Harmonic Analysis on Reductive Groups

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    Harmonic Analysis- "How Lonely Sits The City," by David Bennett Thomas

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    The stated goal of the conference was to explore recent advances in harmonic analysis on both real and p-adic groups. It was the first conference since the AMS Summer Sym posium on Harmonic Analysis on Homogeneous Spaces, held at Williamstown, Massachusetts in , to cover local harmonic analysis on reductive groups in such detail and to such an extent.

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    While the Williamstown conference was longer three weeks and somewhat broader nilpotent groups, solvable groups, as well as semisimple and reductive groups , the structure and timeliness of the two meetings was remarkably similar. The program of the Bowdoin Conference consisted of two parts. First, there were six major lecture series, each consisting of several talks addressing those topics in harmonic analysis on real and p-adic groups which were the focus of intensive research during the previous decade.

    These lectures began at an introductory level and advanced to the current state of research. Sec ond, there was a series of single lectures in which the speakers presented an overview of their latest research. Specifications Series Title Progress in Mathematics.

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    Customer Reviews. Write a review. See any care plans, options and policies that may be associated with this product. Email address. Please enter a valid email address. Borel, Linear Algebraic Groups , Benjamin, Participants will be assumed to have some knowledge of number theory. The main theorems of class field theory will be reviewed in the course on Shimura varieties, but again without proof. A good general reference is, J.

    Residue distributions and harmonic analysis on reductive groups

    Cassels, and A. A good introductory reference to the general theory of automorphic forms is the proceedings of the Edinburgh instructional conference: T. Bailey and A.

    Pure Math. The Clay Mathematics Institute CMI is a private, non-profit foundation, dedicated to increase and to disseminate mathematical knowledge. The primary objectives and purposes of The Clay Mathematics Institute CMI are, to increase and disseminate mathematical knowledge, to educate mathematicians and other scientists about new discoveries in the field of mathematics,to encourage gifted students to pursue mathematical careers, and to recognize extraordinary achievements and advances in mathematical research.

    The final date to register was February 15, , therefore we are no longer accepting applications. About Us. General Scientific Activity. Centre for Mathematical Medicine.


    Operator K-theory and the harmonic analysis of reductive symmetric spaces, 2

    Mathematics Education. Calendar of Events. Mailing List. Fields Live. Video Archive. Resources and Facilities. Overview The Clay Mathematics Institute is organizing a summer school in automorphic forms in June, We shall begin with a brief overview of the subject, taking motivation from the case of compact quotient. We shall then prove as much of the general formula as we can.

    Harmonic analysis of spherical functions on real reductive groups - Ghent University Library

    In the process, we shall introduce the orbital integrals and characters, and their weighted variants, that are the main terms in the trace formula. The deeper study of these local objects will be the subject of the course of Kottwitz, and the lectures of DeBacker and Hales in the final week. General applications of the trace formula will actually require two successive refinements, the invariant trace formula and the stable trace formula. If time permits, we shall discuss these refinements, and the local problems of comparison whose solutions are required for applications.

    June 2- 20 Introduction to Shimura Varieties Instructor: James Milne Shimura varieties are the natural generalization of elliptic modular curves. The main emphasis will be on the classification and stucture of reductive algebraic groups. June Harmonic Analysis on Reductive Groups and Lie Algebras Instructor: Robert Kottwitz This course will introduce the basic objects of study in harmonic analysis on reductive groups and Lie algebras over local fields: orbital integrals, their Fourier transforms in the Lie algebra case and characters of irreducible representations in the group case.

    The emphasis will be on p-adic fields and the Lie algebra case to which the group case can often be reduced using the exponential map. Some of the main theorems involving these objects will be discussed: Howe's finiteness theorem; Shalika germs, the local character expansion and its Lie algebra analog; local integrability of Fourier transforms of orbital integrals; and the Lie algebra analog of the local trace formula.