TO BE REVISED
The scientific activity in this area has significant connections with geometry and computer science, and takes place mainly in the following fields: algebraic number theory, study of p-adic field extensions, ramification; Galois module structure; study of the dynamics of polynomial maps; rational points of algebraic varieties; computational commutative algebra and algebraic geometry (with particular reference to the study and creation of algorithms for factorization analysis, determination of minimal systems of generators for projective algebraic varieties, correcting codes and cryptography, study of the topology of real algebraic varieties); Lie algebras and algebraic combinatorics; and representation theory (with particular reference to the study of geometric properties of algebraic groups, symmetrical and spherical varieties). Study of the cohomology of complex braid groups, ring cohomology of toric complementary arrangements, combinatorial and topology of wonderful models for arrangements of hyperplanes linked to groups of complex reflections.
lista dei membri
lista dei postdocs
lista degli studenti di dottorato
lista dei collaboratori esterni
lista dei grants in corso
Lines of research in progress:
Lie theory: nilpotent orbit, B-orbits in symmetric varieties, Bruhat order, Kazhdan-Lusztig polynomials, vertex algebras and opers with two singularities, decomposition of tensor products.
Commutative algebra and its interactions with computational algebra and combinatorics. Classification of Hilbert functions, Eisenbud-Green-Harris’s conjectures and Evans’ Lex-Plus-Power. Jet-schemes of determinantal varieties and modules with straightening laws.
Commutative algebra and real algebraic geometry, with special attention to constructive and computational aspects. Correcting codes.
Study of the ramification jumps in Abelian extensions. Classification of wild extensions of p-adic fields (branching steps; wild extensions). Study of the dynamics of polynomial maps; rational points of variety of cyclotomic extensions (keywords: polynomial maps, Hilbert irreducibility theorem, cyclotomic extension).
Study of Hopf-Galois structures of field extensions: classification problems, existence/non-existence. Algebraic structures associated with the Yang-Baxter equation: the language of skew braces.
Construction of (real and complex) models of subspace arrangements and toric arrangements, configuration spaces. Study of the cohomology rings of the the above mentioned objects and of the associated group actions (in the cases when Coxeter groups or complex reflection groups are involved). Combinatorics of nestohedra and permutonestohedra, nested set complexes.
Michele D’Adderio (Univ. Libre de Bruxelles)
Corrado De Concini (Sapienza Università di Roma)
Emanuele Delucchi (Univ. Fribourg)
Oscar Papini (dottorando)
Arithmetic of abelian varieties. Elliptic curves and abelian varieties of higher dimension, Galois representations, Mumford-Tate and Sato-Tate conjectures. Local-global principles for isogenies and torsion points; reduction of points of infinite order. Low genus curves: theoretical and computational aspects.
National coordinator: O’GRADY Kieran Gregory
Local Principal Investigator: SALVETTI Mario
Title: Moduli and Lie theory
National coordinator: CORVAJA Pietro
Local Principal Investigator: DVORNICICH Roberto
Title: Geometric, algebraic and analytic methods in arithmetic