'Characters tell all': Harmonic analysis on reductive, p-adic groupsLoren Spice, Texas Christian |
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April 5, 2010 Abstracthas been said that the ÔproperÕ realisation of a group always involves its action by symmetries on some space. This principle manifests everywhere from geometry, to classical analysis, to number theory. Unfortunately, most symmetries are too hard to study directly, so we must usually linearise them. The study of linearised group actions is called representation theory. In the late 1960's and early 1970's, Langlands proposed a far-reaching collection of conjectures unifying algebraic, geometric, and analytic perspectives on representation theory. Much deep work has been done in the pursuit of these conjectures, but, until recently, the fundamental objects of harmonic analysis, group characters, have not been put to their full use. In this talk, we will discuss the application of character formulas to questions about stable distributions on reductive, p-adic groups. |