Conference on Lie Theory and Its Applications. Intellectual merit: In recent years, the representation theory of Lie groups has received a great deal of attention. This is a reflection of the depth of the ideas surrounding Lie theory and the consequent breadth of its applications. Representation theory is, however, only a small part of the mathematics touched by Lie theory. Lie theoretic ideas are influential in geometry and physics?important results by Nolan Wallach and others on quantifying entanglement of quantum states using invariant theory constitute one of their newest applications in physics, and have prompted new developments in invariant theory. In pure mathematics, Nolan Wallach and his collaborators have found significant applications to combinatorics, and to the theory of automorphic forms provides a central point of view in modern number theory that is becoming a leading application of Lie theoretic ideas.

Broader impact: These recent results in Lie theory demonstrate the potential impact of a conference emphasizing the applicability of Lie theory to other areas of mathematics and physics. We plan to begin the conference with two expository talks aimed at students and non-experts, in support of the goal of broadening participation in the mathematical sciences by members of under-represented groups, and to provide a foundation for research talks on the most beautiful and exciting work currently being done by both senior and junior mathematicians. By co-hosting one or more of the talks with the UCSD chapter of the Association for Women in Mathematics we expect to attract attendance from members of the quite diverse population of UCSD graduate students, in addition to participants from around the country and the world.

Project Report

held at the University of California/San Diego (UCSD) in March 2012. The talks at the conference were chosen to emphasize the diversity of Lie theory and its applications to other branches of mathematics and science. In mathematics, this includes algebra, differential equations, ring theory, combinatorics, number theory and geometry. There were also several talks on connections with physics: in quantum mechanics and to solutions of Maxwell's equations. A unifying theme was the contributions of Nolan Wallach (UCSD), a leading figure in the subject. A list of the speakers and their talk titles and abstracts can be found at: Springer-Verlag has signed a contract with conference organizers Roger Howe, Markus Hunziker and Jeb Willenbring to produce a volume of invited contributions drawn primarily from the talks at the conference. This work is expected to be completed in 2013. The conference was attended by numerous graduate students and postdoctoral researchers as well as junior and senior faculty members in mathematics, from across the United States (including California, New York, Connecticut, Massachussetts, Maryland, Texas, and Wisconsin) and the world (other countries represented by participants included Canada, Argentina, Switzerland, Korea, and Japan).

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Bruce P. Palka
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University of California San Diego
La Jolla
United States
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