Seminar Differentialgeometrie: Geometry of Lie Groups

Sommersemester 2016

Dr. Daniele Alessandrini and Dr. Gye-Seon Lee

Time and Location
Tuesdays 4:00 - 6:30 p.m. and INF 205, SR 2

Organization meeting
April 19, at 4 p.m. in INF 205, SR 2

Description
The goal of this seminar is to familiarize students with the basic language of Lie groups and to introduce some important theorems about this topic, e.g. the Lie correspondence, the closed subgroup theorem and the quotient manifold theorem, and thereafter we begin the study of homogeneous spaces and, in particular, symmetric spaces. Moreover, we also briefly touch on lattices in Lie groups. At the organizational meeting we will propose several topices (see the syllabus for more details). Among them, you can choose one topic you are interested in. During the first half of the semester, students will work on their project, which they will present during the second half of the semester. If the topic is difficult, it is also possible for students to get together in teams to carry out one of the topics. Every student is expected to hand in a short report as well.

Prerequisites
This seminar is aimed at students who are interested in differential geometry. Students are expected to have a good knowledge of calculus and a certain familiarity with the differential geometry of manifolds. There are several topics for students to choose from, and hence any interested students are welcome to attend. The seminar is open for bachelor and master students. The seminar will be taught in English.

Organization
Students who would like to sign up for the seminar should come to the organization meeting, or send an email to Daniele (alessandrini@mathi.uni-heidelberg.de) or Gye-Seon (lee@mathi.uni-heidelberg.de). Please register at MÜSLI and let us know what project you would like to carry out. Once you have agreed on the topic of your project with us, you should contact us to discuss the content of your project in more detail. Please let us help you during the preparation of your presentation.

Schedule

Date	Time	Speaker	Title	Advisor
May 17	16:00 - 17:00	Gönenc	Lie groups	Daniele
	17:15 - 18:15	Oskar	The Lie algebra of a Lie group	Gye-Seon
May 31	16:00 - 17:00	Philipp	The closed subgroup theorem	Daniele
	17:15 - 18:15	Marilena	The Lie correspondence	Daniele
June 7	16:00 - 17:00	Sven	Classical groups and their real form	Daniele
	17:15 - 18:15	Stephan	The quotient manifold theorem	Daniele
July 5	16:00 - 17:00	Menelaos	Homogeneous spaces	Gye-Seon
	17:15 - 18:15	Mareike	Symmetric spaces	Gye-Seon
July 12	16:00 - 17:00	Markus	Bieberbach's theorems I	Gye-Seon
	17:15 - 18:15	Tim	Bieberbach's theorems II	Gye-Seon
July 19	16:00 - 17:00	Sebastian	A example of arithmetic groups	Daniele