Instructional Conference, May 7-11, 2007, Lorentz Center.
Back to the website of the instructional conference | Prerequisites | Hand-outs and exercises
The lectures are in Room 201 on the second floor and the social activities in the Common room on the third floor. On Monday-Thursday mornings there are lectures. In the afternoons there are exercise sessions where the participants can practice with the theory discussed in the morning lectures. On Friday there will be a series of lectures meant for a general audience.
MONDAY MAY 7 | |
09:30-10:00 | Picking up badges, hand-outs etc. from Common Room |
10:00-10:50 | Samir Siksek: Preliminaries on curves of genus 1 |
11:00-11:50 | Yann Bugeaud: Preliminaries on linear forms in logarithms |
14:00-16:00 | Exercise session |
16:00-17:00 | Discussion of solutions |
17:00-18:00 | Wine and cheese party in Common Room |
TUESDAY MAY 8 | |
09:00-09:50 | Nils Bruin: Preliminaries on Chabauty's method |
10:00-10:50 | Samir Siksek: Preliminaries on Modular/Frey curves |
11:00-11:50 | Yann Bugeaud: Linear forms in logarithms II |
14:00-16:00 | Exercise session |
16:00-17:00 | Discussion of solutions |
WEDNESDAY MAY 9 | |
09:00-09:50 | Nils Bruin: Chabauty's method II |
10:00-10:50 | Samir Siksek: Modular/Frey curves II |
11:00-11:50 | Mike Bennett:The hypergeometric method |
14:00-16:00 | Exercise session |
16:00-17:00 | Discussion of solutions |
17:00-22:00 | Boat trip on Kager plassen and dinner on boat.
The bus will depart on 17:15. |
THURSDAY MAY 10 | |
09:00-09:50 | Mike Bennett: Modular/Frey curves III |
10:00-10:50 | Nils Bruin: Chabauty's method III |
11:00-11:50 | Yann Bugeaud: Linear forms in p-adic logarithms |
14:00-16:00 | Exercise session |
16:00-17:00 | Discussion of solutions |
FRIDAY MAY 11 | |
11:00-12:00 | Johnny Edwards (Utrecht): x^{2}+ y^{3}= z^{5} and similar equations. |
13:30-14:30 | Nils Bruin (SFU, Burnaby): Some hyperbolic cases of the generalized Fermat equation. |
14:45-15:45 | Frits Beukers (Utrecht): Integral points on cubic surfaces. |
16:00-17:00 | Rob Tijdeman (Leiden): Arithmetical properties of arithmetical progressions. |
Algebraic number theory:
Ideals, unit groups, S-unit groups, class groups, completions, p-adic
valuations, p-adic analysis.
S. Lang, Algebraic Number Theory, Chapters 1,2,7 or
J. Neukirch, Algebraic Number Theory, Chapters 1,2
More about p-adic analysis (basics about p-adic power series):
Z.I Borevich, I.R. Shafarevich, Number Theory, Chapter 4
Algebraic curves and elliptic curves:
Function fields, divisors, Picard group, differentials,
basic facts about elliptic curves and reduction modulo p of an
elliptic curve (vague idea of how this works).
Part of this will be recalled briefly during the course.
J.H. Silverman, The arithmetic of elliptic curves,
Chapters 1,2,
Chapter 3 sections 1,2,3; sections 4,5 will be useful,
Chapter 7, sections 1,2; sections 3,4,5 will be useful.
Recommended for further reading:
p-adic methods and some facts about genus 2 curves (not required but useful)
N.P. Smart, The effective resolution of Diophantine equations,
Chapter 2, Chapter 14, sections 1,2
J.W.S. Cassels, E.V. Flyn, Prolegomena to a Middlebrow Arithmetic of
Curves of genus 2,
Chapters 1,2,13