“CIMPA Course”
Groups and Algebraic Curves
Prof Michel Jambu, Laboratoire Dieudonné, Université Cote d’Azur
On 2 – 6 March 2020 at College of Science; SUE- Erbil, Kurdistan Region- Iraq
Coordinator
Fatima M. Aboud, Department of mathematics, College of Sciences, University of Diyala.
Herish Omer, Department of mathematics, College of Sciences, Salahaddin University.
Sponsors: CIMPA, Salahaddin University
Date: From 2 to 6 March 2020
Time: From 10:30-11:30 AM
Location: College of Sciences- University of Salahaddin-Erbil
Groups and Algebraic Curves
Michel Jambu
Professor Emeritus University of Cˆote d’Azur, Nice, France Michel.JAMBU@univ-cotedazur.fr
The group law on elliptic curves has very important applications and it deserves to be well understood. In order to achieve this goal, we will start by an elementary example that we will develop in details, the group law on a circle. The framework is inside projective geometry and we will begin by a crash course on this topic.
Then, we will show that in this context, the group law on elliptic curves is a natural extension of the group law on circle. Moreover, we will introduce a natural group law on non degenerate and degenerate conics and we will show that Pappus theorem and Pascal theorem play a crucial role.
The trigonometric functions parametrize the circle, the elliptic functions parametrize the elliptic curves. The main theorem is due to Cayley and Bacharak and it extends Pappus and Pascal theorems. Finally, if possible, we will give some ideas about the abelian varieties.
Content of the course :
- Projective Geometry.
- The Circle.
- The Conics.
- The Elliptic Curves
- Conclusion
For more information about the CIMPA activities, please visit
https://www.cimpa.info/en/activities/future
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