Seminar: Simplicial Topology, WS 2015/16
Prof. Dr. C. Löh
/
Dr. Dmitri Pavlov
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 (8:3010:00)
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.unir.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, ... (socalled 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.
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.