[PAST EVENT] Mathematics Colloquium: Pierre Clare (William & Mary)
Symmetries in Harmonic Analysis
It is a fundamental principle in Analysis that taking into account the symmetries of an object simplifies the study of functions on that object. Starting from elementary examples and the classical theory of Fourier series, we will explore various instances of this principle and its natural connections to the theory of groups and their representations. Following Alain Connes' philosophy of noncommutative geometry, certain spaces of representations will be studied by means of algebras of linear operators, leading to the characterization of a new class of representations, of particular topological relevance. Unexpected symmetries will be shown to appear in that context.