Infinite Dimensional Groups and Algebras in Quantum Physics

Representation theory of the Lorentz group
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Thematic Research Program: Operator Algebras, Groups and Applications to Quantum Information"

Its rich yet rigid structure admits a powerful general theory. Operator algebras have important applications to quantum mechanics, number theory, dynamical systems, and ergodic theory.

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Unfortunately, even compared to other areas of mathematics, operator algebras has suffered from a severe gender imbalance. The application was successful, and BIRS provided all accommodation and meals, and very good working facilities. We are very grateful for all the support we have received. Prior to the workshop, the women organized themselves into teams focusing on a research question to which they could contribute. The research groups were:. Wang explaining the project she will lead.

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Most of the workshop was spent working in these small groups, but on Monday and Friday each small group gave a 10 minute presentation to all participants on their project and progress. Several of the groups were so pleased with their progress and prospects for future success that they have already made arrangements to meet again.

Quantum group

This article originally appeared on page of the January-February issue of the newsletter of the Association for Women in Mathematics. These models though quite simplistic relative to their realistic counterparts, exhibit properties which are hard to study using conventional methods.

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Another class of simplistic but extremely interesting quantum field theories are topological quantum field theories. In these theories the "dynamics" is absent and all they "know" in the topology of the "underlying space-time". The theories provided new topological invariants.

One of the major directions of the project is to reconcile two approaches. Another direction of research is related to random discrete surfaces and related structures such as random partition, random tilings of a plane, random spanning trees on a planar graph etc.

Some of the questions in this direction are closely related to the limit when a topological quantum field theory known as Chern-Simons theory turns into a topological string theory. Part of the project is focused on the study of quantum groups at roots of unity. The goal is to investigate the category of generic modules as a monoidal category fibered over the corresponding group, and when it is the case, as as a braided monoidal category fibered over a braided group. The results will be applied to construct and study invariants of 3-manifolds with flat connections.

This direction is closely related to the possible relation between the A-polynomial and Jones invariant of knots, which was discussed in the literature in the last few years. The research will also be focused on dimer models and on related models in statistical mechanics.

Quantum group - Wikipedia

For example, the limit shapes for the 6-vertex model may have singular boundaries, and one of the goals is to study the fluctuations such singularities. Some full text articles may not yet be available without a charge during the embargo administrative interval. Some links on this page may take you to non-federal websites.

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