Universität Wien

250140 VU Topics from Habilitations (2025W)

1.00 ECTS (0.50 SWS), SPL 25 - Mathematik
Continuous assessment of course work

Details

Language: English

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 11.11. 11:30 - 13:00 Seminarraum 5 Oskar-Morgenstern-Platz 1 1.Stock
  • Tuesday 18.11. 11:30 - 13:00 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
  • Tuesday 25.11. 11:30 - 13:00 Seminarraum 5 Oskar-Morgenstern-Platz 1 1.Stock

Information

Aims, contents and method of the course

Researchers who want to get a habilitation need to show experience in teaching. This course is a platform for candidates to prove their teaching skills by providing small lectures. Students who want to get credits are supposed to attend one of the lectures and pass an exam. The number of lectures depends on the number of candidates and may be zero. The individual lectures will be announced in due time.

Lecture by Serhii Bardyla: Semigroups of ultrafilters

Abstract: This course will provide an introduction to the algebraic
and topological structure of the semigroup of ultrafilters, as well as
their applications in Ramsey theory.
We begin with a semigroup S, most often the additive semigroup of
natural numbers, and then introduce a natural multiplication on
ultrafilters over S. By endowing the set of all ultrafilters on
S with a natural topology, one obtains the Stone–Čech compactification
β(S) of the discrete space S. Using compactness of β(S) we establish
the existence of idempotent ultrafilters on S and use them to prove
Hindman’s theorem, a cornerstone result in Ramsey theory. Further
applications of ultrafilter methods to combinatorial problems will be
discussed. In the final part of the course, we turn to Schur
ultrafilters and examine their connection with the Bohr
compactification of topological groups. This minicourse is open to all
students interested in exploring ultrafilters and their diverse
applications in Algebra and Combinatorics.

Assessment and permitted materials

Students need to take an oral exam with (one of) the instructor(s).

As an alternative, students may write a *thorough* report on the lectures, including an assessment of the pedagogical quality. This report is not submitted to the lecturer who is assessed but instead to the director of studies, Roland Donninger, who will assign the 1 ECTS and provide the lecturer with the report in an anonymized way.

Minimum requirements and assessment criteria

Students need to understand the essential content and be able to reproduce it in an exam.

Examination topics

The content of the course needs to be studied.

Reading list

Literature will be announced in the course.

Association in the course directory

MEL, MFE

Last modified: Th 02.10.2025 15:47