暇つぶし2chat MATH

- 暇つぶし2ch851:8, 3-4:30 p.m. Lafayette L307 Anton Hilado, Elliptic Curves and the abc Conjecture In this talk we state the famous "abc conjecture" of Masser and Oesterle, and explain how it can be formulated as a statement involving important quantities related to elliptic curves (Szpiro's conjecture). We give an introduction to Weierstrass equations, reduction types, and the conductor and minimal discriminant of an elliptic curve, which are all needed to state Szpiro's conjecture. We also show how the abc conjecture is related to Fermat's Last Theorem, and introduce the Frey curve, which was used to prove the latter, and relate Szpiro's conjecture to the abc conjecture. Slides http://www.uvm.edu/~unqvnts/Talk%201%20%28Szpiro%27s%20Conjecture%29.pdf Elliptic Curves and the abc Conjecture Anton Hilado University of Vermont October 16, 2018