|Title: The 1729 K3 surface|
|Seminar: Algebra and Number Theory|
|Speaker: Sarah Trebat-Leder of Emory University|
|Contact: Michael H. Mertens, firstname.lastname@example.org|
|Date: 2015-12-08 at 4:00PM|
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.
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