Algebraic and Arithmetic Geometry

• Algebraic curves
• Group schemes and torsors
• Birational geometry
• Motivic geometry
• Diophantine geometry

Algebraic and Analytic Number Theory

• Iwasawa theory of number fields
• p-adic representations of local fields
• Langlands programme
• L-functions and zeta functions
• Arithmetic of modular forms

Algorithmic Arithmetic, Cryptology and Discrete Mathematics

• Algorithmic number theory, in particular in connection with the Langlands programme
• Applications in cryptography (with a focus on post-quantum cryptography based on error-correcting codes, lattices and isogenies)
• Arithmetic and discrete mathematics