Number theory and algebraic geometry 

Head: Christophe Breuil
Assistant: Olga Jamin
Weekly seminar: Tuesdays, 2pm

The team has a long tradition of research in the areas of algebraic geometry and arithmetic, both understood in a broad sense. Adding to these classical themes, the team now also has members working in representation theory and mathematical logic.

More precisely, the team's current research directions are the following:

• Algebraic geometry (both complex and in positive characteristic, sometimes derived), Hodge theory and the study of algebraic cycles, the construction and study of moduli spaces, enumerative geometry, birational geometry, algebraic or arithmetic dynamics, and motivic homotopy theory
• Arithmetic geometry, Arakelov or diophantine geometry, the study of rational points on algebraic groups and algebraic varieties, various incarnations of the 'local-global' principle
• Analytic number theory (including probabilistic and statistical aspects), trace functions, modular forms, L-functions, Diophantine approximation
• Representation theory of p-adic or adelic groups (in its p-adic, l-adic or mod p incarnations), automorphic forms, Iwasawa theory, the study of Galois representations and all aspects of the Langlands program (global, local, geometric)
• Algebraic and geometric representation theory (quantum groups, W-algebras, quiver varieties)
• Model theory and higher category theory.