The group studies varieties and manifolds, in particular algebraic and complex varieties and some generalizations such as supermanifolds, from an algebraic, topological or differential perspective.
A great emphasis is put on Moduli spaces and stability conditions, Hyperkähler varieties, Fano and Calabi-Yau varieties, elliptic fibrations, toric varieties, Homogeneous and spherical varieties (including their noncommutative generalizations using Lie supergroups.
The group also studies enumerative algebraic geometry, arithmetic geometry, algebraic number theory and applications of algebraic geometry to Physics.