Character values and their relation with finite groups structure

Research will be conducted on character theory of finite groups, specifically on characters' values and fields of values. Two new ambitious problems will be investigated. One is a global-local problem, concerning irreducible characters of a group and of his Sylow normalizers, and it will be investigated using machine learning methods. The other consists in searching for a family of irreducible characters which ""behaves well"" in relation with elements of prime power order. My research will have a considerable impact in the field of character theory and it will have possible applications in other fields of group theory. The use of of machine learning methods in my research may have an impact extending beyond group theory, as it could suggest a similar use in other fields of mathematics.Research to be conducted in Kaiserslautern, under the supervision of prof. Malle, eminent researcher in the field of character theory of finite groups of Lie type. Training on machine learning to be conducted in the CS department of the hosting university. Further training will be conducted on character theory of non-abelian simple groups, and possibly as a teaching assistant in group theory.""