The ABC-conjecture: an introduction and some applications (Dietrich Burde)

When 10 Mar 2015
from 10:00 AM to 12:00 PM
Where A142
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We want to give an introduction to the abc-conjecture, which was first proposed by David Masser (1985) and Joseph Oesterle (1988) as an integer analogue of the Mason-Stothers theorem for polynomials. One can formulate the conjecture in an elementaryway (there are even high school projects like Reken mee met abc), but it is also equivalent to a not so elementary 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 (already proved in general by Andrew Wiles), Faltings theorem (former Mordell conjecture), the Szpiro conjecture, and the Fermat-Catalan conjecture. Although it is hard to say something on the status of Mochizuki’s proof we try to say a few words (really few) on the philosophy of his work on the abc-conjecture, e.g., on Grothendieck’s anabelian program.