This quantity includes the court cases of the convention on illustration idea 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, particularly as a result of connections to geometry, topology, quantity conception, physics, combinatorics, and lots of different components. illustration conception is among the cornerstones of the Langlands software in quantity idea, courting to the Seventies. Zuckerman's paintings on derived functors, the interpretation precept, and coherent continuation lie on the middle of the trendy concept 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 predicated seriously on Zuckerman's paintings. lately there was a fruitful interaction among arithmetic and physics, in geometric illustration idea, string thought, and different components. New advancements on chiral algebras, illustration concept of affine Kac-Moody algebras, and the geometric Langlands correspondence are a number of the focal issues of this quantity. contemporary advancements within the geometric Langlands software element to fascinating connections among yes automorphic representations and twin fibrations in geometric replicate symmetry.
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