MATH Seminar

Title: The 1729 K3 surface
Seminar: Algebra and Number Theory
Speaker: Sarah Trebat-Leder of Emory University
Contact: Michael H. Mertens, michael.mertens@emory.edu
Date: 2015-12-08 at 4:00PM
Venue: W304
Download Flyer
Abstract: We revisit the mathematics that Ramanujan developed in connection with the famous "taxi-cab" number 1729. A study of his writings reveals that he had been studying Euler's diophantine equation a^3+b^3=c^3+d^3. It turns out that Ramanujan's work anticipated deep structures and phenomena which have become fundamental objects in arithmetic geometry and number theory. We find that he discovered a K3 surface with Picard number 18, one which can be used to obtain infinitely many cubic twists over Q with rank >= 2.