Instructional part: September 23 - 26
Organizers: H.W. Lenstra, P. Stevenhagen

NWO-OTKA workshop: September 27 - Oct 2
Organizers: P. Stevenhagen, R. Tijdeman

Organizers:

P. Stevenhagen
H.W. Lenstra
H.W. Lenstra

The title Explicit algebraic number theory is borrowed from the series of Oberwolfach meetings on Explicit methods in number theory. Those meetings are characterized by a lively interaction between abstract and advanced arithmetic theories on the one hand and concrete and elementary questions on the other. The spirit of the present workshop, which consists of 4 instructional days and 4 days of talks by (invited) participants, is similar, but within the smaller compass of algebraic number theory.

Instructional part

The instructional part emphasizes problems that are inspired by questions from other areas of mathematics, including elementary and algorithmic number theory, arithmetic algebraic geometry, and computer algebra. The advanced techniques from algebraic number theory that apply to these problems include class field theory, infinite Galois theory, and the theory of quadratic forms. The purpose of this part is to impart a working knowledge of these theories to the participants, to provide ample illustrations of their use, and to formulate several open problems that may be approachable by means of the same techniques.

Prerequisites: basic algebra, number theory, and point set topology, including Galois theory, algebraic number theory and a knowledge of p-adic numbers.

Lecturers:

• Hendrik Lenstra
• Peter Stevenhagen
• Bart de Smit
• Rene Schoof

Schedule: lectures in the morning, problems and exercises in the afternoon.

The first day of the of the NWO-OTKA workshop (friday) will try to provide illustrations of the material dealt with earlier in the week. Schedule: 4 one hour talks.

The schedule on the 3 last days will be more flexible, leaving room for shorter talks and research announcements. We hope that many of our younger researchers will seize the occasion to present something here. Expected topics are explicit computations in algebraic number theory (units, class groups) and (factorization of) polynomials.

Please register on-line if you want to attend. This will put you on the list of participants. Registered participants are entitled to free coffee and tea. There is no registration fee.