Geometry

The scientific activities of the group are focused on different aspects of Algebraic and Arithmetic Geometry, Combinatorics of Evolutionary Structures, Complex and Differential Geometry, and Geometric Topology.

The group runs the following Seminars Series:

Usually, the group organizes workshops, conferences, and summer schools. A list of the upcoming ones is available on this page.

Research Topics

Algebraic and arithmetic geometry
Members
Andrea Di Lorenzo
andrea.dilorenzo@unipi.it
Marco Franciosi
marco.franciosi@unipi.it
Rita Pardini
rita.pardini@unipi.it
Gregory James Pearlstein
greg.pearlstein@unipi.it
Francesco Sala
francesco.sala@unipi.it
Tamás Szamuely
tamas.szamuely@unipi.it
Mattia Talpo
mattia.talpo@unipi.it
Dario Weißmann
dario.weissmann@dm.unipi.it

Below is the list of the specific topics studied in this research area, each of them with a detailed description and the lists of members and collaborators.

Cohomology of varieties and arithmetic questions

Given an algebraic variety $X$ defined over a field $k$, one can associate to it various cohomology groups: coherent, étale, $p$-adic, or even motivic. These groups reflect the geometry, and in case $k$ is of arithmetic interest, the arithmetic of the variety $X$. Using cohomological methods we study, among other things:

  • algebraic cycles
  • algebraic fundamental groups
  • local-global principles for rational points
Members
Tamás Szamuely
tamas.szamuely@unipi.it
Collaborators
Philippe Gille (Université Claude Bernard Lyon 1)
David Harari (Université de Paris-Saclay)
Damian Rössler (University of Oxford)
Logarithmic and tropical algebraic geometry

Logarithmic geometry is an enhanced version of algebraic geometry, where spaces are equipped with an additional structure sheaf, which encodes information of a combinatorial nature (e.g. toric varieties). This recent theory has been fruitfully applied to questions regarding special kinds of degenerations of varieties or other more complicated objects, and compactifications of moduli spaces, for example in the context of mirror symmetry. There are also very interesting interactions with the field of tropical (and non-Archimedean) geometry. Our activity focuses for example on

  • the study of moduli spaces of parabolic bundles (some notion of coherent sheaf, adapted to log schemes)
  • sheaf-counting on log smooth varieties
  • interactions between (log) algebraic and tropical moduli spaces (e.g. for curves with level structures)
Members
Andrea Di Lorenzo
andrea.dilorenzo@unipi.it
Mattia Talpo
mattia.talpo@unipi.it
Collaborators
Sarah Scherotzke (University of Luxembourg)
Nicolò Sibilla (SISSA, Trieste)
Bernd Siebert (University of Texas at Austin)
Richard Thomas (Imperial College London)
Martin Ulirsch (Johann Wolfgang Goethe-Universität)
Moduli spaces of surfaces

The moduli space of surfaces of general type is well known to have an intricate structure. Its “geography” has been extensively studied. Furthermore, a modular compactification of it is the moduli
space of stable surfaces, i.e. semi-log-canonical surfaces with ample canonical divisor. The activity of the group is focused on the analysis of the compactified moduli space $\mathcal{M}(a,b)$ (where $a=K^2$ and $b$ is the holomorphic Euler characteristic), with particular attention to the case of surfaces with low numerical invariants. Such analysis is given by studying log-canonical pairs via a classical approach and analyzing the singularities, via Deformation Theory, and a detailed study of the canonical ring.
Related goals are to extend the knowledge of the moduli space by analyzing $\mathbb{Q}$-Gorenstein surfaces and to study the Hodge theoretic approach, by associating to a variety its cohomology and analyzing the induced variation of Hodge structures.

Members
Marco Franciosi
marco.franciosi@unipi.it
Rita Pardini
rita.pardini@unipi.it
Gregory James Pearlstein
greg.pearlstein@unipi.it
Collaborators
Stephen Coughlan (Institute of Mathematics of the Czech Academy of Sciences)
Barbara Fantechi (SISSA, Trieste)
fantechi@sissa.it
Matthias Leopold Nickel (Università di Pisa)
matthias.nickel@dm.unipi.it
Julie F. Rana (Lawrence University)
Sönke Rollenske (Philipps-Universität Marburg)
Moduli stacks, cohomological Hall algebras, and quantum groups

Quantum groups encode the ‘hidden symmetries’ of quantum physics through integrability. The geometric approach to these groups has proven successful in various areas, including representation theory (e.g. the theory of Maulik-Okounkov Yangians), the theory of moduli stacks and spaces (e.g. the proof of Beauville and Voisin’s conjectures of Maulik-Negut), and theoretical physics (e.g. the proof of the Alday-Gaiotto-Tachikawa conjecture).
Our group aims to investigate quantum groups through their geometric incarnations, focusing on Hall algebras and their refined versions (such as cohomological, K-theoretical, and categorified) associated with moduli stacks of coherent sheaves on curves or surfaces.

Members
Francesco Sala
francesco.sala@unipi.it
Collaborators
Duiliu-Emanuel Diaconescu (Rutgers, The State University of New Jersey)
Andrei Neguţ (Massachusetts Institute of Technology (MIT))
Mauro Porta (Université de Strasbourg)
porta@math.unistra.fr
Olivier Schiffmann (CNRS, Université de Paris-Saclay)
olivier.schiffmann@universite-paris-saclay.fr
Eric Vasserot (Université Paris Cité)
Moduli stacks of curves and their invariants

The interests of this group focus on moduli stacks of curves and surfaces, and on explicit computations of some of their invariants (e.g. Chow rings, unramified cohomology, Brauer groups). The stacks studied by the group are: moduli stacks of smooth/stable marked curves, moduli stacks of Weierstrass fibrations, moduli stacks of polarized K3 surfaces, moduli stacks of stable maps.

Members
Andrea Di Lorenzo
andrea.dilorenzo@unipi.it
Collaborators
Giovanni Inchiostro (University of Washington)
ginchios@uw.edu
Michele Pernice (KTH Royal Institute of Technology)
m.pernice@kth.se
Roberto Pirisi (Università degli Studi di Napoli Federico II)
roberto.pirisi@unina.it
Angelo Vistoli (SNS, Pisa)
angelo.vistoli@sns.it
Combinatorics of evolutionary structures

I am interested in combinatorial methods and structures of use in the study of the evolutionary relationships among or within groups of organisms. A particular focus is on coalescent models of evolution, in which gene trees, representing the evolutionary history of individual genes sampled from a set of species, evolve along the branches of species trees, reflecting the history of species divergences. In order to understand how features of the species tree can influence the distribution of the possible gene trees, the number and probability of the combinatorially different configurations that gene trees can assume within a given species tree are investigated. When individual gene copies are selected within a single species, the gene tree is modeled as a random coalescent tree that evolves independently of the branching pattern of the species tree, and the goal is to describe the distributive properties of its combinatorial parameters.

Members
Filippo Disanto
filippo.disanto@unipi.it
Collaborators
Michael Fuchs (National Yang Ming Chiao Tung University (NYCU))
Noah A. Rosenberg (Stanford University)
Thomas Wiehe (Universität zu Köln)
Complex and differential geometry

The group focuses on different aspects of complex and differential geometry from both an analytical and a geometric viewpoint.

Members
Marco Abate
marco.abate@unipi.it
Fabrizio Bianchi
fabrizio.bianchi@unipi.it
Diego Conti
diego.conti@unipi.it

Below is the list of the specific topics studied in this research area, each of them with a detailed description and the lists of members and collaborators.

Complex differential geometry

We studied complex Finsler manifolds, having in mind as a guiding example hyperbolic manifolds endowed with the Kobayashi metric, and in particular Kähler-Finsler manifolds with constant holomorphic curvature. Using techniques coming from both differential geometry and algebraic topology we studied the rich geometrical structure of analytic varieties that can be obtained as fixed point sets of a holomorphic self-map, proving a number of index theorems generalising to this setting classical Baum-Bott and Lehmann-Suwa theorems known for holomorphic foliations, and with applications to holomorphic dynamics.

Members
Marco Abate
marco.abate@unipi.it
Collaborators
Einstein and special metrics

We study the aspect of differential geometry that revolves around the explicit construction of Einstein or special metrics, with special emphasis on the case where the metric is either homogeneous or of cohomogeneity one.

Riemannian homogeneous Einstein metrics of negative scalar curvature can be identified with left-invariant metrics on a Lie group, and more precisely standard metrics on a solvable Lie algebra. In the pseudo-Riemannian case, homogeneous Einstein metric need not be standard, and the Lie algebra may be nilpotent. Our goal is to prove more general structure results for arbitrary signature, and obtain classifications under suitable extra assumptions.

Regardless of any assumption of invariance, among Einstein metrics one finds those of special holonomy and those that admit a Killing spinor; weaker geometries can also be considered. All these fall into the class of special metrics. Of particular interest to us is the interplay between the intrinsic torsion and curvature of a special metric. We also aim at producing examples, both by direct inspection of left-invariant metrics on Lie groups and by exploiting the well-posedness of the Cauchy problem for hypersurfaces, which often holds in the context of special metrics.

Members
Diego Conti
diego.conti@unipi.it
Collaborators and Ph.D. students at other institutions
Thomas Madsen (University of West London)
Thomas.Madsen@uwl.ac.uk
Federico Rossi (Università degli Studi di Perugia)
federicoalberto.rossi@unipg.it
Romeo Segnan Dalmasso (University of Surrey)
r.segnandalmasso@surrey.ac.uk
Geometric function theory

A characteristic feature of complex analysis is the use of geometrical tools to study analytic phenomena. A typical example consists in using the behaviour of the natural invariant (under biholomorphisms) metrics and distances defined on complex manifolds to study the boundary behaviour of holomorphic functions or the action of integral operators on spaces of holomorphic functions. In particular, we are using the Kobayashi metric and distance in pseudoconvex and convex domains to study the boundary behaviour of the derivatives of a holomorphic function at a specific point in the boundary and, more recently, to study the mapping properties of Toeplitz operators on weighted Bergmann spaces using characterisations of Carleson measures expressed in terms of Kobayashi balls.

Members
Marco Abate
marco.abate@unipi.it
Fabrizio Bianchi
fabrizio.bianchi@unipi.it
Collaborators
Matteo Fiacchi (Università di Pisa)
matteo.fiacchi@dm.unipi.it
Jasmin Raissy (Université de Bordeaux)
Karim Rakhimov (National University of Uzbekistan)
Holomorphic dynamical systems

In the last forty years, the study of holomorphic dynamical systems has become one of the most important topics in complex analysis and complex geometry of one and several variables, at the forefront of contemporary mathematical research. In Pisa, we are particularly interested in studying:

  • the global dynamics of holomorphic self-maps of hyperbolic manifolds and domains, and more generally of non-expanding self-maps of Gromov hyperbolic metric spaces;
  • the local dynamics around a non-hyperbolic fixed point;
  • the dynamics of meromorphic connections on hyperbolic Riemann surfaces;
  • the global dynamics of complex dynamical systems in any dimension (endomorphisms of projective spaces, Hénon maps, automorphisms of Kahler manifolds), usually through pluripotential theory methods;
  • Stability and bifurcation phenomena in one and several complex variables.
Members
Marco Abate
marco.abate@unipi.it
Fabrizio Bianchi
fabrizio.bianchi@unipi.it
Collaborators
Matteo Fiacchi (Università di Pisa)
matteo.fiacchi@dm.unipi.it
Jasmin Raissy (Université de Bordeaux)
Karim Rakhimov (National University of Uzbekistan)
Geometric topology
Members
Riccardo Benedetti
riccardobenedetti53@gmail.com
Filippo Gianluca Callegaro
filippo.callegaro@unipi.it
Michele D'Adderio
michele.dadderio@unipi.it
Roberto Frigerio
roberto.frigerio@unipi.it
Giovanni Gaiffi
giovanni.gaiffi@unipi.it
Paolo Lisca
paolo.lisca@unipi.it
Bruno Martelli
bruno.martelli@unipi.it
Carlo Petronio
carlo.petronio@unipi.it
Mario Salvetti
mario.salvetti@unipi.it
Andrea Tamburelli
andrea.tamburelli@unipi.it

Below is the list of the specific topics studied in this research area, each of them with a detailed description and the lists of members and collaborators.

Classical and higher rank Teichmüller theory

This area of research studies the geometric and dynamical properties of representations of the fundamental group of a surface $S$ (of negative Euler characteristic) into a Lie group $G$. For example, when $G=\mathbb{P}\mathrm{SL}(2, \mathbb{R})$, conjugacy classes of discrete and faithful representations are in bijection with the Teichmüller space of $S$, the space of marked hyperbolic (or complex) structures on $S$. More in general, and especially for Lie groups of rank $2$ (i.e., $G=\mathrm{SL}(3,\mathbb{R}), \mathrm{Sp}(4, \mathbb{R}, \mathrm{SO}(2,2), G_{2}$), researchers have identified special connected components of the character variety $\mathrm{Hom}(\pi_{1}(S), G)/G$ that parametrize geometric structures on $S$, or fiber bundles over $S$, and share a lot of similarities with the classical Teichmüller space.

The main goal of this research is to understand to which extent the classical Teichmüller theory generalizes to the higher rank. Some aspects include:

  • the study of diverging sequences of representations and the definition of the analogue of Thurston’s boundary for higher rank Teichmüller spaces;
  • the analysis of equivariant harmonic maps from the universal cover of $S$ into the symmetric space $G/K$ and the real Euclidean building modeled on $\mathfrak{g}$;
  • the definition of natural (pseudo)-Riemannian metrics on these higher Teichmüller components and the study of their global geometry.
Members
Andrea Tamburelli
andrea.tamburelli@unipi.it
Collaborators
John Loftin (Rutgers, The State University of New Jersey)
Charles Ouyang (University of Massachusetts, Amherst)
Michael Wolf (Georgia Institute of Technology)
Hyperbolic geometry

The uniformisation of surfaces of Koebe and Poincaré and the geometrisation of 3-manifolds of Thurston and Perelman have shown that every manifold of dimensions 2 and 3 admits a geometric structure (after cutting along some canonical spheres and tori in dimension 3). The prominent role among these geometric structures is played by hyperbolic geometry, that is by far the prevalent
structure. It is also the richest and most studied structure in dimensions 2 and 3.

The deformation spaces of hyperbolic 2- and 3-manifolds are the focus of a vast literature concerning Teichmueller spaces and hyperbolic fillings of open manifolds. Moreover, the topology of hyperbolic 3-manifolds is a central topic in low-dimensional topology. But hyperbolic manifolds are abundant in any dimension, and a major goal is to understand their topology as well as their deformation spaces. To this aim, the members of the research group rely on many techniques, from the decomposition of manifolds into hyperbolic polytopes to the study of the topology of fibrations over the circle, to the investigation of the variety of representations of discrete groups into the Lie group of the isometries of hyperbolic space.

Members
Roberto Frigerio
roberto.frigerio@unipi.it
Bruno Martelli
bruno.martelli@unipi.it
Carlo Petronio
carlo.petronio@unipi.it
Collaborators and Ph.D. students at other institutions
Jacopo Guoyi Chen (SNS, Pisa)
Giovanni Italiano (SNS, Pisa)
Matteo Migliorini (SNS, Pisa)
Leone Slavich (Università degli Studi di Pavia)
Hyperplane arrangements

The group investigates the combinatorial and topological properties of hyperplane arrangements. From such a point of view, we study the theory of Coxeter groups (seen as reflection groups), Artin groups (seen as fundamental groups of the complements of reflection arrangements), and the computation of cohomology groups of the complements of hyperplane arrangements, both in the linear and the toric cases.
To obtain an explicit characterization of the cohomology ring of the complement of a toric arrangement, the group is studying wonderful compactifications of the complements. This approach allows the definition of a certain differential graded algebra, which ‘governs’ the cohomology ring.
At the moment, the group is interested in the following topics:

  • the $K(\pi, 1)$ conjecture for all possible Coxeter groups and the corresponding hyperplane arrangements (for example, the affine simplicial arrangements, which are a natural generalization of the affine reflection arrangements);
  • the study of the so-called dual Coxeter groups, which depend on an element of the group and an interval formed by its divisors;
  • the study of combinatorial properties (such as the shellability property) for intervals as above;
  • the construction of an explicit basis of the integral ring cohomology of complements of toric arrangements and the explicit characterization of the corresponding differential graded algebra in specific examples.
Members
Filippo Gianluca Callegaro
filippo.callegaro@unipi.it
Michele D'Adderio
michele.dadderio@unipi.it
Giovanni Gaiffi
giovanni.gaiffi@unipi.it
Mario Salvetti
mario.salvetti@unipi.it
Collaborators
Emanuele Delucchi (Scuola Universitaria Professionale della Svizzera Italiana (SUPSI))
emanuele.delucchi@supsi.ch
Roberto Pagaria (Università di Bologna)
roberto.pagaria@unibo.it
Giovanni Paolini (California Institute of Technology)
Oscar Papini (ISTI -- CNR)
Viola Siconolfi (Politecnico di Bari)
Lorenzo Venturello (Università degli Studi di Siena)
Low-dimensional topology

This wide research area encompasses several subjects of interest for the research group.
In dimension 2, for example, we investigate the Hurwitz problem concerning the existence of branched covering between surfaces realizing a fixed combinatorial datum. To this aim, one may exploit Grothendieck’s dessins d’enfant, as well as the geometry of spherical, flat, and hyperbolic 2-orbifolds.

In dimension 3 some topics of interest for the group are the Heegaard-Floer homology of rational homology 3-spheres (with particular attention towards possible applications to the L-space conjecture) and the theory of knots and links in the sphere and in general 3-manifolds. A particular interest is devoted to Legendrian links, and to the study of Khovanov homology. 3-manifold topology is also involved in the study of apparent contours of surfaces in 3-space and in general 3-manifolds.

The topology of 4-manifolds is a very active research field, and the group is also interested in this area. Among the topics covered by the group, there are the study of handlebody decompositions of 4-manifolds, Heegaard-Floer homology, and  3-dimensional knot theory from a 4-dimensional viewpoint.

Members
Collaborators and Ph.D. students at other institutions
Alessio Di Prisa (SNS, Pisa)
Alice Merz (Università di Pisa)
alice.merz@phd.unipi.it
Simplicial volume and bounded cohomology

The simplicial volume is a homotopy invariant of manifolds defined by Gromov in 1982. Despite its purely topological definition, it is deeply related to the geometric structures that a manifold can carry.

Thanks to Thurston’s (now proved) Geometrization Conjecture, the simplicial volume of closed 3-manifolds is well understood. Much less is known in higher dimensions, or for open manifolds, and the group is interested in further investigating these research fields (with particular care devoted to aspherical manifolds).

A powerful tool for the computation of the simplicial volume is the so-called bounded cohomology (of groups and of spaces), which is itself a very active research field. Computing the bounded cohomology of groups is very challenging (for example, the problem of whether it vanishes or not for free groups in degrees bigger than 3 is still open), and the research group aims at achieving some progress in this direction, as well as at studying the relationship between bounded cohomology and other related areas like representation theory, group actions on the circle, ergodic theory of groups.

Members
Roberto Frigerio
roberto.frigerio@unipi.it
Bruno Martelli
bruno.martelli@unipi.it
Collaborators and Ph.D. students at other institutions
Giuseppe Bargagnati (Università di Pisa)
giuseppe.bargagnati@phd.unipi.it
Federica Bertolotti (SNS, Pisa)
Michelle Bucher (Université de Genève)
Pietro Capovilla (SNS, Pisa)
Clara Loeh (Universität Regensburg)
clara.loeh@mathematik.uni-regensburg.de
Domenico Marasco (Università di Pisa)
domenico.marasco@phd.unipi.it
Francesco Milizia (SNS, Pisa)
Marco Moraschini (Università di Bologna)
Maria Beatrice Pozzetti (Universität Heidelberg)
Roman Sauer (Karlsruher Institut für Technologie (KIT))
Alessandro Sisto (Heriot-Watt University)

People

Faculty
Name Surname Email Personal Card
Marco Abate marco.abate@unipi.it
Fabrizio Bianchi fabrizio.bianchi@unipi.it
Filippo Gianluca Callegaro filippo.callegaro@unipi.it
Diego Conti diego.conti@unipi.it
Andrea Di Lorenzo andrea.dilorenzo@unipi.it
Filippo Disanto filippo.disanto@unipi.it
Marco Franciosi marco.franciosi@unipi.it
Roberto Frigerio roberto.frigerio@unipi.it
Paolo Lisca paolo.lisca@unipi.it
Sandro Manfredini sandro.manfredini@unipi.it
Bruno Martelli bruno.martelli@unipi.it
Rita Pardini rita.pardini@unipi.it
Gregory James Pearlstein greg.pearlstein@unipi.it
Ekaterina Pervova ekaterina.pervova@unipi.it
Carlo Petronio carlo.petronio@unipi.it
Francesco Sala francesco.sala@unipi.it
Mario Salvetti mario.salvetti@unipi.it
Tamás Szamuely tamas.szamuely@unipi.it
Mattia Talpo mattia.talpo@unipi.it
Andrea Tamburelli andrea.tamburelli@unipi.it
Affiliate Members
Name Surname Email Personal Card
Francesca Acquistapace francesca.acquistapace@unipi.it
Riccardo Benedetti riccardobenedetti53@gmail.com
Fabrizio Broglia broglia@dm.unipi.it
Elisabetta Fortuna elisabetta.fortuna@unipi.it
Fulvio Lazzeri fulvio.lazzeri@unipi.it
Former Members
Name Surname
Fabrizio M. E. Catanese
Postdoctoral Fellows
Name Surname Email Personal Card
Carlo Collari carlo.collari@dm.unipi.it
Filippo Sarti filippo.sarti@dm.unipi.it
Dario Weißmann dario.weissmann@dm.unipi.it
Ph.D. Students at the University of Pisa
Name Surname Email Personal Card
Filippo Bianchi filippo.bianchi@phd.unipi.it
Francesco Conti francesco.conti@phd.unipi.it
Giovanni Framba giovanni.framba@phd.unipi.it
Viola Giovannini v.giovannini1@studenti.unipi.it
Mattia Pirani mattia.pirani@phd.unipi.it
Ph.D. Students at other institutions
Name Surname Affiliation
Federica Bertolotti SNS, Pisa
Pietro Capovilla SNS, Pisa
Jacopo Guoyi Chen SNS, Pisa
Gemma Di Petrillo Università degli Studi di Trento
Alessio Di Prisa SNS, Pisa
Giovanni Italiano SNS, Pisa
Qiangru Kuang SISSA, Trieste
Francesco Milizia SNS, Pisa
Romeo Segnan Dalmasso University of Surrey

Ph.D. Theses supervised by members of the group

awarded by the University of Pisa
Year Name Surname Title of the Thesis Supervisor(s)
2024 Alice Merz Braids, homomorphism defects of link invariants and combinatorial aspects of strongly invertible links Paolo Lisca
2024 Giuseppe Bargagnati Simplicial volume of open manifolds Roberto Frigerio
2023 Andrea Parma Horizontal decompositions and smooth embeddings of rational homology balls Paolo Lisca
2023 Domenico Marasco Efficient cycles for $H^2 \times H^2$ and products in bounded cohomology Roberto Frigerio
2022 Ludovico Battista Hyperbolic 4-manifolds, perfect circle-valued Morse functions and infinitesimal rigidity Bruno Martelli
2021 Chiara Spagnoli The eventual map for irregular varieties Rita Pardini
2021 Leonardo Henrique Caldeira Pires Ferrari Hyperbolic manifolds and coloured polytopes Bruno Martelli
2021 Federico Cesare Giorgio Conti Surfaces close to the Severi lines Rita Pardini
2020 Karim Rakhimov Dynamics of geodesics for meromorphic connections on Riemann surfaces Marco Abate
2018 Kirill Kuzmin Quasi-isometric rigidity for universal covers of manifolds with a geometric decomposition Roberto Frigerio
2018 Marco Moraschini On Gromov’s theory of multicomplexes: the original approach to bounded cohomology and simplicial volume Roberto Frigerio
2017 Stefano Riolo Cone-manifolds and hyperbolic surgeries Bruno Martelli
2016 Fabrizio Bianchi Motions of Julia sets and dynamical stability in several complex variables Marco Abate and François Berteloot
2016 Federico Franceschini Simplicial volume and relative bounded cohomology Roberto Frigerio
2016 Alessio Carrega Shadows and quantum invariants Bruno Martelli
2015 Matteo Serventi Combinatorial and geometric invariants of configuration spaces Giovanni Gaiffi and Mario Salvetti
2012 Cristina Pagliantini Relative (continuous) bounded cohomology and simplicial volume of hyperbolic manifolds with geodesic boundary Roberto Frigerio
2011 Isaia Nisoli A general approach to Lehmann-Suwa-Khanedani index theorems: partial holomorphic connections and extensions of foliations Marco Abate
2011 Fionntan Roukema Dehn surgery on the minimally twisted five-chain link Bruno Martelli and Carlo Petronio
2010 Tiziano Casavecchia Rigidity of holomorphic generators of one-parameter semigroups and a non-autonomous Denjoy-Wolff theorem Marco Abate
2010 Ana Garcia Lecuona On the slice-ribbon conjecture for Montesinos knots Paolo Lisca
2010 Francesca Mori Minimality of hyperplane arrangements and configuration spaces: a combinatorial approach Mario Salvetti
2010 Jasmin Raissy Geometrical methods in the normalization of germs of biholomorphisms Marco Abate
2009 Kartoué Mady Demdah Théorèmes de h-cobordisme et de s-cobordisme semi-algébriques Fabrizio Broglia and Michel Coste
2004 Gennaro Amendola Minimal spines and skeleta of non-orientable 3-manifolds and bricks Carlo Petronio
2003 Simona Settepanella Cohomologies of generalized pure braid groups and Milnor fibre of reflection arrangements Mario Salvetti
2000 Claudia Landi Cohomology rings of Artin groups Mario Salvetti
1999 Silvia Benvenuti Hops algebras and invariants of combed and framed 3-manifolds Riccardo Benedetti
1995 Francesco Zucconi Su alcune questioni relative alla applicazione canonica composta con un fascio di grado 3 Fabrizio M. E. Catanese
1993 Gianfranco Casnati Rivestimenti ramificati di Gorenstein Fabrizio M. E. Catanese
1993 Marco Franciosi Immersioni di superficie razionali Fabrizio M. E. Catanese
1993 Francesca Tovena Alcune applicazioni geometriche della teoria dei fibrati stabili Fabrizio M. E. Catanese
1992 Domenico Luminati Immersions of surfaces and apparent contours Riccardo Benedetti
1991 Sandro Manfredini Geometria delle applicazioni polinomiali complesse in una variabile Fabrizio M. E. Catanese
1987 Francesco Capocasa Teoria delle funzioni meromorfe sui quasi-tori Fabrizio M. E. Catanese
awarded by another institution
Year Name Surname Title of the Thesis Institution Supervisor(s)
2023 Matteo Migliorini Bestvina-Brady Morse theory on hyperbolic manifolds SNS, Pisa Bruno Martelli
2023 Diego Santoro L-spaces and taut foliations on 3-manifolds SNS, Pisa Paolo Lisca and Bruno Martelli
2023 Nicholas Rungi Pseudo-Kähler geometry of Hitchin representations and convex projective structures SISSA, Trieste Andrea Tamburelli
2020 Edoardo Fossati Symplectic fillings of virtually overtwisted contact structures on lens spaces SNS, Pisa Paolo Lisca
2020 Giulio Belletti Asymptotic behavior of quantum invariants SNS, Pisa Bruno Martelli and Francesco Costantino
2019 Roberto Pagaria Cohomology and Combinatorics of Toric Arrangements SNS, Pisa Filippo Gianluca Callegaro
2017 Carlo Collari Transverse and concordance invariants from Khovanov sl(2) and sl(3) homologies Università degli Studi di Firenze Paolo Lisca
2016 Daniele Celoria Grid homology in lens spaces Università degli Studi di Firenze Paolo Lisca
2015 Paolo Aceto Rational homology cobordisms of plumbed manifolds and arborescent link concordance Università degli Studi di Firenze Paolo Lisca
2014 Leone Slavich Hyperbolic 4-manifolds and 24-cells Università degli Studi di Firenze Bruno Martelli
2013 Valentina Disarlo Combinatorial methods in Teichmüller theory SNS, Pisa Carlo Petronio and Athanase Papadopoulos
2012 Michele Tocchet Generalized Mom-structures and volume estimates for hyperbolic 3-manifolds with geodesic boundary and toric cusps Sapienza Università di Roma Carlo Petronio and Ekaterina Pervova
2011 Matteo Ruggiero The valuative tree, rigid germs and Kato varieties SNS, Pisa Marco Abate
2011 Vito Sasso Complexity of unitrivalent graph-pairs and knots in 3-manifolds Università degli Studi di Roma Tor Vergata Carlo Petronio and Ekaterina Pervova
2010 Maria Antonietta Pascali Branched covers between surfaces Sapienza Università di Roma Carlo Petronio
2007 Daniele Alessandrini SNS, Pisa Riccardo Benedetti
2005 Roberto Frigerio Deforming triangulations of hyperbolic 3-manifolds with geodesic boundary SNS, Pisa Carlo Petronio
2005 Francesco Bonsante Deforming the Minkowskian cone of a closed hyperbolic manifold SNS, Pisa Riccardo Benedetti
2004 Paolo Ghiggini Classification of Tight Contact Structures on Some Seifert Manifolds SNS, Pisa Paolo Lisca
2004 Francesco Costantino Shadows and branched shadows of 3 and 4-manifolds SNS, Pisa Riccardo Benedetti
2004 Stefano Francaviglia Hyperbolicity equations for cusped 3-manifolds and volume-rigidity of representations SNS, Pisa Carlo Petronio
2002 Bruno Martelli Complexity of three-manifolds Università degli Studi di Firenze Carlo Petronio
1995 Carlo Petronio Standard spines and 3-manifolds SNS, Pisa Riccardo Benedetti
1995 Marco Manetti Degenerations of Algebraic Surfaces and applications to Moduli problems SNS, Pisa Fabrizio M. E. Catanese
1992 Alessio Corti Families of Del Pezzo Surfaces University of Utah Fabrizio M. E. Catanese and János Kollár
1990 Rita Pardini SNS, Pisa Fabrizio M. E. Catanese

Grants

Current
Past

Visitors

Prospective
First Name Last Name Affiliation
Andrei Neguţ Massachusetts Institute of Technology (MIT)
Peter Smillie Universität Heidelberg
Current
First Name Last Name Affiliation Building Floor Office
Kenneth L. Baker University of Miami Building A First floor 317
Ciro Ciliberto Università degli Studi di Roma Tor Vergata Building A First floor 215
Grouped by year
2024
First Name Last Name Affiliation From To
Kenneth L. Baker University of Miami Aug 01, 2023 Jul 31, 2024
Keegan Boyle University of British Columbia Mar 20, 2024 Mar 25, 2024
Michael Brandenbursky Ben Gurion University of the Negev Apr 10, 2024 Apr 13, 2024
Ciro Ciliberto Università degli Studi di Roma Tor Vergata Apr 16, 2024 Apr 19, 2024
Alessio D'Alì Politecnico di Milano Mar 26, 2024 Mar 28, 2024
Emanuele Delucchi Scuola Universitaria Professionale della Svizzera Italiana (SUPSI) Jan 09, 2024 Jan 12, 2024
Barbara Fantechi SISSA, Trieste Mar 11, 2024 Mar 15, 2024
Concettina Galati Università della Calabria Mar 11, 2024 Mar 15, 2024
Marco Golla Université de Nantes Apr 14, 2024 Apr 16, 2024
Christopher Hacon University of Utah Feb 17, 2024 Feb 24, 2024
Ariyan Javanpeykar Radboud University Nijmegen Mar 18, 2024 Mar 21, 2024
Marc Levine Universität Duisburg-Essen Feb 18, 2024 Feb 20, 2024
Clara Loeh Universität Regensburg Mar 19, 2024 Mar 21, 2024
Andrei Neguţ Massachusetts Institute of Technology (MIT) May 08, 2024 May 12, 2024
Roberto Pignatelli Università degli Studi di Trento Apr 02, 2024 Apr 06, 2024
Diego Santoro Universität Wien Mar 17, 2024 Mar 22, 2024
Luca Schaffler Università degli Studi Roma Tre Apr 02, 2024 Apr 06, 2024
Tanushree Shah Universität Wien Mar 26, 2024 Mar 28, 2024
Peter Smillie Universität Heidelberg May 09, 2024 May 10, 2024
2023
First Name Last Name Affiliation From To
Paolo Aceto Université de Lille Sep 03, 2023 Sep 06, 2023
Antonio Alfieri Université du Quebec à Montréal (UQAM) Apr 01, 2023 Apr 13, 2023
Giuseppe Ancona Université de Strasbourg Feb 22, 2023 Feb 24, 2023
Younghan Bae ETH Zürich Dec 05, 2023 Dec 07, 2023
Valentina Bais SISSA, Trieste Nov 21, 2023 Nov 23, 2023
Kenneth L. Baker University of Miami Aug 01, 2023 Jul 31, 2024
Bruno Benedetti University of Miami May 31, 2023 May 31, 2023
Patrick Brosnan University of Maryland Jun 05, 2023 Jun 30, 2023
Margot Bruneaux Université Claude Bernard Lyon 1 Nov 06, 2023 Nov 10, 2023
Dylan Butson University of Oxford Nov 14, 2023 Nov 18, 2023
Léo Bénard Georg-August-Universität Göttingen Apr 18, 2023 Apr 24, 2023
Luigi Caputi Università di Torino Jun 26, 2023 Jul 01, 2023
Francesca Carocci Université de Genève Nov 21, 2023 Nov 23, 2023
Cinzia Casagrande Università di Torino Mar 22, 2023 Mar 22, 2023
Nicola Cavallucci Karlsruher Institut für Technologie (KIT) Sep 04, 2023 Sep 06, 2023
Corrado De Concini Sapienza Università di Roma Mar 24, 2023 Mar 25, 2023
Marco De Renzi Université de Montpellier Dec 20, 2023 Dec 22, 2023
Emanuele Delucchi Scuola Universitaria Professionale della Svizzera Italiana (SUPSI) Jan 12, 2023 Jan 22, 2023
Emanuele Delucchi Scuola Universitaria Professionale della Svizzera Italiana (SUPSI) Jun 20, 2023 Jun 24, 2023
Donatella Donatelli Università degli Studi dell'Aquila Sep 03, 2023 Sep 09, 2023
Charles Doran Bard College Jun 16, 2023 Jun 18, 2023
Bruno Drieux École Polytechnique Apr 03, 2023 Jul 21, 2023
Federica Fanoni CNRS Sep 03, 2023 Sep 06, 2023
Alejandro Gil Garcìa Universität Hamburg May 10, 2023 May 15, 2023
Viola Giovannini University of Luxembourg Mar 17, 2023 Mar 21, 2023
Souvnik Goswami Universitat Autònoma de Barcelona Jul 08, 2023 Jul 15, 2023
Souvnik Goswami Universitat Autònoma de Barcelona Oct 24, 2023 Oct 26, 2023
Lars Halle Università di Bologna Mar 28, 2023 Mar 29, 2023
Leo Herr Leiden University Nov 14, 2023 Nov 17, 2023
Hyeonhee Jin Max-Planck-Institut für Mathematik - Bonn Feb 12, 2023 Feb 15, 2023
Qiangru Kuang SISSA, Trieste Apr 16, 2023 Apr 21, 2023
Lukas Lewark Universität Regensburg Feb 26, 2023 Mar 03, 2023
Claudio Llosa Inserich Karlsruher Institut für Technologie (KIT) May 02, 2023 May 04, 2023
Andrew Lobb Durham University May 31, 2023 Jun 02, 2023
Oliviero Malech SISSA, Trieste Nov 14, 2023 Nov 16, 2023
Mirko Mauri IST Austria Jun 07, 2023 Jun 08, 2023
Enrica Mazzon Universität Regensburg Jun 07, 2023 Jun 08, 2023
Sergej Monavari École Polytechnique Fédérale de Lausanne (EPFL) Nov 07, 2023 Nov 09, 2023
Marco Moraschini Università di Bologna Sep 03, 2023 Sep 05, 2023
Christopher Nicol École Polytechnique Mar 20, 2023 Jul 28, 2023
Leonardo Patimo Albert-Ludwigs-Universität Freiburg Apr 13, 2023 Apr 13, 2023
Bram Petri Sorbonne Université Mar 29, 2023 Mar 31, 2023
Mauro Porta Université de Strasbourg Apr 02, 2023 Apr 16, 2023
Arunima Ray Max-Planck-Institut für Mathematik - Bonn Jun 07, 2023 Jun 09, 2023
Jules Ribolzi École Normale Supérieure de Lyon May 02, 2023 Aug 02, 2023
Luca Schaffler Università degli Studi Roma Tre Jun 26, 2023 Jun 30, 2023
Olivier Schiffmann CNRS, Université de Paris-Saclay Apr 01, 2023 May 01, 2023
Jakob Scholbach Università di Padova Nov 15, 2023 Nov 16, 2023
Alessandro Sisto Heriot-Watt University Feb 28, 2023 Mar 03, 2023
Vera Vertési Universität Wien Oct 19, 2023 Oct 21, 2023
Gabriele Viaggi Universität Heidelberg May 17, 2023 May 18, 2023
Campbell Wheeler Max-Planck-Institut für Mathematik - Bonn Mar 27, 2023 Mar 29, 2023
Thomas Wiehe Universität zu Köln Dec 11, 2023 Dec 13, 2023
Thomas Wiehe Universität zu Köln Dec 11, 2023 Dec 13, 2023
Raphael Zentner Durham University Apr 12, 2023 Apr 14, 2023
Refik İnanç Baykur University of Massachusetts, Amherst May 10, 2023 May 12, 2023
2022
First Name Last Name Affiliation From To
Federico Binda Università degli Studi di Milano (La Statale) Nov 16, 2022 Nov 17, 2022
Sam DeHority Columbia University Oct 04, 2022 Oct 08, 2022
Jerónimo García Mejía Karlsruher Institut für Technologie (KIT) Oct 04, 2022 Oct 04, 2022
Philippe Gille Université Claude Bernard Lyon 1 Oct 24, 2022 Oct 30, 2022
Antonella Grassi Università di Bologna Nov 29, 2022 Dec 01, 2022
Adam Gyenge Budapest University of Technology and Economics Oct 19, 2022 Oct 21, 2022
David Harari Université de Paris-Saclay Nov 07, 2022 Nov 12, 2022
James Lewis University of Alberta Nov 26, 2022 Dec 05, 2022
Agnese Mantione Universität Münster Nov 22, 2022 Dec 22, 2022
Mauro Porta Université de Strasbourg May 07, 2022 Jun 08, 2022
Andrea Tobia Ricolfi SISSA, Trieste Nov 23, 2022 Nov 23, 2022
Bernd Siebert University of Texas at Austin Jul 05, 2022 Jul 07, 2022
Richard Thomas Imperial College London Jul 05, 2022 Jul 07, 2022
Rodolfo Verenucci Università degli Studi di Milano (La Statale) Nov 16, 2022 Nov 17, 2022
Alberto Vezzani Università degli Studi di Milano (La Statale) Nov 16, 2022 Nov 17, 2022

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