The main problem on which I am going to work with the help of RA is as follows.
In my previous work on the vector invariants of the exceptional simple group of type G_2 acting on several copies of octonions, I described the generators of the corresponding rings of invariants. The next step would be to describe separating invariants of exceptional simple group F_4 acting on several copies of Albert algebra (the simple 27-dimensional Jordan algebra). During the last decade such kind of problems is under intensive investigating by many experts in the computational invariant theory of algebraic groups and Lie groups. So, any nontrivial contribution to this area will be highly estimated. So, the minimal requirement to RA is to be experienced in the theory of algebraic groups over any infinite field of arbitrary characteristic. As for possible extension and application, I plan to generalize this work for the simple algebraic supergroups, since it fits the principal aim of my start-up grant “Harish-Chandra pairs method for group superschemes and generalized Schur superalgebras”, i.e. the investigation of group superschemes and algebraic supergroups as well as some related superalgebras.
to be familiar with basic fact in algebraic geometry, the theory of algebraic groups and invariant theory
to be experienced in the theory of agebraic groups, the theory of representations of algebraic groups and their invariants
Division College of Science - (COS)
Department Mathematical Sciences - (COS)
Job Close Date 31-12-2020
Job Category Academic - Research Assistant