Aksel Bergfeldt: Harmonic analysis on the Heisenberg group

Abstract: One of the simplest non-Abelian Lie groups that resemble Euclidean space is the Heisenberg group. The components of its algebra satisfy [X, Y] = Z, a relation that we recognise from commuting position and momentum operators in quantum mechanics, or commuting translation in frequency with translation in space in time-frequency analysis. Using this group as the underlying space, I have used non-Abelian harmonic analysis to
study the regularity properties of fractional Schrödinger equations. In this talk I will give some insight about how this equation differs from its counterpart on Euclidean space, and about some of the key techniques and ideas that are useful. We shall see that, though many things are strikingly different, there are basic ideas that carry over from the Euclidean mindset and can be made to work with the right twist.