2022/2023

Research Seminar "Harmonic Analysis and Unitary Representations"

Type: Optional course (faculty)

Delivered by: Faculty of Mathematics

When: 1, 2 module

Open to: students of all HSE University campuses

Instructors: Alexei Yu. Pirkovskii

Language: English

ECTS credits: 3

Contact hours: 32

Course Syllabus

Abstract

Harmonic analysis on groups and unitary representation theory are closely related areas of mathematics, complementary to each other. They play an important role in analysis, geometry, topology, physics, and other fields of science. In essence, they grew out of two classical topics that are usually studied by undergraduate students in mathematics. The two topics are the theory of trigonometric Fourier series and the representation theory (over C) of finite groups. Among other things, we plan to explain what the above topics have in common, what the representation theory of compact groups looks like, what the Tannaka - Krein duality is, and what all this has to do with the Fourier transform. We are also going to construct harmonic analysis on locally compact abelian groups. This theory includes the Pontryagin duality and generalizes the Fourier transform theory on the real line. As an auxiliary material, the basics of Banach algebra theory will also be given.