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.

250031 VO Topics Course Number Theory (2021W)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik
MIXED

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

Language: English

Lecturers

Classes (iCal) - next class is marked with N

Friday 08.10. 09:45 - 12:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Friday 15.10. 09:45 - 12:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Friday 22.10. 09:45 - 12:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Friday 05.11. 09:45 - 12:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Friday 12.11. 09:45 - 12:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Friday 19.11. 09:45 - 12:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Friday 26.11. 09:45 - 12:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Friday 03.12. 09:45 - 12:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Friday 10.12. 09:45 - 12:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Friday 17.12. 09:45 - 12:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Friday 07.01. 09:45 - 12:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Friday 14.01. 09:45 - 12:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Friday 21.01. 09:45 - 12:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Friday 28.01. 09:45 - 12:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

This course sits at the crossroad between Number Theory, Graph Theory, Group Theory and Representation Theory.

We will be interested in Ramanujan Graphs, some highly connected but sparse graphs. Besides their interest in combinatorics and graph theory, these graphs have applications to computer science and engineering.

The course will be as self contained as possible. We will recall some Graph Theory, some basic Number Theory (as the quadratic reciprocity law and modular forms) and some Group Theory, mainly focussed on the group PGL(2).

Prerequisites for the course are Algebra 1 and Algebra 2 and some basic knowledge of analysis and combinatorics.

Assessment and permitted materials

Written or oral exam

Minimum requirements and assessment criteria

To pass the Written or oral exam

Examination topics

Content of the lecture

Reading list

G. DAVIDOFF, P. SARNAK & A. VALETTE, Elementary Number Theory, Group Theory and Ramanujan Graphs.
A.LUBOTZKY, Discrete groups, expanding graphs and invariant measures, Progress in Mathematics 125, Birkhaeuser, Basel, 1994.
A. LUBOTZKY, R. PHILLIPS, & P. SARNAK, Ramanujan graphs, Combinatorica 8 (1988), 261–277.

Association in the course directory

MALV

Last modified: Mo 27.09.2021 10:29