Nuno Arala Santos: Singular intersections of quadrics and cusp forms

Speaker
Nuno Aralo Santos, University of Warwick

Abstract
We establish an asymptotic formula for the number of common zeros of a pair of quadratic forms in at least 10 variables that determine a projective variety with exactly two singular points, defined over an imaginary quadratic field. The proof uses a form of the circle method and relies on tools from the theory of cusp forms.