Algebraic Geometry, Number Theory and Applications in Cryptography and Robot kinematics

This school aims to offer an intensive teaching session to graduate students and young researchers. That concerns key topics in Algebraic Geometry and Number Theory. Indeed many classical results and methods in these areas are used in flourishing domains of applied mathematics. We selected the following six courses:

•  Algebraic number theory and class field theory.
• Tate module and abelian varieties.
• Quantitative and algorithmic recent results in real algebraic geometry.
• Advanced topics in semi-algebraic geometry.
• Counting points on algebraic varieties.
• Fundamental groups in Algebraic and Arithmetic Geometry.

These fundamental courses describe all theoretical elements needed for the applications in cryptography and robot kinematics which will be developed at the end of the school.

Beyond lectures, we are also planning sessions devoted to solving exercises and to computer experiments with Pari/GP and Sage.

We expect that at the end of the school every participant will be able to select a suitable hyperelliptic curve for constructing some cryptosystems based on the discrete logarithm problem in its Jacobian.