Minerva Lecture III: Logic, Elliptic curves, and Diophantine stability

Friday, October 17, 2014 -
4:30pm to 5:30pm
Minerva Lecture III:  An introduction to aspects of mathematical logic and the arithmetic of elliptic curves that make these branches of mathematics inspiring to each other.  Specifi cally: algebraic curves - other than the projective line - over number fi elds tend to acquire no new rational points over many extension fi elds. This feature (which I call 'diophantine stability') makes elliptic curves, in particular, useful as vehicles to establish diophantine unsolvability for many large rings. To repay the debt, mathematical logic off ers consequences to the arithmetic of elliptic curves over decidable rings. I will also discuss new results about diophantine stability.
Speaker: 
Barry Charles Mazur
Gerhard Gade University Professor at Harvard University
Event Location: 
McDonnell Hall A01