The aim of this seminar is to give an elementary introduction to the congruence subgroup problem (CSP). We will mainly deal with the congruence subgroup problem for SL_{n} and with some group-theoretic applications of it, following [4]. At the end we will survey some results and techniques concerning the congruence subgroup problem for more general linear algebraic groups.
Other sources for learning about the subject are [1] and [3].
Humphreys, J. E., Arithmetic Groups, Lecture Notes in Mathematics 789, Springer, Berlin, 1980
Lubotzky, A., Group Presentations, p-Adic Analytic Groups and Lattices in SL_{2}(C), Ann. of Math. 118, 1983
Platonov V., Rapinchuk A.S., Algebraic groups and Number Theory, Pure and Applied Mathematics 139, Academic Press, San Diego, 1994
Sury, B., The congruence subgroup problem. An elementary approach aimed at applications, Texts and Readings in Mathematics 24, Hindustan Book Agency, New Delhi, 2003
Tuesday 19.10.21
Seminar room 03.73
Martina Conte
The congruence subgroup problem for SL_{2}(ℤ)
Tuesday 26.10.21
Seminar room 03.73
Moritz Petschick
The congruence subgroup problem for SL_{2}(O)
Tuesday 02.11.21
Seminar room 03.73
Karthika Rajeev
The congruence subgroup problem for SL_{n}(ℤ) with n > 2.
Tuesday 09.11.21
Seminar room 03.73
Margherita Piccolo
The congruence subgroup problem for SL_{n}(O_{S}).
Tuesday 16.11.21
Seminar room 03.73
Iker de las Heras
The metaplectic kernel I.
Tuesday 23.11.21
Seminar room 03.73
Luis de Mendonça
The metaplectic kernel II.
Tuesday 30.11.21
No seminar!
Tuesday 07.12.21
Seminar room 03.73
TBA – maybe you?
Some group-theoretic applications.
Tuesday 14.12.21
Seminar room 03.73
TBA – maybe you?
The congruence subgroup problem in linear algebraic groups: a survey.