2017
Dec
28

# Amitsur Algebra: Ari Shnidman (Boston College), "The behavior of rational points in one-parameter families"

12:00pm to 1:00pm

## Location:

Ross 70, Math Building, Givat Ram

Title: The behavior of rational points in one-parameter families

Abstract: How often does a "random" algebraic plane curve f(x,y) = 0

have a solution with rational coordinates? In one-parameter "twist"

families of elliptic curves, Goldfeld conjectured that there should be

a rational point exactly half of the time. Recent progress towards

this conjecture makes use of Selmer groups, and I'll explain the

geometric idea underlying their construction. I'll also describe

results for families of curves of higher genus, and abelian varieties