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Introduction to topological groups - NMMA654

Title:	Úvod do topologických grup
Guaranteed by:	Department of Mathematical Analysis (32-KMA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2023
Semester:	summer
E-Credits:	3
Hours per week, examination:	summer s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech, English
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	Mgr. Michal Doucha, Ph.D.

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: doc. RNDr. Pavel Pyrih, CSc. (12.05.2022)

Introduction to the study of topological groups with main focus on compact groups. Suitable for the master programme Mathematical analysis.

Literature -

Last update: Mgr. Michal Doucha, Ph.D. (23.05.2022)

K. H. Hofmann, S. A. Morris, The structure of compact groups. A primer for the student – a handbook for the expert.De Gruyter Studies in Mathematics 25. Berlin: De Gruyter, 2020.

M. Stroppel, Locally compact groups, EMS Textbooks in Mathematics. Zürich: European Mathematical Society Publishing House, 2006.

Requirements to the exam -

Last update: Mgr. Michal Doucha, Ph.D. (23.05.2022)

Oral exam based on the presented material. Alternatively, the students can prepare a blackboard presentation or a paper on some advanced topic that extends the presented material.

Syllabus -

Last update: Mgr. Michal Doucha, Ph.D. (04.01.2023)

1. General basics of topological, and especially locally compact, groups.

2. Haar measure on locally compact groups.

3. Unitary representations of locally compact groups and the Peter-Weyl theorem.

4. Pontryagin duality for locally compact abelian groups.

Entry requirements -

Last update: prof. RNDr. Ondřej Kalenda, Ph.D., DSc. (13.05.2022)

Elements of general topology and functional analysis (covered for example by courses NMMA345 General Topology 1 and NMMA331 Introduction to Functional Analysis).