MATHEMATICS SEMINAR by Benjamin Matschke Author:COLLEGE OF SCIENCESTime: 16:00Location: SCI 103
Our algorithms rely on new height bounds, which we obtained using the method of Faltings (Arakelov, Parshin, Szpiro) combined with the Shimura--Taniyama conjecture (without relying on linear forms in logarithms), as well as several improved and new sieves.
As one application we obtained a table of all rational elliptic curves with good reduction outside certain finite sets of primes, including the set {2, 3, 5, 7, 11}, and all sets whose product is at most 1000.
In addition we used the resulting data to motivate several conjectures and questions, such as Baker's explicit abc-conjecture, and a new conjecture on the number of S-integral points of rational elliptic curves.
This is joint work with Rafael von Känel. |