Algebra, Geometry and Topology are very classical research areas in mathematics, sharing a long historical tradition of fruitful interactions among them. Since long ago, mainstream research in these areas has been present in Barcelona by several research groups, which cover a broad range of modern research lines, and mantain real connections and benefitial interactions among them.

The BGSMath currently has six research teams actively working in these three areas of mathematics, specifically covering the topics of commutative and non-commutative algebra, algebraic topology, algebraic and differential geometry, operator algebras, and geometric group theory.

Research Lines

Algebraic geometry

Keywords: Algebraic varieties. Algebraic statistics. Arithmetic geometry. Complex geometry. Moduli spaces. Singularities.

Maria Alberich (UPC)
Miguel Ángel Barja (UPC)
Francesc Bars (UAB)
Marta Casanellas (UPC)
Eduardo Casas-Alvero (UB)
Laura Costa (UB)
Carlos D’Andrea (UB)
Jesús Fernández (UPC)
Rosa M. Miró-Roig (UB)
Joan Carles Naranjo (UB)
Joaquim Roé (UAB)
Martín Sombra (UB)
Xavier Xarles (UAB)

Commutative Algebra

Keywords: Algorithmic Algebra. Combinatorial Algebra. Local rings. D-modules. Singularities. Polynomial maps. Local cohomology. Homological Algebra. Numerical Semigroups.

Josep Álvarez (UPC)
Carlos d’Andrea (UB)
Joan Elias (UB)
Ricardo Garcia (UB)
Francesc Planas (UPC)
Martín Sombra (UB)
Santiago Zarzuela (UB)

Group Theory

Keywords: Geometric Group Theory. Action of groups. Free groups and free-like structures. Solvability of algorithmic problems on groups.  Generic and asymptotic properties of groups. Fusion systems of finite groups and Lie groups.

Carles Broto (UAB)
Jose Burillo (UPC)
Natàlia Castellana (UAB)
Albert Ruiz (UAB)
Enric Ventura (UPC)

Algebraic Topology

Keywords: Homotopical and homological algebra. Rational homotopy theory. Operads. Sheaf homotopy theory. Model categories. Homotopy theory of classifying spaces. Homotopical/homological localizations. Homotopy theory of triangulated categories. Category theory.

Jaume Aguadé (UAB)
Carles Broto (UAB)
Federico Cantero (BGSMath-UB)
Carles Casacuberta (UB)
Natàlia Castellana (UAB)
Imma Gálvez-Carrillo (UPC)
Joachim Kock (UAB)
Javier Gutierrez (UB)
Ignasi Mundet (UB)
Joan Porti (UAB)
Albert Ruiz (UAB)

Differential geometry

Keywords: Hyperbolic geometry. Complex geometry. Integral geometry.
Symplectic geometry. Geometric manifolds. Moduli and representation
spaces. Foliations.

Jaume Amorós (UPC)
Eduardo Gallego (UAB)
Gregori Guasp (UAB)
David Marín (UAB)
Eva Miranda (UPC)
Ignasi Mundet (UB)
Marcel Nicolau (UAB)
Joan Porti (UAB)
Agustí Reventós (UAB)
Gil Solanes (UAB)

Non-commutative algebra

Keywords: Operator Algebras. C*-algebras and Dynamical Systems. K-Theory. The Cuntz semigroup and classification. Homological algebra. Representation Theory. Division rings.

Ramon Antoine (UAB)
Pere Ara (UAB)
Dolors Herbera (UAB)
Francesc Perera (UAB)

Links to research groups

Researchers in the Barcelona area, and more generally in Catalonia, group themselves into smaller research groups, following not only academic but also administrative criteria, like location or research grants.