{"id":49,"date":"2022-03-16T22:31:48","date_gmt":"2022-03-16T22:31:48","guid":{"rendered":"https:\/\/www.dm.unipi.it\/research\/algebra-mat-02-2\/"},"modified":"2026-01-23T10:08:09","modified_gmt":"2026-01-23T09:08:09","slug":"algebra","status":"publish","type":"page","link":"https:\/\/www.dm.unipi.it\/research\/areas\/algebra\/","title":{"rendered":"Algebra"},"content":{"rendered":"\n

The scientific activities of the group are focused on different aspects of number theory and representation theory, with ramifications and applications in Lie theory and algebraic combinatorics.<\/p>\n\n\n\n

The group runs the Seminar on Combinatorics, Lie Theory, and Topology<\/a>.<\/p>\n\n\n\n

<\/div>\n\n\n\n

Research Topics<\/h4>\n\n\n\n
Algebraic combinatorics<\/h5>
\n

Algebraic combinatorics studies mainly discrete structures that occur in algebraic problems. Our research focuses on combinatorics arising from representation theory. More specifically, in recent years we studied $q,t$-combinatorics arising from Macdonald polynomials, plethystic operators on symmetric functions, and diagonal coinvariants.<\/p>\n\n\n\n

Members<\/h6>
\n\n\n
\n
\n
\n<\/i><\/a>\n\nMichele D'Adderio\n\n<\/span>
\n<\/i>michele.dadderio@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i><\/a>\n\nLuis Ferroni\n\n<\/span>
\n<\/i>luis.ferroni@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i><\/a>\n\nLeonardo Patimo\n\n<\/span>
\n<\/i>leonardo.patimo@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n
Collaborators<\/h6>
\n\n\n
\n
\n
\n<\/i>\n\nHoucine Ben Dali (Harvard University)\n\n<\/span>
\n<\/i>bendali@math.harvard.edu<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nMark Dukes (University College Dublin)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nGiovanni Interdonato (SNS, Pisa)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nAlexander Lazar (Universit\u00e9 libre de Bruxelles)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nYvan Le Borgne (Universit\u00e9 de Bordeaux)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nAnton Mellit (Universit\u00e4t Wien)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i><\/a>\n\nVassilis Dionyssis Moustakas (Universit\u00e0 di Pisa)\n\n<\/span>
\n<\/i>vasileios.moustakas@dm.unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nMenghao Qu (SNS, Pisa)\n\n<\/span>
\n<\/i>menghao.qu@sns.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nRoberto Riccardi (SNS, Pisa)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nMarino Romero (Universit\u00e4t Wien)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nViola Siconolfi (Politecnico di Bari)\n\n<\/span>
\n<\/i>viola.siconolfi@poliba.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nAnna Vanden Wyngaerd (Universit\u00e9 libre de Bruxelles)\n\n<\/span>
\n<\/i>anna.vanden.wyngaerd@ulb.be<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n
Arithmetic geometry and number theory<\/h5>
\n

Number theory studies arithmetic problems by using tools from different areas of mathematics. Our research focuses on arithmetically relevant actions of Galois groups on algebro-geometric objects (such as number rings and their class groups, or abelian varieties and their Selmer groups). Via Iwasawa theory, algebraic invariants of such actions can sometimes be related to analytic objects (L-functions).<\/p>\n\n\n\n

Members<\/h6>
\n\n\n
\n
\n
\n<\/i><\/a>\n\nAndrea Bandini\n\n<\/span>
\n<\/i>andrea.bandini@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i><\/a>\n\nGiulio Bresciani\n\n<\/span>
\n<\/i>giulio.bresciani1@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i><\/a>\n\nIlaria Del Corso\n\n<\/span>
\n<\/i>ilaria.delcorso@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i><\/a>\n\nDavide Lombardo\n\n<\/span>
\n<\/i>davide.lombardo@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n
<\/div>\n\n\n\n

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.<\/p>\n\n\n\n

Arithmetic of abelian varieties<\/h5>
\n

Elliptic curves and higher-dimensional abelian varieties are fundamental objects of study in number theory. Our investigations focus mainly on their Galois representations, especially over number fields, in the spirit of the Mumford-Tate and Sato-Tate conjectures. We consider in particular the possible existence of nontrivial endomorphisms on a given abelian variety (with special attention given to the case of Jacobians), with implications for the arithmetic of low-genus curves. We also work on related problems, including the determination of rational points on curves and the study of torsion cosets in subvarieties of algebraic groups.<\/p>\n\n\n\n

Members<\/h6>
\n\n\n
\n
\n
\n<\/i><\/a>\n\nDavide Lombardo\n\n<\/span>
\n<\/i>davide.lombardo@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i><\/a>\n\nLuca Mauri\n\n<\/span>
\n<\/i>luca.mauri@phd.unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n
Collaborators<\/h6>
\n\n\n
\n
\n
\n<\/i><\/a>\n\nLorenzo Furio (Sorbonne Universit\u00e9)\n\n<\/span>
\n<\/i>lorenzo.furio@imj-prg.fr<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nAndrea Gallese (SNS, Pisa)\n\n<\/span>
\n<\/i>andrea.gallese@sns.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nSachi Hashimoto (Brown University)\n\n<\/span>
\n<\/i>sachi_hashimoto@brown.edu<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nSamuel Le Fourn (Universit\u00e9 Grenoble Alpes)\n\n<\/span>
\n<\/i>Samuel.Le-Fourn@univ-grenoble-alpes.fr<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nGuido Lido (Universit\u00e0 degli Studi di Roma Tor Vergata)\n\n<\/span>
\n<\/i>guidomaria.lido@uniroma2.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nNicolas Mascot (Trinity College Dublin)\n\n<\/span>
\n<\/i>mascotn@maths.tcd.ie<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nFrancesco Veneziano (Universit\u00e0 di Genova)\n\n<\/span>
\n<\/i>francesco.veneziano@unige.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nJohn Voight (University of Sidney)\n\n<\/span>
\n<\/i>john.voight@sydney.edu.au<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nUmberto Zannier (SNS, Pisa)\n\n<\/span>
\n<\/i>umberto.zannier@sns.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n
Fundamental groups, arithmetic geometry and stacks<\/h5>
\n

There is a deep connection between fundamental groups and rational solutions of polynomial equations. This was first clearly identified by A. Grothendieck in his “anabelian” program, though its roots go back at least to E. Galois. <\/p>\n\n\n\n

In order to study it, we blend several techniques, old and new: classical algebraic geometry, p-adic geometry, algebraic topology, cohomology, and stacks.<\/p>\n\n\n\n

Our approach is characterized by the application of the stacky formalism to questions in arithmetic geometry. With this approach, we also study minimal fields of definition of varieties, non-abelian cohomology, Brauer groups, singularities.<\/p>\n\n\n\n

Members<\/h6>
\n\n\n
\n
\n
\n<\/i><\/a>\n\nGiulio Bresciani\n\n<\/span>
\n<\/i>giulio.bresciani1@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n
Collaborators<\/h6>
\n\n\n
\n
\n
\n<\/i>\n\nAngelo Vistoli (SNS, Pisa)\n\n<\/span>
\n<\/i>angelo.vistoli@sns.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nTianzhi Yang (SNS, Pisa)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n
(Hopf) Galois module theory and skew braces<\/h5>
\n

Hopf-Galois module theory is a generalisation of Galois module theory, where the action of a Galois group is replaced by that of a $K$-Hopf algebra. This generalisation is fruitful both for enlarging the set of extensions under consideration and for better describing wild extensions. We work on questions in both these settings.
The Hopf-Galois structures on a $G$-Galois field extension are in one-to-one correspondence with suitable subgroups of the permutation group on $G$, and are closely connected with skew braces. The focus of our research is both on the classification of Hopf-Galois structures and on the study of the properties of the skew braces as well as their equivalent from the Hopf-Galois point of view.
We are also employing the language and the properties of the braces in the study of some problems of commutative algebra.<\/p>\n\n\n\n

Members<\/h6>
\n\n\n
\n
\n
\n<\/i><\/a>\n\nIlaria Del Corso\n\n<\/span>
\n<\/i>ilaria.delcorso@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i><\/a>\n\nDavide Lombardo\n\n<\/span>
\n<\/i>davide.lombardo@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n
Collaborators<\/h6>
\n\n\n
\n
\n
\n<\/i>\n\nElena Campedel (Universit\u00e0 degli Studi di Milano-Bicocca)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nAndrea Caranti (Universit\u00e0 degli Studi di Trento)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nFabio Ferri (University of Exeter)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i><\/a>\n\nLorenzo Stefanello (Universit\u00e0 di Pisa)\n\n<\/span>
\n<\/i>lorenzo.stefanello@phd.unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nSenne Trappeniers (Vrije Universiteit Brussel)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nPaul Truman (Keele University)\n\n<\/span>
\n<\/i>p.j.truman@keele.ac.uk<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n
Iwasawa theory and Drinfeld modular forms<\/h5>
\n

Iwasawa theory studies modules (like class groups and Selmer groups) associated to global fields and abelian varieties in all characteristics, in an attempt to link algebraic invariants (like orders of class groups and ranks of elliptic curves) to analytic ones (i.e. special values of $L$-functions).
The study of Drinfeld modular forms is currently focused on their structure in an attempt to define old forms and new forms, and on their slopes with respect to the action of the Hecke algebra. The main goal is to establish an analog of Hida theory for function fields.<\/p>\n\n\n\n

Members<\/h6>
\n\n\n
\n
\n
\n<\/i><\/a>\n\nAndrea Bandini\n\n<\/span>
\n<\/i>andrea.bandini@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n
Collaborators<\/h6>
\n\n\n
\n
\n
\n<\/i>\n\nFrancesc Bars (Universitat Aut\u00f2noma de Barcelona)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nIgnazio Longhi (Universit\u00e0 di Torino)\n\n<\/span>
\n<\/i>ignazio.longhi@unito.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nMaria Valentino (Universit\u00e0 della Calabria)\n\n<\/span>
\n<\/i>maria.valentino@unical.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nStefano Vigni (Universit\u00e0 di Genova)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n
Lie theory<\/h5>
\n
Members<\/h6>
\n\n\n
\n
\n
\n<\/i><\/a>\n\nGiovanni Gaiffi\n\n<\/span>
\n<\/i>giovanni.gaiffi@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i><\/a>\n\nDavide Lombardo\n\n<\/span>
\n<\/i>davide.lombardo@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i><\/a>\n\nAndrea Maffei\n\n<\/span>
\n<\/i>andrea.maffei@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i><\/a>\n\nLeonardo Patimo\n\n<\/span>
\n<\/i>leonardo.patimo@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i><\/a>\n\nFrancesco Sala\n\n<\/span>
\n<\/i>francesco.sala@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n
<\/div>\n\n\n\n

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.<\/p>\n\n\n\n

Opers on the punctured disc<\/h5>
\n

Frenkel and Gaitsgory proposed a version of the Langlands correspondence in the case of the field $\\mathbb{C}((t))$. Given a quasi-simple group $G$ such a proposal relates the geometry of the space of $G$ connections on the disk with a singularity in the origin and representations of the Langlands dual group of $G$. The tool that allows one to build a bridge between these objects is the Feigin-Frenkel theorem which describes the center of the enveloping algebra of an affine Lie algebra at the critical level as the functions on a space of connections for the dual algebra, called the space of Opers, introduced by Beilinson and Drinfeld. In this theory, vertex algebras play a key role in both the proof of the Feigin-Frenkel theorem and the development of the theory of Frenkel and Gaitsgory.<\/p>\n\n\n\n

The local geometric correspondence is largely conjectural, but in the case of “spherical” representations, which corresponds to the case of monodromy-free connections, Frenkel and Gaitsgory gave complete proof.<\/p>\n\n\n\n

We are studying a version of this correspondence in the case of families of connections on the disk with two singular points $0$ and $a$. In this case, we consider an analogue of the affine algebra, which we denote by $\\mathfrak{g}(2)$, on the ring $\\mathbb{C}[[a]]$. In the case $\\mathfrak{g}=\\mathfrak{sl}_2$ we were able to construct a family of elements that generalize Sugawara operators and generate the center of the enveloping algebra of $\\mathfrak{g}(2)$ at the critical level. We have also provided a description of endomorphisms of a Weyl module similar to the one given by Frenkel and Gaitsgory in the usual case. We intend to continue the study started with this work by extending the results in various directions.<\/p>\n\n\n\n

Members<\/h6>
\n\n\n
\n
\n
\n<\/i><\/a>\n\nDavide Lombardo\n\n<\/span>
\n<\/i>davide.lombardo@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i><\/a>\n\nAndrea Maffei\n\n<\/span>
\n<\/i>andrea.maffei@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n
Collaborators and Ph.D. students at other institutions<\/h6>
\n\n\n
\n
\n
\n<\/i>\n\nLuca Casarin (Sapienza Universit\u00e0 di Roma)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nAlberto De Sole (Sapienza Universit\u00e0 di Roma)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nGiorgia Fortuna (Reply)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nValerio Melani (Universit\u00e0 degli Studi di Firenze)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n
Quantum groups and Hall algebras<\/h5>
\n

Quantum groups<\/em> capture the ‘hidden symmetries’ of quantum physics that emerge through integrability. Their geometric interpretation has been remarkably fruitful across diverse domains \u2014 from representation theory, through the study of Maulik\u2013Okounkov Yangians, to the geometry of moduli stacks and spaces, where it underlies results such as the proof of the P = W conjecture in non-abelian Hodge theory, and to applications in gauge and string theories.
Our group investigates quantum groups via their geometric realizations, with a particular focus on Hall algebras and their refined forms \u2014 cohomological, K-theoretic, and categorified \u2014 arising from the geometry of moduli stacks of coherent sheaves on curves and surfaces.<\/p>\n\n\n\n

The group has organized several activities, such as the Summer School on “Enumerative Geometry and Geometric Representation Theory”<\/a> in June and July 2025.<\/p>\n\n\n\n

Members<\/h6>
\n\n\n
\n
\n
\n<\/i><\/a>\n\nFrancesco Sala\n\n<\/span>
\n<\/i>francesco.sala@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i><\/a>\n\nZiwei Wei\n\n<\/span>
\n<\/i>ziwei.wei@phd.unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n
Collaborators<\/h6>
\n\n\n
\n
\n
\n<\/i>\n\nDuiliu-Emanuel Diaconescu (Rutgers, The State University of New Jersey)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nLuca Morstabilini (SISSA, Trieste)\n\n<\/span>
\n<\/i>lmorstab@sissa.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nMauro Porta (Universit\u00e9 de Strasbourg)\n\n<\/span>
\n<\/i>porta@math.unistra.fr<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nOlivier Schiffmann (CNRS, Universit\u00e9 de Paris-Saclay)\n\n<\/span>
\n<\/i>olivier.schiffmann@universite-paris-saclay.fr<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n
Symmetric and spherical varieties<\/h5>
\n

If $G$ is a reductive group and $H$ is the subgroup of points fixed under an involution then $G\/H$ is called a symmetric variety<\/em>. They have been extensively studied in relation to problems coming from representation theory or algebraic geometry and in particular enumerative geometry. Symmetric varieties are a particular case of spherical varieties: normal $G$ variety with a finite number of $B$ orbits. The classification of spherical varieties has been obtained recently. We study different aspects of symmetric and spherical varieties: compactifications, description of the coordinate ring, applications to the study of normality of particular classes of $G$ variety important in representation theory.
An important theme is a study of the classification of $B$ orbits in these varieties and their Bruhat order.<\/p>\n\n\n\n

Members<\/h6>
\n\n\n
\n
\n
\n<\/i><\/a>\n\nAndrea Maffei\n\n<\/span>
\n<\/i>andrea.maffei@unipi.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n
Collaborators<\/h6>
\n\n\n
\n
\n
\n<\/i>\n\nRocco Chiriv\u00ec (Universit\u00e0 del Salento)\n\n<\/span>
\n<\/i>rocco.chirivi@unisalento.it<\/a>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nJacopo Gandini (Universit\u00e0 di Bologna)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nPierluigi Moseneder (Politecnico di Milano)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n<\/i>\n\nPaolo Papi (Sapienza Universit\u00e0 di Roma)\n\n<\/span>
\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n
<\/div>\n\n\n\n

People<\/h4>\n\n\n\n
Faculty<\/h5>
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Name<\/th>\nSurname<\/th>\nEmail<\/th>\nPersonal Card<\/th>\n<\/tr><\/thead>
Andrea<\/td>\nBandini<\/td>\n<\/i>andrea.bandini@unipi.it<\/span><\/a><\/td>\n<\/i><\/a><\/td>\n<\/tr>\n
Giulio<\/td>\nBresciani<\/td>\n<\/i>giulio.bresciani1@unipi.it<\/span><\/a><\/td>\n<\/i><\/a><\/td>\n<\/tr>\n
Massimo<\/td>\nCaboara<\/td>\n<\/i>massimo.caboara@unipi.it<\/span><\/a><\/td>\n<\/i><\/a><\/td>\n<\/tr>\n
Michele<\/td>\nD'Adderio<\/td>\n<\/i>michele.dadderio@unipi.it<\/span><\/a><\/td>\n<\/i><\/a><\/td>\n<\/tr>\n
Ilaria<\/td>\nDel Corso<\/td>\n<\/i>ilaria.delcorso@unipi.it<\/span><\/a><\/td>\n<\/i><\/a><\/td>\n<\/tr>\n
Giovanni<\/td>\nGaiffi<\/td>\n<\/i>giovanni.gaiffi@unipi.it<\/span><\/a><\/td>\n<\/i><\/a><\/td>\n<\/tr>\n
Davide<\/td>\nLombardo<\/td>\n<\/i>davide.lombardo@unipi.it<\/span><\/a><\/td>\n<\/i><\/a><\/td>\n<\/tr>\n
Andrea<\/td>\nMaffei<\/td>\n<\/i>andrea.maffei@unipi.it<\/span><\/a><\/td>\n<\/i><\/a><\/td>\n<\/tr>\n
Leonardo<\/td>\nPatimo<\/td>\n<\/i>leonardo.patimo@unipi.it<\/span><\/a><\/td>\n<\/i><\/a><\/td>\n<\/tr>\n
Enrico<\/td>\nSbarra<\/td>\n<\/i>enrico.sbarra@unipi.it<\/span><\/a><\/td>\n<\/i><\/a><\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n\n\n\n
Affiliate Members<\/h5>
\n\n\n\n\n\n\n
Name<\/th>\nSurname<\/th>\nEmail<\/th>\nPersonal Card<\/th>\n<\/tr><\/thead>
Roberto<\/td>\nDvornicich<\/td>\n<\/i>roberto.dvornicich@gmail.com<\/span><\/a><\/td>\n<\/i><\/a><\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n\n\n\n
Former Members<\/h5>
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there is no data<\/p>\n<\/div><\/div>\n\n\n\n

Postdoctoral Fellows<\/h5>
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there is no data<\/p>\n<\/div><\/div>\n\n\n\n

Ph.D. Students at the University of Pisa<\/h5>
\n\n\n\n\n\n\n\n
Name<\/th>\nSurname<\/th>\nEmail<\/th>\nPersonal Card<\/th>\n<\/tr><\/thead>
Domenico<\/td>\nMarino<\/td>\n<\/i>domenico.marino@phd.unipi.it<\/span><\/a><\/td>\n<\/i><\/a><\/td>\n<\/tr>\n
Luca<\/td>\nMauri<\/td>\n<\/i>luca.mauri@phd.unipi.it<\/span><\/a><\/td>\n<\/i><\/a><\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n\n\n\n
Ph.D. Students at other institutions<\/h5>
\n\n\n\n\n\n\n\n\n\n\n\n
Name<\/th>\nSurname<\/th>\nAffiliation<\/th>\n<\/tr><\/thead>
Andrea<\/td>\nGallese<\/td>\nSNS, Pisa<\/td>\n<\/tr>\n
Giovanni<\/td>\nInterdonato<\/td>\nSNS, Pisa<\/td>\n<\/tr>\n
Menghao<\/td>\nQu<\/td>\nSNS, Pisa<\/td>\n<\/tr>\n
Roberto<\/td>\nRiccardi<\/td>\nSNS, Pisa<\/td>\n<\/tr>\n
Veran<\/td>\nStojanovic<\/td>\nSNS, Pisa<\/td>\n<\/tr>\n
Tianzhi<\/td>\nYang<\/td>\nSNS, Pisa<\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n\n\n\n
<\/div>\n\n\n\n

Ph.D. Theses supervised by members of the group<\/h4>\n\n\n\n
awarded by the University of Pisa<\/h5>
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Year<\/th>\nName<\/th>\nSurname<\/th>\nTitle of the Thesis<\/th>\n Supervisor(s)<\/th>\n<\/tr><\/thead>
2025<\/td>\nLorenzo<\/td>\nFurio<\/td>\nGalois Representations Attached to Elliptic Curves: around Serre\u2019s Uniformity Question<\/td>\nDavide Lombardo<\/a><\/td>\n<\/tr>\n
2024<\/td>\nLorenzo<\/td>\nStefanello<\/td>\nHopf-Galois structures, skew braces, and their connection<\/td>\nIlaria Del Corso<\/a> and Paul Truman<\/td>\n<\/tr>\n
2022<\/td>\nMichele<\/td>\nCarmassi<\/td>\nThe B-orbits on a Hermitian symmetric variety: the characteristic 2 case and the Bruhat G-order<\/td>\nAndrea Maffei<\/a><\/td>\n<\/tr>\n
2021<\/td>\nMatteo<\/td>\nVerzobio<\/td>\nPrimitive divisors of elliptic divisibility sequences<\/td>\nRoberto Dvornicich<\/a><\/td>\n<\/tr>\n
2020<\/td>\nAlessio<\/td>\nMoscariello<\/td>\nLacunary polynomials and compositions<\/td>\nRoberto Dvornicich<\/a> and Umberto Zannier<\/td>\n<\/tr>\n
2019<\/td>\nAlessandro<\/td>\nIraci<\/td>\nMacdonald polynomials and the Delta conjecture<\/td>\nMichele D'Adderio<\/a> and Giovanni Gaiffi<\/a><\/td>\n<\/tr>\n
2018<\/td>\nOscar<\/td>\nPapini<\/td>\nComputational Aspects of Line and Toric Arrangements<\/td>\nGiovanni Gaiffi<\/a> and Mario Salvetti<\/a><\/td>\n<\/tr>\n
2016<\/td>\nMaria Rosaria<\/td>\nPati<\/td>\nExtensions of p-power degree of a p-adic field<\/td>\nRoberto Dvornicich<\/a><\/td>\n<\/tr>\n
2016<\/td>\nFrancesco<\/td>\nStrazzanti<\/td>\nA family of quotients of the Rees algebra and rigidity properties of local cohomology modules<\/td>\nEnrico Sbarra<\/a><\/td>\n<\/tr>\n
2009<\/td>\nLuca<\/td>\nCaputo<\/td>\nOn the structure of \u00e9tale wild kernels of number fields<\/td>\nRoberto Dvornicich<\/a> and Jean-Fran\u00e7ois Jaulent<\/td>\n<\/tr>\n
2009<\/td>\nMarco<\/td>\nStrambi<\/td>\nEffective estimates for coverings of curves over number fields<\/td>\nYuri F. Bilu and Roberto Dvornicich<\/a><\/td>\n<\/tr>\n
2008<\/td>\nLaura<\/td>\nPaladino<\/td>\nLocal-global divisibility problems for elliptic curves<\/td>\nRoberto Dvornicich<\/a><\/td>\n<\/tr>\n
2007<\/td>\nGabriele<\/td>\nRanieri<\/td>\nRang de l'image du groupe des unites; conjecture de Bremner<\/td>\nFrancesco Amoroso and Roberto Dvornicich<\/a><\/td>\n<\/tr>\n
1997<\/td>\nGiampiero<\/td>\nChiaselotti<\/td>\nAlcune presentazioni dei gruppi lineari speciali su campi finiti<\/td>\nRoberto Dvornicich<\/a><\/td>\n<\/tr>\n<\/tbody><\/table>\n<\/div><\/div>\n\n\n\n
awarded by another institution<\/h5>
\n\n

there is no data<\/p>\n<\/div><\/div>\n\n\n\n

<\/div>\n\n\n\n

Grants<\/h4>\n\n\n\n
Current<\/h5>
\n\n