Algebra and Geometry (AG)

Concentrating his skills on two areas of excellence, algebraic geometry and arithmetic geometry (Lie theory, singularities, the Langlands program, computer algebra), the team is constantly developing attractive training, scientific links with the most major national and international institutions leading to scientific work of the highest level.

Research Topics

  • Complex algebraic geometry. Quantum cohomology and K-theory, Fano varieties, varieties with group action,
    Schubert calculus, spherical manifolds, Frobenius splitting.
    Geometric study of functional or differential equations in complex fields (sheets, fabrics, etc.).
    Modular spaces of flat surfaces, hypergeometric functions, complex hyperbolic geometry.
  • Local standardization and desingularization of diagrams in positive characteristic and in arithmetic.
    Associated invariants: tangent cones, polyhedra, graduated algebras. Effective calculations on singularities. Arc space on singular algebraic varieties.
  • Complex and modular representations of Lie groups and algebras and p-adic reductive groups. Local Langlands correspondences and functorials. Representations of reflection groups and Hecke algebras. Invariants of nodes.
  • Number of points, zeta functions, Frobenius distribution, infinite turns and asymptotic theory.
  • Galois theory of functional equations.
  • History of mathematics in the 19th and 20th centuries.
  • Didactics of first degree mathematics.


Seminars and working groups :

Formations (faisant partie du Master in Mathematics and Applications from Paris-Saclay University) :



International collaborations:

Conférences et colloques


Team Members

Manager : Luc Pirio

Teachers and Directors of Research

Andler Martin PR émérite
Castravet Ana-Maria PR
Cossart Vincent PR émérite
Di Vizio Lucia DR
Plamondon Pierre-Guy PR
Sécherre Vincent PR
Tsfasman Mikhail DR émérite
Zvonkine Dimitri DR

Assistant Professors and Research Officers

Bai LiqianChercheur invité
Ginouillac Stéphane MCF
Krir Mohamed MCF
Lanard Thomas CR
Moreno-Socias Guillermo MCF
Piltant Olivier CR - HDR
Pirio Luc CR

PhD student and post-doc

Abad Aldonza MaríaDoctorante
Bodin PierreDoctorant
Garcia MonicaDoctorante, ATER
Gupta EshaDoctorante
Gubarevich DanilDoctorant
Krawchuk ColinDoctorant invité
Muñoz‐‐Bertrand RubénATER
Specka ErnestDoctorant
Yurikusa ToshiyaPost-doctorant

Volunteer collaborator

De Seguins Pazzis Clément Enseignant au lycée, en détachement
Pouchain Guillaume Enseignant au lycée Henri IV à Paris
Rémy Pascal Ministère de l'Éducation Nationale