# Quadratic families of elliptic curves and unirationality of degree 1 conic bundles

 Members' Seminar Topic: Quadratic families of elliptic curves and unirationality of degree 1 conic bundles Speaker: János Kollár Affiliation: Princeton University Date: Monday, April 13 Time/Room: 2:00pm - 3:00pm/S-101 Video Link: http://video.ias.edu/membersem/2015/0413-JánosKollár

We consider elliptic curves whose coefficients are degree 2 polynomials in a variable $t$. We prove that for infinitely many values of $t$ the resulting elliptic curve has rank at least 1. All such curves together form an algebraic surface which is birational to a conic bundle with 7 singular fibers. The main step of the proof is to show that such conic bundles are unirational. (joint work with M. Mella)