Universität Wien FIND

Due to the COVID-19 pandemic, changes to courses and exams may be necessary at short notice (e.g. cancellation of on-site teaching and conversion to online exams). Register for courses/exams via u:space, find out about the current status on u:find and on the moodle learning platform.

Further information about on-site teaching and access tests can be found at https://studieren.univie.ac.at/en/info.

Warning! The directory is not yet complete and will be amended until the beginning of the term.

250007 SE Seminar: Algebra (2021W)

4.00 ECTS (2.00 SWS), SPL 25 - Mathematik
Continuous assessment of course work
ON-SITE

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

max. 25 participants
Language: English

Lecturers

Classes (iCal) - next class is marked with N

Monday 11.10. 10:00 - 11:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Monday 18.10. 10:00 - 11:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Monday 25.10. 10:00 - 11:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Monday 08.11. 10:00 - 11:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Monday 15.11. 10:00 - 11:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Monday 22.11. 10:00 - 11:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Monday 29.11. 10:00 - 11:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Monday 06.12. 10:00 - 11:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Monday 13.12. 10:00 - 11:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Monday 10.01. 10:00 - 11:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Monday 17.01. 10:00 - 11:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Monday 24.01. 10:00 - 11:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Monday 31.01. 10:00 - 11:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

In this seminar on Algebra we want to

- to work on and explore one common topic from the field of algebra to which all participants contribute with their talks

- in doing so we want to comply with the preparation and the previous knowledge of the participants.

In the first place the seminar adresses students who finished their bachelor, i.e. beginnning master students; in particular, prerequisites are elementary number theory
and Algebra 1,2. If participants happen to have more knowledge (e.g. from algebraic number theory) it is possible
to explore further topics from the field of algebra/number theory.

A description of possible themes for the seminar can be found in the moodle account corresponding to the seminar (2021W 250007-1 Seminar: Algebra)

a. Field theory (prerequisites Algebra 1,2): We want to explore the structure of algebraic and not necessarily algebraic field extensions in more detail. This
needs more methods and tools from Algebra beyond the content of Algebra 1,2 which generally are of fundamental
importance (tensor product of modules, Derivations and Differentials). Applications include the structure theorem for normal extensions, Galois theory for inseparable extensions, methods for computing Galois groups, Dimension of fields, ...

b. Quadratic forms (prerequisites Algebra 1,2). Topics are classification of quadratic forms, Witt ring of a field k (this is an algebraic invariant of k), structure of orthogonal and symplectic groups, Clifford algebras and Spin groups.

c. Algebraic curves (prerequisites: Algebra 1,2, basic topology, complex and multivariable analysis). Literature: F. Kirwan "Complex algebraic curves"

Previous knowledge of participants and the seminar's topic will be discussed in the first meeting on 4th of October.

Assessment and permitted materials

Oral presentation; participation in the discussions

Minimum requirements and assessment criteria

positively evaluated oral presentation

Examination topics

Content of the seminar

Reading list

compare first meeting in 4th of october 2021. Also see the moodle account corresponding to the seminar

Association in the course directory

MALS

Last modified: We 15.09.2021 12:48