This quantity comprises the complaints of the convention on illustration conception and Mathematical Physics, in honor of Gregg Zuckerman's sixtieth birthday, held October 24-27, 2009, at Yale collage. Lie teams and their representations play a primary position of arithmetic, specifically due to connections to geometry, topology, quantity thought, physics, combinatorics, and plenty of different components. illustration idea is without doubt one of the cornerstones of the Langlands software in quantity idea, courting to the Nineteen Seventies. Zuckerman's paintings on derived functors, the interpretation precept, and coherent continuation lie on the middle of the trendy conception of representations of Lie teams. one of many significant unsolved difficulties in illustration conception is that of the unitary twin. the truth that there's, in precept, a finite set of rules for computing the unitary twin is based seriously on Zuckerman's paintings. lately there was a fruitful interaction among arithmetic and physics, in geometric illustration concept, string thought, and different parts. New advancements on chiral algebras, illustration concept of affine Kac-Moody algebras, and the geometric Langlands correspondence are the various focal issues of this quantity. contemporary advancements within the geometric Langlands application aspect to fascinating connections among convinced automorphic representations and twin fibrations in geometric replicate symmetry.

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