250044 SE Algebra (2024S)
Continuous assessment of course work
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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).
- Registration is open from Th 01.02.2024 00:00 to Mo 26.02.2024 23:59
- Deregistration possible until Su 31.03.2024 23:59
Details
max. 25 participants
Language: English
Lecturers
Classes (iCal) - next class is marked with N
During the first meeting on Monday 04.03. we will give a brief introduction to the three topics chosen for the seminar and schedule the presentations.
Monday
04.03.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday
11.03.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday
18.03.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday
08.04.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday
15.04.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday
22.04.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday
29.04.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday
06.05.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday
13.05.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
N
Monday
27.05.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday
03.06.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday
10.06.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday
17.06.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday
24.06.
11:30 - 13:00
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Information
Aims, contents and method of the course
Assessment and permitted materials
Regular participation to the presentations and presentation of a topic.
Minimum requirements and assessment criteria
Examination topics
Reading list
Will be assigned individually for each topic.
Association in the course directory
MALS
Last modified: We 28.02.2024 19:46
Dirichlet's Prime Number TheoremThis is a topic form number theory, which describes how the prime numbers are distributed among the invertible classes modulo m. In four lectures, we are going to reprove Dirichlet's theorem that the primes are in fact "equally distributed" among such classes. This implies as a famous corollary that for each pair of coprime natural numbers (m,n), there must be infinitely many prime numbers p, which are congruent to n modulo m. Nevertheless this result is algebraic in its nature, our methods will comprise analytic tools, such as "Dirichlet L-functions", which can be seen as a generalization of the Riemann zeta-function.Topic 2. (J. Mahnkopf)
Topics from Category Theory (for students who have a little background in category theory or are willing to acquire a little background)a.) Freyd's theorem on the existence of adjoint functors: the theorem gives a very general criterion for a functor F to have a left adjoint functor
(note that many theorems from algebra, topology... can be reformulated as the existence of a left adjoint functor which makes this a very general theorem)b.) Introduction to Morita equivalence: two rings are called Morita equivalent iff their respective categories of modules are equivalent (i.e. the rings "have the same representation theory"). The (first) main theorem of Morita Theory is a general criterion for rings to be Morita equivalent
and a description of the equivalence between their module categories. This can be illustrated by typical examples.c.) The embedding Theorem for abelian categories: any abelian category embeds into a category of modules over some ring R.The topics can be prepared by a single student or by two students.Topic 3. (L. Summerer)
Roth's TheoremThis topic is from Diophantine Approximation and focused on Roth's celebrated result about the bound for the quality of approximation of algebraic numbers by rationals. The talks are aimed to shed light on the context of Roth's Theorem along with an outline of the proof, applications of Roth's result and the generalisation towards the subspace Theorem of W. Schmidt.