Universität Wien
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250031 VO Topics Course Number Theory (2021W)

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

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

The zoom room is: 974 9324 6659
Please contact the teacher for the password.

  • Friday 01.10. 09:45 - 12:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • 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 quaternions) 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: Fr 08.07.2022 12:30