Geometry

Research axes and themes

The Geometry team is divided into 4 sub-themes. Each of these themes works in several research directions:

Complex geometry

• Classification of compact Kählerian manifolds
• Hyperkählerian manifolds
• Moduli spaces of semistable bundles
• Transcendental methods in algebraic geometry
• Spaces of cycles
• Singularities
• Hyperbolicity
• Birational geometry

Differential geometry

• Riemannian geometry
• Geometry of submanifolds
• Spinorial geometry
• Geometric analysis
• Dynamical systems
• Representations of lattices in symmetric spaces
• Geometry of non-positive curvature in infinite dimension
• Geometric group theory

Algebraic groups

• Generalizations of Bruhat-Tits buildings
• Lie superalgebras
• Quantum cohomology of flag varieties

Arithmetic geometry

• Geometric Langlands program
• Shimura varieties

 

Each of these themes works in several research directions:

  • Complex geometry | CG: study of complex manifolds, in particular classification of compact Kählerian manifolds, hyperkählerian manifolds, moduli spaces of semistable bundles, transcendental methods in algebraic geometry, spaces of cycles, singularities, hyperbolicity, birational geometry.

  • Differential geometry | DG:

    Riemannian geometry, geometry of submanifolds, spinorial geometry, geometric analysis, dynamical systems, lattice representations in symmetric spaces, non-positive curvature geometry in infinite dimension, geometric theory of groups.

  • Algebraic groups | AG: generalizations of Bruhat-Tits buildings, Lie superalgebras, quantum cohomology of flag varieties.
  • Arithmetic geometry | AG: geometric Langlands program, Shimura varieties.
Activities of the team

The life of the team is punctuated by numerous seminars, conferences and working groups:

Seminars

  • Seminar “Complex geometry” (GC and GAR).

  • Seminar “Differential geometry” (GD).

  • Geometry team seminar.

  • Internal seminar

  • Biannual seminar Basel-Freiburg-Nancy-Saarbrücken-Strasbourg of algebraic geometry and complex geometry (GC).

  • Biannual seminar Luxembourg-Nancy-Strasbourg of differential geometry (GD).

Recurrent conference

  • Journées Nancéiennes de Géométrie (annual).

  • Journées Complexes Lorraines (every four years).

Working groups of the last 4 years

GC & GAR

Stability conditions

GC & GAR

O-minimality

GC

Hyperbolicity

 

Singular BB decomposition

GAR

Intersection cohomology

GARFrobenius splitting
GAR

Kac-Moody groups

GA

Infinite-categories, higher algebra and derived algebraic geometry

EpiGA

The team is also behind a peer-reviewed scientific journal founded in 2016: The Epijournal of Algebraic Geometry (EpiGA). Several of its members are responsible for the follow-up and the practical management of the journal.

The areas covered by the journal are algebraic geometry in a broad sense, including complex and arithmetic geometry, algebraic group and representation theory.

For more information: see the journal’s website 

Logo EPIGA

Team leader: Gianluca Pacienza