Conference on Lie Theory and Its Applications

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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.