developments link knot theory to remote branches such as number theory, Lie theory, statistical physics, etc, and employ tools far beyond the traditional ones from algebraic topology. These ideas mark the beginning of a new era in knot theory that include relationships with four-dimensional problems and the creation of new forms of algebraic topology relevant to knot theory. The conference provided a place for world experts as well as young mathematicians to discuss and exchange ideas of these new developments in the interaction between knot theory and algebra. Broader Impact: The conference brought together participants from all over the world, third-world countries, women, minorities, and provided an opportunity for researchers and students to share their latest ideas and to collaborate with each other. The knowledge obtained during this occasion will be disseminated by participants throughout the world. The presentations included plenary talks by distinguished researchers, as well as short talks by other participants.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Christopher W. Stark
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Georgia Tech Research Corporation
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