General Events - Department of Mathematics

Title: A new conjecture for rational points in families

Abstract: I’ll discuss the problem of counting how often a Diophantine equation has solutions in every p-adic field and the reals as one varies the coefficients of the equation. I’ll present a new conjecture on the asymptotic formula for this counting function and discuss a recently proved example in the case of the family of diagonal planar conics, which resolves a problem of Serre.