The Algebra and Algebraic Geometry group at CRM boasts a wide range of research interests, reflecting the diversity of its members. Despite this diversity, the group maintains fluid and dynamic interactions through common seminars and frequent discussions on topics at the intersection of their respective fields.
The research on non-commutative algebra revolves around the structure theory of C*-algebras, with classification results in sight. In particular, we study pureness in the sense of Winter and properties of the central sequence algebra, using techniques that are partly based on the structure of the Cuntz semigroup.
On the commutative algebra side, we developed fundamental aspects of computational algebra and the complexity of algorithms. Additionally, we apply combinatorial techniques to study some particular algebras and local cohomology modules. Our research also uses differential operators and methods in positive characteristic to examine invariants of singularities. Furthermore, we explore the arithmetic aspects of varieties through the lens of Arakelov geometry.
The group has a long tradition of addressing classical problems in algebraic geometry, employing both traditional and modern techniques. Our topics of interest include the study of the structure and properties of both moduli spaces of vector bundles and moduli spaces of curves. The study of fibrations over curves and also higher-dimensional base spaces is a cornerstone of our research. Bridgeland-type stability conditions, recently developed for families of algebraic varieties, play a crucial role in this research. Another classical theme for the members of the group is the study of Abelian varieties over the complex numbers but also over number fields.
GROUP LEADERS
