Introduction to Profinite Groups

Short Intensive Course

Mathematisches Institut
Universität Leipzig
Dec. 12 - Dec. 16, 2022

Lecturer: John S. Wilson

This short intensive course is an introduction to the area of profinite groups. Profinite groups are important in many areas of mathematics, from algebraic number theory through analysis to infinite combinatorics. This course will explain some of their relevance, and provide enough foundational material to enable participants to use them. Prerequisites are elementary group and ring theory, finite Galois theory, and familiarity with basic notions concerning topological spaces (compactness, connectedness, Hausdorff spaces).

The course is intended for advanced undergraduates, PhD students, as well as interested mathematical researchers. If the attendance is good, this course will be followed with a more advanced one in the Summer Semester 2022-23.

Leipzig students can take this course as an equivalent of 1 SWS (Semesterwochenstunde). Another 1 SWS short intensive course will be offered in the Summer Semester 2022-23. It will be either a continuation of this one, or a course in the areas of algebra/geometry/combinatorics.


Handout 1


Mon 10:00 - 11:30 (S017) and 14:00 - 15:30 (S017)

Tue 10:00 - 11:30 (S017)

Wed 10:00 - 11:30 (S015) and 14:00 - 15:30 (S015)

Thu 10:00 - 11:30 (S017)

Fri 10:00 - 11:30 (S017) and 14:00 - 15:30 (S015)

Both S015 and S017 are in the ground floor of the Seminargebäude in the Augustusplatz campus.


Wilson, John S., Profinite Groups. London Mathematical Society Monographs, Oxford University Press, 1999.

Financial Support

We offer a small number of grants of up to €400 towards hotel and/or travel expenses for undergraduates and PhD students who are not based in Leipzig, and who would like to participate in the whole course.

To apply for a grant please send a short letter to Lukasz Grabowski explaining your mathematical interests and why taking this course would be beneficial to you, and arrange a letter of support from your supervisor or another member of staff to be sent to the same address. The deadline for applications is Wednesday, Nov. 30. The decisions will be announced by email shortly afterwards.