This quantity comprises the complaints of the convention on illustration thought and Mathematical Physics, in honor of Gregg Zuckerman's sixtieth birthday, held October 24-27, 2009, at Yale college. Lie teams and their representations play a primary function of arithmetic, specifically as a result of connections to geometry, topology, quantity concept, physics, combinatorics, and plenty of different parts. illustration idea is without doubt one of the cornerstones of the Langlands software in quantity conception, courting to the Nineteen Seventies. Zuckerman's paintings on derived functors, the interpretation precept, and coherent continuation lie on the middle of the trendy idea of representations of Lie teams. one of many significant unsolved difficulties in illustration concept 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. in recent times there was a fruitful interaction among arithmetic and physics, in geometric illustration thought, string idea, and different components. New advancements on chiral algebras, illustration thought of affine Kac-Moody algebras, and the geometric Langlands correspondence are a few of the focal issues of this quantity. fresh advancements within the geometric Langlands application element to interesting connections among definite automorphic representations and twin fibrations in geometric replicate symmetry.
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