Universität Wien

250092 VO Selcted topics in Number Theory and Algebra (2015W)

7.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 06.10. 08:00 - 09:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 07.10. 08:00 - 09:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 13.10. 08:00 - 09:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 14.10. 08:00 - 09:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 20.10. 08:00 - 09:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 21.10. 08:00 - 09:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 27.10. 08:00 - 09:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 28.10. 08:00 - 09:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 03.11. 08:00 - 09:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 04.11. 08:00 - 09:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 10.11. 08:00 - 09:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 11.11. 08:00 - 09:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 17.11. 08:00 - 09:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 18.11. 08:00 - 09:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 24.11. 08:00 - 09:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 25.11. 08:00 - 09:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 01.12. 08:00 - 09:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 02.12. 08:00 - 09:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 09.12. 08:00 - 09:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 15.12. 08:00 - 09:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 16.12. 08:00 - 09:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 12.01. 08:00 - 09:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 13.01. 08:00 - 09:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 19.01. 08:00 - 09:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 20.01. 08:00 - 09:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 26.01. 08:00 - 09:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 27.01. 08:00 - 09:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

Theory of arithmetic groups [Continuation of course SS 2015]-- An arithmetic group, roughly speaking, is a group of integral matrices defined by polynomial equations. For example, a subgroup of finite index in the special linear group of (n x n)--matrices with entries in the ring of integers of an algebraic number field k is an arithmetic group. Such groups arise in a wide variety of contexts: number theory, Fourier analysis, quadratic forms, discrete subgroups of Lie groups, locally symmetric spaces, hyperbolic manifolds, automorphic forms etc. In this course I attempt to develop in an elementary way several of the underlying themes, illustrated by specific groups to be considered. While no special knowledge of Lie groups or algebraic groups is needed to appreciate these particular examples, I will emphasize methods which carry over to a more general setting.

Topics: [dealt with in SS 2015: special linear groups over k and its arithmetic subgroups, or, more generally, groups originating with orders in division algebras [e.g. quaternion algebras] over k; construction of non-congruence subgroups];
WS 2015/16: homogenous spaces and discrete groups; reduction theory and fundamental domains; unit groups of quadratic forms; cohomology of arithmetic groups

Assessment and permitted materials

oral examination, regular participation

Minimum requirements and assessment criteria

Introduction into the theory of arithmetic groups and the arithmetic of algebraic groups

Examination topics

Reading list

to be announced during the lecture.

Association in the course directory

MALV

Last modified: Mo 07.09.2020 15:40