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.
Activities
– Seminars and working groups :
– Formations (faisant partie du Master in Mathematics and Applications from Paris-Saclay University) :
- Master 1 Mathématiques en Interactions (MINT)
- Master 2 Algèbre appliquée (Professionnel et Recherche)
– ANR :
- ANR FLAIR (Familles de fonctions L : analyse, interactions, résultats effectifs)
- ANR CATORE (categorifications in topology and representation theory)
- ANR De Rerum Natura
– GDR :
- GDR « Algebraic Geometry and Complex Geometry »
- GDR « Mathematical Informatics » and its working group
- GDR « Singularités et Applications »
- GDR « Structuration de la théorie des nombres »
- GDR « Théorie de Lie Algébrique et Géométrique »
- GDR « Équations fonctionnelles et applications »
– International collaborations:
- As part of the European SOCRATES project, a UVSQ / University of Valladolid agreement provides access to postgraduate courses in Valladolid.
- Algebraic modeling of topological and computational structures (AlModTopCom), Grèce
- GDRI « Representation theory »
- PICS franco-espagnol MIAS « More Invariants from Arc Schemes »
– Archives:
- ANR ACG (Aspects conformes de la géométrie)
- ANR HaMoT (Hauteurs Modularité Transcendance)
- ANR q-diff (q-difference equations & related topics)
- ANR ThéHopaD (Théorie de Hodge p-adique et Développements)
- ECOS Nord France-Colombia “Équations aux q-différences & groupes quantiques”
- Les membres de cette équipe font partie du réseau européen EAGER
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 Liqian | Chercheur 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 María | Doctorante |
| Bodin Pierre | Doctorant |
| Garcia Monica | Doctorante, ATER |
| Gupta Esha | Doctorante |
| Gubarevich Danil | Doctorant |
| Krawchuk Colin | Doctorant invité |
| Muñoz‐‐Bertrand Rubén | ATER |
| Specka Ernest | Doctorant |
| Yurikusa Toshiya | Post-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 |