MATH Seminar
Title: The 1729 K3 surface |
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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 |
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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. |
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