Research group in Algebra
Academic staff
Valentina Barucci, Paolo Bravi, Flavio D'Alessandro, Alessandro D'Andrea, Corrado De Concini, Alberto De Sole, Claudia Malvenuto, Paolo Papi, Claudio Procesi, Ernesto Spinelli, Antonietta Venezia
Post-docs and graduate students
Salvatore Dolce, Laura Fedele, Matteo Gardini, Veronica Vignoli, Salvatore Stella
Research areas
- Combinatorial topology (De Concini, Procesi): Hyperplane arrangements, tori arrangements, partition function and applications also in relation with Lie theory.
- Combinatorics (Malvenuto, Venezia): algebraic combinatorics, extremal combinatorics of permutations, Hopf Algebras of Combinatorial structures, symmetric and quasi-symmetric functions.
- Commutative Algebras (Barucci): Rings of curve singularities and one-dimensional analytically unramified rings. Numerical semigroups. Semigroup rings. Rees algebras and associated graded rings.
- Invariant theory and algebraic groups (Bravi, De Concini, Papi): algebraic varieties with an algebraic group action, covariants in exterior algebras of simple Lie algebras, spherical varieties.
- Lie Theory (Cerulli Irelli, D’Andrea, De Concini, De Sole, Malvenuto, Papi): algebraic Dirac operators, combinatorics of finite and affine root systems, Lie superalgebras, transversally elliptic differential operators, cluster algebras.
- PI Theory (Procesi, Spinelli): codimension growth, minimal varieties, Lie structure of group algebras.
- Vertex algebras (D'Andrea, De Sole, Papi): conformal embeddings of affine vertex algebras, Lie pseudoalgebras, orbifold vertex operator algebras, structure of classical (finite and affine) W-algebras, Dirac reduction for Poisson vertex algebras, Poisson structures and applications to the theory of integrable systems.