Universität Wien
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250086 VO From Elliptic Curves to Fermat's Last Theorem (2024S)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Monday 04.03. 16:45 - 17:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 05.03. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 11.03. 16:45 - 17:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 18.03. 16:45 - 17:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 19.03. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 08.04. 16:45 - 17:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 09.04. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 15.04. 16:45 - 17:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 16.04. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 22.04. 16:45 - 17:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 23.04. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 29.04. 16:45 - 17:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 30.04. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 06.05. 16:45 - 17:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 07.05. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 13.05. 16:45 - 17:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 14.05. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 21.05. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 27.05. 16:45 - 17:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 28.05. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 03.06. 16:45 - 17:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 04.06. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 10.06. 16:45 - 17:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 11.06. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 17.06. 16:45 - 17:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 18.06. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 24.06. 16:45 - 17:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 25.06. 16:45 - 18:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

Elliptic Curves represent a paradigma for the confluence of various mathematical theories and techniques: Algebraic Geometry, Group Theory, Complex Analysis, Number Theory, Algebraic Topology, and Differential Geometry, with numerous applications in Coding Theory and Cryptography.

The objective of the course is to illustrate this multi-faceted situation by comparing the different approaches: the study of equations, double periodic functions, tori, and Riemann surfaces of genus 1. Special interest will then be laid on number theoretic results, looking at Q-rational points on elliptic curves (Mordell's theorem), modularity (Shimura-Taniyama conjecture) and the relation to Fermat's last theorem, respectively, the ABC-conjecture. These last items can only be described roughly as the required methods would go far beyond the scope of the course. However, we very much hope to be able to give a reasonable account on the phenomena and results which have been observed.

Assessment and permitted materials

Oral exams or write-up of additional aspects of the material covered in class.

Minimum requirements and assessment criteria

Examination topics

Reading list

Among the vast literture, there is a very nice book of Neil Koblitz on elliptic curves. Also the classical texts of Joseph Silverman can be recommanded.

Association in the course directory

MALV; MGEV;

Last modified: Th 29.08.2024 16:06