Seminar: Simplicial Topology, WS 2015/16

News

Please register in FlexNow before January 31, 2016. The grades will then be entered in FlexNow.
There will be an additional overview talk on January 13 (8:30--10:00) on infinity categories.
The first talk will be on October 28!
If you have any questions about the seminar or your talk, you can ask Dmitri Pavlov (dmitri.pavlov@mathematik.uni-r.de, M 005) for assistance.
The Templates for reports/handouts are online (see below); of course, you can also produce the report/handout by other means.
This seminar will be held in English. The written report can be in English or German. The handouts should be in English.

Seminar: Simplicial Topology

Many topological spaces admit accessible combinatorial descriptions. For example, many spaces can be constructed by gluing lines, triangles, tetrahedra, ... (so-called simplices). On the one hand, we can then define topological invariants in combinatorial/simplicial terms and calculate these invariants by algorithmic means. On the other hand, simplicial structures are so fundamental that they can also be translated to other fields of mathematics.

torus

In this seminar, we will cover the following topics:

Simplicial complexes
Simplicial homology
Classification of compact surfaces
Simplicial sets
Applications of simplicial methods in theoretical and practical mathematics

Time/Location

Wednesdays, 8:30 -- 10:00, M101.
First talk: October 28.

Material

Overview of all talks (and some organisatorial hints). We will cover topics 1,2,3,4,7,8,10,11.
LaTeX template for handouts: .tex, .pdf
LaTeX template for reports: .tex, .pdf
Hints on wrting mathematical texts (in German)

Prerequisites

Analysis I/II (in particular, basic point set topology), Linear Algebra I/II;
Knowledge about manifolds as in Analysis IV is not necessary, but helpful.
This seminar complements the course Algebraic Topology I, but many of the topics are also accessible without participating in the course.

Formalities/Credits

Sufficient for successfully passing this seminar are:

Giving a presentation.
Active participation in the seminar sessions.
A handout (one or two pages), containing a summary of the central aspects of the talk as well as some exercises.
A detailed written report (in German or English) on the topic of the talk (to be handed in one week before the talk).
Depending on the applicable Prüfungsordnung/Modulkatalog, the grade will be based either only on the presentation or only on the written report.
Depending on the applicable Prüfungsordnung/Modulkatalog, this seminar will be awarded with 6 or 4.5 credits.

This seminar is suitable for Bachelor/Master students and Lehramtsstudenten with an interest in topology, and could be the starting point for a project under my supervision (e.g., bachelor thesis).

Please register in FlexNow before January 31, 2016. The grades will then be entered in FlexNow.

Last Change: January 18, 2016.