Algebra and Geometry Seminar

Classical topics in the arithmetic study of quadratic forms include their reduction theory and representation problem. In this talk, we discuss their nonlinear analogues for SL2-characters of surface groups. First, we prove that the set of integral SL2-characters of a surface group with prescribed invariants can be effectively determined and finitely generated, under mapping class group action and related dynamics. Second, we prove that the set of values of an integral SL2-character of a finitely generated group is a decidable subset of the integers.