Coursebooks

Arithmetic of elliptic curves

MATH-695

Lecturer(s) :

Michel Philippe
Viazovska Maryna

Language:

English

Frequency

Only this year

Remarque

Next time: Fall 2018

Summary

The arithmetic of elliptic curves is an area of modern number theory which studies properties of points on elliptic curves over various fields. Due to the relative simplicity, this subject has been well studied and many patterns and regularities have been discovered.

Content

The arithmetic of elliptic curves is an area of modern number theory which studies properties of points on elliptic curves over various fields. 'Due to the relative simplicity, this subject has been well studied and many patterns and regularities have been 'discovered. A few examples of such statements are: Sato-Tate conjecture, Birch and Swinnerton-Dyer conjecture, Modularity theorem. In this course we plan to discuss basic properties of elliptic curves, recent results, and open conjectures.

 

Note

This course will take place in a form of a seminar. Each participant is expected to give a talk. The talks will be distributed  during the first lecture

Learning Prerequisites

Required courses

Participants are expected to have basic knowledge in algebra, number theory, and complex analysis.

In the programs

    • Semester
    • Exam form
       Oral presentation
    • Credits
      3
    • Subject examined
      Arithmetic of elliptic curves
    • Lecture
      24 Hour(s)
    • Practical work
      18 Hour(s)

Reference week

 
      Lecture
      Exercise, TP
      Project, other

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  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German