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

Barry Charles Mazur, Gerhard Gade University Professor at Harvard University
McDonnell Hall A01
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. Specifically: algebraic curves  other than the projective line  over number fields tend to acquire no new rational points over many extension fields. 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 offers consequences to the arithmetic of elliptic curves over decidable rings. I will also discuss new results about diophantine stability.