Geometry (2021)

Arrangements, configuration spaces and braid groups 
Local cohomology of the complement of an arrangement. Cohomology ring of the complement of a toric arrangement. Homology of braid groups with coefficients in symplectic representations. Homology of regular orbit spaces for groups of complex reflections for classifying the fundamental groups of these spaces. Combinatorics of wonderful models and some of their blow-ups, in relation to certain actions of the symmetric group. Homological stability for complex braid groups. Combinatorial methods for Artin and Coxeter groups and description of new algebraic structures for the infinite series of Coxeter groups
Filippo Callegaro
Mario Salvetti
Giovanni Gaiffi 
Ivan Marin  (Univ. Picardie) 
Fred Cohen (Univ. Rochester)
Emanuele Delucchi (Univ. Fribourg)  Michele D’Adderio (Univ. Libre de Bruxelles) 
Lorenzo Guerra (PhD student, SNS)
Giovanni Paolini (PhD student, SNS) 
Roberto Pagaria (PhD student, SNS) 
Oscar Papini (PhD student, Dept. of Mathematics, Univ. of Pisa)
Recent grants
PRIN 2015-2016 “Moduli Spaces and Lie theory”
National coordinator: Kieran O’Grady
Local coordinator: Mario Salvetti
FIRB 2012 project ”Perspectives in Lie Theory”” (grant n. RBFR12RA9W 003)
Local coordinator: Filippo Callegaro
Supporting institution MIUR

Algebraic Geometry
Algebraic varieties of maximal Albanese dimension: eventual behaviour of linear systems and numerical inequalities of Clifford-Severi type. The KSBA compactification of the moduli space of surfaces of general type with small K2. Singular algebraic curves: numerical connectedness and properties of the dualizing sheaf. Stratifications of configuration spaces of k points in complex affine and projective space and Grassmannians.
Algebraic stacks. Logarithmic geometry and moduli spaces of parabolic sheaves.
Derived algebraic geometry. Shifted Poisson and symplectic structures.
Hall algebras (classical, cohomological, categorified), their relation to the theory of Yangians and quantum affine algebras, and their relation to the topology of moduli spaces of stable sheaves on smooth surfaces and Nakajima quiver varieties.

People Rita Pardini Marco Franciosi
Sandro Manfredini
Valerio Melani
Francesco Sala
Tamas Szamueli
Mattia Talpo

Miguel Ángel Barja (UPC, Barcelona)
Mauro Porta (Université de Strasbourg, France)
Sönke Rollenske (Univ. Marburg, Germania)
Sarah Scherotzke (Univ. Luxembourg)
Olivier Schiffmann (CNRS and Université Paris-Saclay, France)
Nicolò Sibilla (SISSA, Trieste)
Lidia Stoppino (Univ. Insubria)

Recent Grants
PRIN 2017- 2017SSNZAW “Advances in Moduli Theory and Birational Classification”
National coordinator: Lucia Caporaso
Local coordinator: Rita Pardini
Supporting institution: MIUR

PRIN 2015 “Geometria delle Varieta’ Algebriche”
Web page:
National coordinator: Alessandro Verra
Local coordinator: Rita Pardini
Supporting institution: MIUR

Real and Analytic Algebraic Geometry
Algebraic properties of algebra of global analytic functions on a real analytic space (Nullstellensatz, …). HIlbert’s 17th problem for global analytical functions. Global semianaliticity of notable subgroups (points of inconsistency, points of regularity of fixed dimension, ….) of C-spaces. Algebraic properties of quasianalytic germ function algebra (division and preparation theorem of Weierstrass, Nullstellensatz, Noetherian properties, …). Local study of semi-analytical, local algebraic approximation with conservation of geometric properties and multiplicity of a point. Semi-analytical and sub-analytical sets. Real algebraic curves.
Francesca Acquistapace
Fabrizio Broglia
Jose’ Fernando (Univ. Complutense Madrid)  
Carlos Ueno (Kodály Zoltán Gimnázium, Pécs, Hungary)  
Andreea Nicoara (Trinity College, Dublin)
Elisabetta Fortuna
Massimo Ferrarotti (Polytechnic Univ. of Turin)
Les Wilson (University of Hawaii, Manoa, Honolulu, USA)
Margherita Galbiati
Recent grants
PRIN 2010-11 “Varieta’ reali e complesse: geometria, topologia e analisi armonica”
National coordinator: Fulvio Ricci – SNS Pisa  
Local coordinator: Riccardo Benedetti
Supporting institution: MIUR

GRAYAS 2015-2018 “Geometria Real y aplicaciones”, MTM2014-55565-P
Scientific coordinators: Jose Javier Etayo, Jose F. Fernando
Supporting institution: MINECO
STRANO 2018-2021 “Estructuras algebraicas, analiticas y ominimales”, MTM2017-82105-P
Scientific coordinators: Jose Javier Etayo, Jose F. Fernando
Supporting institution: MINECO

Low-dimensional Geometry and Topology
Analytical families of “quantum-hyperbolic” invariants of 3-manifolds (with particular attention to families that dominate the geometric component of the range of characters of hyperbolic 3-manifold with a cusp); asymptotic behavior when the level approaches infinity (variants of “Volume conjecture”); study of the anomaly and functional identity of the symmetrization factor; the relationship with other “quantum” invariants of 3-manifolds ‘. Limited cohomology of discrete groups, with particular reference to simplicial volume applications, and on geometric group theory, with particular attention to metric spaces with curvature constraints (CAT(k) spaces). Hyperbolic ranges in dimension 3 and above; complexity of 3- and 4-manifolds, quantum invariants of 3-manifolds. Complexity of torus knots in lens spaces: extension of the techniques of Tillman et al. Existence of branched coverings between surfaces which induce covers between hyperbolic orbifolds with high-dimensional Teichmuller space. Apparent contours of surfaces on 3-manifold spines with respect to generic vector fields. Contact 3-manifolds, Stein fillings, Heegaard Floer homology, Heegaard Floer homology, Khovanov homology and its variations, Legendrian and transverse link invariants. Symmetric unions. Topological spin models. Classical concordance group. Casson-Gordon invariants. Rational homology 4-balls and their embeddings.
Riccardo Benedetti
Roberto Frigerio
​Paolo Lisca​
Bruno Martelli
Carlo Petronio
Former students and collaborators:
Stephane Baseilhac (Universita’ di Montpellier, France)
Giulio Belletti (post-doc, Università di Heidelberg)
Michelle Bucher (Università di Ginevra)
Carlo Collari (post-doc, New York University Abu Dhabi)
Marco Golla (Nantes University)
Marco Moraschini (post-doc, Università di Regensburg)
Brendan Owens (Glasgow University)
Maria Beatrice Pozzetti (Università di Heidelberg)
Stefano Riolo (assegnista PRIN)
Alessandro Sisto (Heriot-Watt University)
Leone Slavich (Università di Pavia)
PhD students:
Ludovico Battista, Giuseppe Bargagnati, Leonardo Ferrari, Domenico Marasco, Alice Merz (University of Pisa)
Federica Bertolotti, Giovanni Italiano, Matteo Migliorini, Francesco Milizia, Diego Santoro (Scuola Normale Superiore)
Recent grants
PRIN 2010-11 “Varieta’ reali e complesse: geometria, topologia e analisi armonica”
National coordinator: Fulvio Ricci – SNS Pisa  
Local coordinator:  Riccardo Benedetti
Supporting institution: MIUR
FIRB 2011 project “Geometria e topologia delle varietà in bassa dimensione (Geometry and topology of low-dimensional manifolds)”
National coordinator: Bruno Martelli
Local coordinators:
Francesco Bonsante (Pavia) Gabriele Mondello (Rome) Bruno Martelli (Pisa)
Supporting institution: MIUR
PRA 2016-2017 “Geometria e topologia delle varietà”.
Supporting institution: Università di Pisa
MIUR PRIN project 2017 “Real and Complex Manifolds: Topology, Geometry and holomorphic dynamics”
National coordinator: Filippo Bracci – Roma Tor Vergata 
Local coordinator: ​Paolo Lisca​
Web page of the project

Holomorphic dynamical systems
Parabolic holomorphic dynamic and, more generally, non-hyperbolic, from a topological, holomorphic and formal point of view; discrete and continuous dynamic in convex and pseudoconvex and, more generally, in taut varieties. Study of the geodesic flow of meromorphic connections on Riemann surfaces. Geometric theory of functions, with particular reference to the study of Carleson’s measures, Toeplitz’s operators and boundary behavior of analytical functions in pseudoconvex domains. Index theorems index for applications and holomorphic foliations.
Marco Abate
Jasmin Raissy (Universite’ Paul Sabatier, Toulouse, France)
Fabrizio Bianchi (Imperial College, London)
Karim Rakhimov (Ph.D. student, Pisa)
Recent grants
FIRB 2012 project ”Geometria Differenziale e Teoria Geometrica delle Funzioni” (grant n. RBFR12W1AQ 002).
Local coordinator: Jasmin Raissy (Universite’ Paul Sabatier, Toulouse, France)
Supporting institution: MIUR
PRA 2015-2016 “Connessioni fra dinamica olomorfa, teoria ergodica e logica matematica nei sistemi dinamici”
PRA 2017-2018 “Sistemi dinamici in analisi, geometria, logica e meccanica celeste”
Supporting institution: University of Pisa

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