Symmetry breaking in higher rank
Name of applicant
Jonathan Ditlevsen
Title
Researcher
Institution
University of Tokyo
Amount
DKK 1,020,000
Year
2024
Type of grant
Internationalisation Fellowships
What?
Symmetry breaking describes the effect of a reduction of symmetries, i.e. passing from a system with high symmetry to one with less symmetry. For instance, in a physical system such a reduction of symmetries could naturally occur after reaching a certain critical temperature. I plan to study the phenomenon of symmetry breaking mathematically in the language of representations of Lie groups.
Why?
Many problems in modern mathematics and physics uses symmetries to simplify otherwise very complex problems. However, we know very little about symmetry breaking for so-called higher rank groups which is what I want to investigate. By doing so I will develop new tools that other researchers can use in their work.
How?
I will start off my studying symmetry breaking for a specific example and this is to get a general picture to approach other cases. In doing so I will use distribution theory and harmonic analysis.