Wednesday 30 April 2014 h. 14:30, room 2BC30

Martino Garonzi (Padova, Dip. Mat.)

"An introduction to representation theory of groups"

Abstract

Label the faces of a cube with the numbers from 1 to 6 in some order, then perform the following operation: replace the number labeling each given face with the arithmetic mean of the numbers labeling the adjacent faces. What numbers will appear on the faces of the cube after this operation is iterated many times? This is a sample problem whose solution is a model of the application of the theory of representations of groups to diverse problems of mathematics, mechanics, and physics that possess symmetry of one kind or another.

In this introductory talk I will present the tools from representation theory needed to solve this problem. I will also point out the connection with harmonic analysis by expressing Fourier analysis as an instance of representation theory of the circle group (the multiplicative group of complex numbers with absolute value 1) and by stating a version of Heisenberg's uncertainty principle for finite cyclic groups.