The research group of algebra and geometry is focused on the following topics.
- Algebraic geometry:
- Moduli spaces of curves and bundles: Geometry of moduli spaces and their applications;
- Algebraic Surfaces, classification problems, fibrations and topology;
- Hodge theory, variation of Hodge structures, period maps, infinitesimal invariants, second fundamental form;
- Rational function fields and geometric Galois theory.
- Category theory and homological algebra
- Derived categories of algebraic varieties and algebraic stacks, Fourier-Mukai functors
- Triangulated categories and dg-categories, higher category theory
- Differential geometry and hyperbolic geometry:
- Teichmueller theory, harmonic maps and minimal Lagrangians, universal Teichmueller space, projective structures, hyperbolic structures with conic singularities;
- Group actions on Kaehler manifolds, momentum map;
- Lorentzian geometry, isometric immersions of surfaces, Minkowski problem.
- Real geometry
- Analytic spaces;
- Sums of squares;
- Regularity of the roots of polynomials.
The group organises the Seminars of Algebra and Geometry.