"Geometry and Analysis on Groups" Research Seminar

Time: 2017.11.21, 15:15–17:00
Location: Seminarraum 9, Oskar-Morgenstern-Platz 1, 2.Stock
Title: "Szpiro's conjecture, ABC and anabelian geometry."
Speaker: Dietrich Burde (Universitšt Wien)
Abstract: We want to give an introduction to the \(abc\)-conjecture, which was first proposed by David Masser (1985) and Joseph Oesterlé (1988) as an integer analogue of the Mason-Stothers theorem for polynomials. One can formulate the conjecture in an elementary way, but it is also equivalent to a more technical conjecture on elliptic curves. The \(abc\)-conjecture has a large number of non-trivial consequences, such as Fermat's Last Theorem for all sufficiently large exponents, Faltings theorem (former Mordell conjecture), the Szpiro conjecture, and the Fermat-Catalan conjecture. We cannot say anything about the proposed proof by S. Mochizuki, but one might try to say some words on his work related to Grothendieck's anabelian program, and why one might hope this is useful in attacking \(abc\).