Expanding Theories of Symmetries to New Areas 

Seidon Alsaody received his Ph.D. in Mathematics from Uppsala University in 2015. Thanks to a grant from the Knut and Alice Wallenberg Foundation, he will hold a postdoctoral position with Professor Philippe Gille at the Institut Camille Jordan in Lyon, France. 

One common way of analyzing the geometry of a three-dimensional object is by looking at it from different angles and by trying to understand its symmetries. Symmetries also play a major role in understanding geometry in more abstract settings. Developing new methods to further such understanding is the subject of Seidon Alsaody’s project. 

Algebraic groups are important concepts of modern mathematics that were developed to study symmetries. Interesting examples of such groups are groups of type D4 and G2. Groups of type D4 are unique because of their threefold symmetry, which is thought to possibly lie at the root of the mathematical description of supersymmetry in theoretical physics. The 14-dimensional G2 type groups are the smallest of the so-called exceptional groups, i.e. the groups, which fall outside the regular classification. 

Mathematicians’ understanding of algebraic groups has developed rapidly over the last few decades. New ways to study symmetries have become available and analyzing symmetries in new contexts has yielded additional insights. The goal of Seidon Alsaody’s project is to further extend and refine such methods, particularly for the D4 and G2 type groups. Earlier attempts have encountered technical difficulties, which Seidon Alsaody hopes to manage to overcome in this project.