** "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 (Universität 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 \(abc\).