1. If the canonical height isn't zero, is it irrational?

2. I come from a background in applied science. Can you briefly walk through any applications of cubic equations?

3. Is was fascinated by Mordell's result--that you only need finitely many solutions and that you can get all the rest through secants and tangents. Can you give us some idea why that is true or how to show that result?

4. How did Michael find that solution to that principle -- methods for factoring integers?

5. In the quadratic equations, at least in the circle, ellipses, hyperbolas, and paraboloas...can you generate different triplets depending on whether it's a circle?

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