Hi Nullset, I’m sure some of you have begun preparing for midterms week (can’t believe it’s almost here). There’s no better way to take a break from midterm studying than to head to the next Math Colloquium, which is coming up this Friday!
We will be featuring Dr. Yunqing Tang with a talk on elliptic curves. Here are some curves.
Who? Dr. Yunqing Tang
What? Arithmetic of elliptic curves
When? Friday, October 18 at 5:00pm
Where? Fine Room 214
Food? Your choice of Bubble Tea
Abstract: Given an elliptic curve E over the ring of integers (in other words, consider the curve defined by y^2=x^3+Ax+B with A, B integers), we may ask what we can say about the mod p reduction of E. Elkies proved that there are infinitely many primes p such that E mod p are supersingular (equivalently, the above equation in x and y has exactly p solutions). I will give a very brief sketch of Elkies’s proof using the modular curve (the moduli space of elliptic curves) and also talk about how similar ideas can be used to prove other results, for instance, Habegger’s theorem, which asserts that there are only finitely many CM elliptic curves whose j-invariants are algebraic integers. If time permits, I will give some ideas on what to expect for higher dimensional generalizations.
We hope to see you there!
Your academic chairs, Nathan and Tristan