Number Theory Seminar
Ramin Takloo-Bighash
UIC
Rational points on zero loci of Brauer elements
Abstract: We consider the problem of counting the number of rational points of
bounded height in the zero-loci of Brauer group elements on semi-simple algebraic
groups over number fields. We obtain asymptotic formulae for the counting problem
for wonderful compactifications using the spectral theory of automorphic forms.
Applications include asymptotic formulae for the number of matrices over Q whose
determinant is a sum of two squares. These results provide a positive answer to some
cases of a question of Serre concerning such counting problems. This is joint work with Daniel Loughran
and Sho Tanimoto.
Tuesday February 14, 2017 at 11:00 AM in SEO 612