• 1981: diploma di maturità, liceo classico “E. De Amicis”, Imperia (with full marks, 60/60)

• 1986: laurea in matematica, Università di Genova, cum laude

• 1986 – 1987: “Istituto Nazionale di Alta Matematica” (Roma)

• 1990: dottorato di ricerca in matematica, Università degli Studi di Milano (thesis: “Elementi di geometria globale delle supervarietà”, advisor: U. Bruzzo)

• 1993: Ph.D. in Mathematics, University of Warwick, (thesis: “Foundations of graded differential geometry”, supervisor: N. Hitchin)

• 1998: Qualification aux fonctions de professeur des universités (sect. 25), Ministère de l’Education Nationale, de la Recherche et de la Technologie, France

• 2019: Abilitazione scientifica nazionale (art. 16, legge 240/2010) per Professore universitario di prima fascia per il settore concorsuale 01/A2 - Geometria e Algebra, settore scientifico-disciplinare MAT/03 - Geometria, Italy

Permanent appointments

• 1990 – 1999: Ricercatore di Fisica matematica, Dipartimento di Matematica, Università di Genova

• 1999 – 2018: Professore associato di Fisica matematica (mat/07), Dipartimento di Matematica, Università di Genova

• from June 2018: Professore associato di Geometria (mat/03), Dipartimento di Matematica, Università di Genova

Temporary appointments

• February – November 1994: visiting assistant professor, Department of Mathematics, State University of New York at Stony Brook (N.Y.)

• May – July 1996: chercheur visiteur, Institut de Mathématiques de Jussieu, Université Paris VII, Paris

• April 2001: visiting scholar, Department of Mathematics, University of Pennsylvania, Philadelphia

• June – July 2006: directeur d’études invité, École des Hautes Études en Sciences Sociales, Centre d’analyse et de mathématique sociale, Paris

• March – November 2007: visiting professor, SISSA, Trieste

• January – April 2011: fellow, The Italian Academy, Columbia University, New York

• June – July 2011: directeur d’études invité, École des Hautes Études en Sciences Sociales, Centre d’analyse et de mathématique sociale, Paris

• May 2013: directeur d’études invité, École des Hautes Études en Sciences Sociales, Centre d’analyse et de mathématique sociale, Paris

• January – February 2016: professeur invité, Université Paris Diderot, Laboratoire SPHere, Paris

• Fellow, The Italian Academy, Columbia University, New York (spring semester 2011)

• Premio Galileo per la divulgazione scientifica, 9a ed., Padova 2015, selezione della Giuria scientifica

• Chercheur associé étranger, Laboratoire SPHERE, Université Paris Diderot (since 2019)

• Accademico corrispondente, classe di Scienze, Accademia Ligure di Scienze e Lettere (since 2022)

• Departamento de Matemática Pura y Aplicada, Universidad de Salamanca,1- 15/XII/1988

• SISSA, Trieste, March 1989

• Departamento de Matemática Pura y Aplicada, Universidad de Salamanca,15/V-15/VI/1989

• Université de Paris VII - D. Diderot, UFR de Mathématiques, 1-20/XII/1992

• Departamento de Matemática Pura y Aplicada, Universidad de Salamanca, May 1995

• Centre Émile Borel, Institut Henri Poincaré, Paris,13-23/II/1995 and 19-30/VI/1995

• Departamento de Matemática Pura y Aplicada, Universidad de Salamanca, October 1996

• Institut de Mathématiques de Jussieu, Université Paris VII -D. Diderot, 2/V-2/VII/1996

• Tata Institute of fundamental Research, Bombay,1-23/III/1997

• SISSA, Trieste, 19/IV-9/V1997

• SISSA, Trieste,18-30/V/1998

• Departamento de Matemática Pura y Aplicada, Universidad de Salamanca, 6-12/VII/1998

• Tata Institute of fundamental Research, Bombay, 4-18/X/1998

• Departamento de Matemática Pura y Aplicada, Universidad de Salamanca, 20-27/VI/1999

• Institut für Mathematik, Humboldt-Universität zu Berlin,17-24/X/1999

• Department of Mathematics and Statistics, Boston University, 23-30/IV/2001

• Department of Mathematics and Statistics, Boston University, 25-29/V/2002

• Isaac Newton Institute for Mathematical Sciences, Cambridge (UK), 23-29/VII/2002

• Departamento de Matemática Pura y Aplicada, Universidad de Salamanca, 28/IX-5/X/2002

• Department of Mathematics and Statistics, University of Massachusetts at Amherst, 14-18/IV/2003

• Mathematisches Forschungsinstitut Oberwolfach, “RiP Research Stay”, 1-14/II/2004

• Departamento de Matemática Pura y Aplicada, Universidad de Salamanca, 7-12/VI/2004

• Departamento de Matemática Pura y Aplicada, Univ. de Salamanca, 25/VI/-3/VII/2005

• Departamento de Matemática Pura y Aplicada, Univ. de Salamanca, 2-10/II/2007

• Korea Institute for Advanced Study (KIAS), Seoul, 23-30/VI/2007

• IMPA, Rio de Janeiro, 12-17/II/2008

• Instituto de Matemática, Universidade Estadual de Campinas, 17-22/II/2008

• Departamento de Matemática Pura y Aplicada, Univ. de Salamanca, 4-10/VI/2009

• SISSA, Trieste, 20-24/IX/2011

• IMT Institute for Advanced Studies, Lucca, 27-29/IV/2012

• Departamento de Matemática Pura y Aplicada, Univ. de Salamanca, 17-24/III/2013

• Max Planck Institute for the History of Science, Berlin, 10-15/III/2014

• IMECC, Universidade Estadual de Campinas (Brazil), 21-28/VIII/2015

• Institut de Mathématiques de Bourgogne, Université de Bourgogne, Dijon (France), 6-9/XI/2017

• SISSA, Trieste, 18-21/XII/2017

• Department of Mathematics, University of Kent, Canterbury (UK), 22-26/I/2018

• Département d’histoire et philosophie des sciences, Université Paris Diderot, Paris, 4-24/VI/2018

• Departamento de Matemática Pura y Aplicada, Univ. de Salamanca, 3-7/X/2018

• SISSA, Trieste, 5-8/XI/2018

• SISSA, Trieste, 30/I-1/II/2019

• Département d’histoire et philosophie des sciences, Université Paris Diderot, Paris, 10-30/VI/2019

• Département d’histoire et philosophie des sciences, Université de Paris, Paris, 22/XI-17/XII/2021

• Departamento de Matemática Pura y Aplicada, Univ. de Salamanca, 18-24/IX/2022.

Conferences, workshops, schools

• “Cohomological methods in supermanifold theory” (with U. Bruzzo), XIV International Colloquium on Group Methods in Physics, Varna (Bulgaria), 15-21/VI/1987

• “Coomologia dei fasci in geometria delle supervarietà”, XIII Congresso dell’Unione Matematica Italiana, Torino, 3-9/IX/1987

• “Foundations of super vector bundles”, invited talk, International Conference on Differential Geometry and Applications, Dubrovnik (Yugoslavia), 26/VI-3/VII/1988

• “Some topics in the theory of super line bundles”, invited talk, VIII Convegno Nazionale di Relatività Generale e Fisica della Gravitazione, Trento, 29/IX-3/X/1988

• XIXth International Conference on Differential Geometric Methods in Theoretical Physics, Rapallo, 19-24/VI/1990 (member of the organizing committee)

• “Instantons on K3 surfaces”, invited talk, XIXth International Colloquium on Group Theoretical Methods in Physics, Salamanca, 29/VI4/VII/1992

• “Axiomatic approach to supermanifolds”, poster, Conférence Européenne de Mathématiques, Paris, 6-10/VII/1992

• “Mukai-Nahm transform on K3 surfaces”, invited talk, X Convegno Nazionale di Relatività Generale e Fisica della Gravitazione, Bardonecchia (Torino), 1-5/IX/1992

• “Fourier-Mukai transform on 4-tori and K3 surfaces”, International Conference on Algebraic vector bundles and applications, CIRM, Trento, 27/IX -1/X/1993

• “Fourier-Mukai transform and the moduli spaces of stable sheaves on K3 surfaces”, AMS Summer Research Institute on Algebraic Geometry, Santa Cruz (CA), 11-26/VII/1995

• “A generalized Fourier-Mukai transform”, invited talk, C.I.R.M. Conference Trends in Algebraic Geometry and Relations with Physics, Levico Terme (TN), 9-13/IX/1996

• “Fourier transform of stable pairs”, invited talk, Summer Workshop on Algebraic Geometry and Physics, SISSA (Trieste), 16-19/IX/1996

• Complex geometry: relations with mathematical physics, Oberwolfach, 24-30/VIII/1997 (invited participant)

• “Fourier-Mukai transform and mirror duality”. invited talk, Summer Workshop on Algebraic Geometry and Physics, Medina del Campo (Spagna) 15-20/IX/1997

• “Special Lagrangian fibrations on K3 surfaces and Fourier-Mukai transform”, invited talk, Arbeitsgemeinschaft on Mirror Symmetry, Oberwolfach, 5-10/X/1997

• “Mirror symmetry for K3 surfaces”, invited talk, Mathematical aspects of string theory, Oberwolfach, 18-24/IV/1999

• Summer School on Algebraic Geometry and Physics, Luminy, Marseille, 6-14/IX/1999 (member of the scientific committee)

• “L’ombra negata: dimostrazioni matematiche e immaginazione visiva”, invited talk, conference Il pensiero visivo, Istituto Statale d’Arte, Monza, 15-17/III/2001

• “Complex surfaces and integrable systems: an overview”, invited talk, workshop Dualities and Bihamiltonian Structures in Field and String Theories, SISSA (Trieste), 11-13/X/2001

• “A Nahm transform for instantons over ALE spaces” (with M. Jardim), invited talk, 6th Conference on Clifford Algebras and their Applications in Mathematical Physics, Tennessee Technological University, Cookeville, Tennessee, 20-25/V/2002

• Workshop on Algebraic Geometry and Physics - K-theory, derived categories and strings, Dipartimento di Matematica, Università di Genova, 18-21/VI/2002 (member of the scientific and organizing committee)

• “Nahm-Mukai transform for instantons over ALE spaces”, invited talk, The AMS 2003 Spring Eastern Section Meeting, Special session: Algebraic Geometry, Integrable Systems and Gauge Theory, Courant Institute, New York, 12-13/IV/2003

• “Instantons and Nahm transforms”, 5 lectures, School on Fourier-Mukai and Nahm transform, Departamento de Matemática Pura y Aplicada, Universidad de Salamanca 19-23/VI/2003

• Workshop on Algebraic Geometry and Physics - Geometric integral transforms and applications (member of the scientific committee), Departamento de Matemática Pura y Aplicada, Universidad de Salamanca, 24-27/VI/2003

• “Nahm-Fourier transform for ALE instantons”, invited talk, Atelier sur les structures algébriques et espaces de modules, Centre de recherches mathématiques, Université de Montréal, 14-20/VII/2003

• “Hyperkähler Nahm transforms”, invited talk, Workshop on geometric integral transforms, SISSA (Trieste), 6-7/X/2003

• “Special Kähler geometry of classical integrable systems”, invited talk, Mini-Workshop on Poisson structures, SISSA (Trieste), 2-6/XII/2003

• “Special Kähler geometry of classical integrable systems”, invited talk, 2004 Workshop on Algebraic Geometry and Physics, IST, Lisbon, 7-12/IX/2004

• “La ragionevole inefficacia della matematica”, invited talk, International Conference God and the laws of nature, Varenna, Villa Monastero 11-13/X/2004

• “I fondamenti concettuali della relatività”, plenary address, Conference Albert Einstein 2005, Ravenna, 18/II/2005

• International Conference More geometrico: ruolo e significato del pensiero geometrico nelle scienze contemporanee, Università degli Studi di Milano, 3-4/V/2005 (member of the scientific committee)

• Workshop Heterotic Strings, Derived Categories, and Stacks, invited participant, Oberwolfach, 13-19/XI/2005

• “Il rigore immaginativo. La tensione essenziale tra letteratura e matematica nel ‘900”, invited talk, Convegno Belgirate IX (organized by Centro Pristem, Università Bocconi, Milano), Lago d’Iseo, 19 febbraio 2006

• “Instantons on ALE spaces”, invited talk, Mini-Workshop Instantonic Calculus, Trieste, SISSA, 2-3/X/2006

• “Moduli spaces: local vs global aspects”, invited talk, International Conference Changement d'échelle – changement de niveau, Université René Descartes - Paris V, Paris, 2-4/V/2007

• “Letteratura e matematica”, plenary address, Convegno Cavalcare la luce: scienza e letteratura. XV Biennale Piemonte e Letteratura, Alessandria, 23-25/V/2007

• “Fourier-Mukai transforms and equivalences of derived categories”, 5 invited lectures, College on Mirror Symmetry, Chern Institute of Mathematics, Nankai University, Tianjin, 16-22/VI/2007

• “Moduli spaces of sheaves on elliptic fibrations”, invited talk, Atelier Transformées intégrales non-linéaires: Fourier-Mukai and Nahm, Centre de recherches mathématiques, Université de Montréal, 27-31/VIII/2007

• “Storie di mondi possibili. La matematica come attività finzionale?”, invited talk, Convegno Belgirate XI (organized by Centro Pristem, Università Bocconi, Milano), Portobuffolé (Pordenone), 24/II/2008

• “Geometry of integrable systems”, invited talk, Workshop De l’univers au monde quantique: structures géométriques et topologiques, Fondation des Treilles, Tourtour (France), 5-10/V/2008

• “Quaternionic structures associated to special Kähler manifolds”, invited talk, International Workshop Bundles, Gerbes and Derived Categories in String Theory, Universidad de Salamanca, Salamanca,14-16/V/2008

• Workshop Moduli spaces, enumerative problems, and integrable systems, Dipartimento di Matematica, Università di Genova, 25-28/VI/2008 (member of the organizing committee)

• “Some remarks on the geometric ideas underlying Gödel’s cosmological model”, invited talk, International workshop Mechanics, mathematical physics and foundations of mathematics in the 18th and 19th Centuries, Scuola Normale Superiore, Pisa, 7-12/VII/2008

• “Il rigore immaginativo. La matematica nei Cahiers di Paul Valéry”, invited talk, Conference Matematica e cultura 2009, Venezia, 27/III/2009

• “Geometric interpretation of the bi-hamiltonian structure of the Calogero-Moser system”, invited talk, International Workshop Generalized complex and Poisson geometry, Banff International Research Station for Mathematical Innovations and Discovery, Banff (Canada), 11-16/IV/2010

• “Hopeful monsters and pathological examples in mathematics”, invited talk, International workshop Karl Popper oggi: una riflessione multidisciplinare, Università di Pisa, Pisa, 26/IV/2010

• Journée d’étude Les enjeux et perspectives internationales in sciences humaines et sociales, invited discussant, CNRS, Campus Gérard Mégie, Paris, 11/V/2010

• “Moduli spaces of framed sheaves on Hirzebruch surfaces”, invited talk, Convegno in onore di Roberto Catenacci, Dipartimento di Scienza e Innovazione, Università del Piemonte, Alessandria, 13/IV/2012

• “Una piramide di problemi”, invited lecture, Centro di ricerca matematica “Ennio De Giorgi”, Scuola Normale Superiore, Pisa, 27/IV/2012

• “Tennis balls as physico-mathematical models in Galileo and Newton”, invited talk, Workshop Tennis and the scientific revolution, Museo Galileo, Firenze, 15/VI/2012

• “Monadic description of framed sheaves on Hirzebruch surfaces”, invited talk, International Workshop Geometry, Integrability, Quantization, SISSA, Trieste, 9/VII/2012

• “La matematica come attività culturale”, invited talk, Congresso Nazionale Mathesis 2012, Rovigo, 18/X/2012

• “ADHM data for sheaves on Hirzebruch surfaces”, invited talk, International Workshop on Moduli Spaces and Mathematical Physics, Centro de Investigación en Matemáticas (CIMAT), Guanajuato (Mexico), 28/I-4/II/2013

• “Solving the universe: Clifford’s geometric algebras”, invited talk, International Conference Geometry and Logic, Scuola Normale Superiore, Pisa, 17-19/VI/2013

• “La prova logico-matematica”, invited talk, Workshop Dialoghi sulla prova: una riflessione tra diritto, scienza, medicina e filosofia, Università degli Studi di Milano, 4/IV/2014

• “Analogy and invention: some remarks on Poincaré’s Analysis situs papers”, invited talk, International Colloquium Philosophers and Mathematics, Center for Philosophy of the University of Lisbon, 29-30/X/2014

• “Poincaré e la topologia algebrica”, invited talk, Workshop Geometrie e filosofie dall’Ottocento a oggi, Dipartimento di Lettere e Filosofia, Università di Firenze, 7-8/V/2015

• “Framed sheaves on Hirzebruch surfaces”, invited talk, International Conference Interactions between geometry and physics, Guarujá (São Paulo, Brazil), 17-21/VIII/2015

• Workshop on Arithmetic and Geometry (invited participant), Cetraro (CS), 26/VIII-4/IX/2016

• “Points: from Euclid to geometry”, invited talk, Colloque International Huitième Rencontre Française de Philosophie des Mathématiques, Marseille, 3-5/XI/2016

• “La geometria del caos: dalle mappe di Poincaré ai tori di Arnol’d”, invited talk (public lecture), Inaugural Conference of the Arnold-Regge Center for Algebra, Geometry and Theoretical Physics, Alessandria, 1/III/2017

• “Moduli spaces of sheaves on algebraic surfaces as quiver varieties”, invited talk, International Workshop Group Actions in Algebraic and Symplectic Geometry, ICMAT, Madrid, 2/X/2018

• “Una nuova idea di spazio: la rivoluzione di Riemann”, invited talk, International Workshop Il punto di vista geometrico (organized by Università di Padova, Scuola Normale Superiore and Università di Udine), Istituto Veneto di Scienze, Lettere ed Arti, Venezia, 9/XI/2018

• “Representations of quivers with relations in the category of sheaves”, talk, International Workshop Quiver varieties, moduli spaces, and applications to mathematical physics (4th Christmas workshop), Genova, 20/XII/2018

• “Poisson-Nijenhuis structures on quiver path algebras”, invited talk, International Conference Noncommutative Manifolds and their Symmetries, Scalea (CS), 19/IX/2019

• “L’invenzione dell’insieme vuoto”, invited talk, International Workshop Il punto di vista aritmetico (organized by Università di Padova), Istituto Veneto di Scienze, Lettere ed Arti, Venezia, 12/XI/2021

• "Insight and heuristics: the emergence of Poincaré’s conjecture", PHILMATHMED 5 - Geometry and Logic, Dipartimento di Matematica, Università di Torino, 1/IV/22

• “From formal schemes to Quot scheme: the emergence of moduli theory in Grothendieck FGA”, invited talk, International Conference Grothendieck a Multifarious Giant: Mathematics, Logic and Philosophy, Chapman University, 28/V/2022.

Invited talks and departmental colloquia (a selection)

• “Supermanifolds”, Department of Mathematics, University of Leeds, Leeds, 29/X/1987

• “Chern-Weil theory for super bundles”, DPMMS, Cambridge (UK), 19/XI/1987

• “A new class of supermanifolds”, King’s College, London, 4/III/1988

• “Super line bundles on graded Riemann surfaces”, Departamento de Matemática Pura y Aplicada, Universidad de Salamanca, Salamanca, 13/XII/1988

• “Line bundles over supercurves”, SISSA, Trieste, 15/III/1989

• “Moduli spaces of instantons and the geometry of the loop group”, series of 4 talks, Departamento de Matemática Pura y Aplicada, Universidad de Salamanca, June 1989

• “Fourier-Mukai transform on abelian surfaces”, Dipartimento di Matematica, Università di Roma II, Roma, March 1992

• “Moduli spaces of stable sheaves on algebraic surfaces”, series of 5 talks, SISSA, Trieste, October 1992

• “Fourier-Mukai transform for instantons on K3 surfaces”, Department of Mathematics, SUNY at Stony Brook, marzo 1994

• “Seiberg-Witten theory”, series of 4 talks, SISSA, Trieste, April 1995

• “Fourier transform of generalized instantons”, Dipartimento di Matematica, Università di Roma II, Roma, January 1996

• “Transformée de Mukai-Nahm”, Institut de Mathématiques de Jussieu, Paris, 30/V/1996

• “Seiberg-Witten invariants for algebraic surfaces”, Departamento de Matemática Pura y Aplicada, Universidad de Salamanca, Salamanca, 7/X/1996

• “Fourier-Mukai functors on symplectic complex surfaces”, Tata Institute of Fundamental Research, Mumbai, 7/III/1997

• “Special Lagrangian foliations: an introduction”, Dipartimento di Matematica, Università di Roma II, Roma, 19/V/1997

• “Transformée de Fourier-Mukai sur le surfaces K3”, UFR Mathématiques, Université de Lille, Lille, 10/XII/1997

• “Mirror symmetry for special Lagrangian fibrations”, Tata Institute of Fundamental Research, Mumbai, 13/X/1998

• “Generalized Hecke correspondence on elliptic fibrations”, Forschungsseminar Algebraische Geometrie, Humboldt Universität zu Berlin, Berlin,19/X/1999

• “Hyperkähler geometry and Fourier-Mukai transform” Department of Mathematics, University of Pennsylvania, Philadelphia, 11/IV/2001

• “Fourier-Mukai transforms of quaternionic instantons”, Department of Mathematics, Boston University, Boston, 25/IV/2001

• “Hyperelliptic integrable systems”, Dipartimento di Matematica, Università di Milano Bicocca, Milano, 24/IX/2001

• “Integrable systems and Poisson complex surfaces” Department of Mathematics and Statistics, University of Massachusetts at Amherst, 16/IV/2003

• “Poincaré matematico”, Dipartimento di filosofia, Università degli Studi di Milano, Milano,13/V/2003

• “L’idea di punto materiale da Newton a Poincaré”, Dipartimento di filosofia, Università di Milano, Milano, 2/XII/2004

• “La geometria dell'universo fisico”, Dipartimento di Matematica, Università di Trieste, Trieste, 17/I/2005

• “L’idée d'espaces de modules”, EHESS, Paris, 18/VI/2006

• “Racconti matematici”, round table with M. Berisso, L. Montecucco and P. Zublena, Facoltà di Lettere e Filosofia, Università di Genova, Genova, 1/XII/2006

• “Raccontare l’invisibile. Interazioni fra letteratura e matematica nel ‘900”, Politecnico di Milano, Seminari di Cultura matematica, Milano, 16/V/2007

• “L’anima dell’esattezza: consonanze tra matematica e letteratura nel ‘900”, Master in Comunicazione della Scienza, SISSA, Trieste, 1/VI/2007

• “Chi crede ancora nell’unità della natura?”, L’idea di natura (forum organized by the Italian Ministry for the environment), Venice International University, Venezia, 15-16/IX/2007

• “Analogie tra analogie. La matematica nella cultura del nostro tempo”, lectio magistralis, Università della Basilicata, Potenza, 14/XI/2007

• Discussant of the lectio magistralis “Humans in the Age of Genetics and Computers” by Victor Gómez Pin, Venice International University (VIU), Venezia, 21/XI/2007

• “Relative Fourier-Mukai transforms and moduli of sheaves on elliptic fibrations”, IMPA, Rio de Janeiro, 14/II/2008

• “Gli intrecci tra matematica e fisica: dalla relatività alla teoria delle stringhe” plenary address, Giornata di studi in onore di Ludovico Geymonat, Università degli Studi di Milano, Milano, 26/V/2008

• “Scienze umane e naturali: il funzionamento dei due paradigmi”, Istituto di Scienze Umane, Firenze, 8/X/2008

• “Il dominio dell’arbitrario. Lo sguardo di Paul Valéry sulla matematica”, Gabinetto Vieusseux, Palazzo Strozzi, Firenze, 14/IX/2008

• “I nuovi universi della geometria: da Gauss a Einstein”, Institute of Advanced Studies, Università di Bologna, 22/IV/2009

• “La matematica e il racconto”, a dialogue with Salvatore Nigro, Scuola Normale Superiore, Pisa, 28/V/2009

• “Geometrie del pensiero”, round table with M. Frixione, W. Gerbino, G. Giorello and A. Treves, international conference More geometrico: An interdisciplinary conference on geometry, cognition, space and movement, SISSA, Trieste, 7/X/2009

• “L’italiano tra arte, scienza e tecnologia”, Stockholms Universitet, Stockholm,19/X/2009

• “Letteratura, scienza e tecnica: il caso Primo Levi”, round table with P. Grossi, M. Belpoliti and E. Zinato, Stockholms Universitet, Stockholm, 20/X/2009

• “Integrali per dimagrire: la matematica dell’Uomo senza qualità”, Dipartimento di Matematica, Università di Camerino, 19/V/2010

• “Mostri matematici”, Dipartimento di Matematica, Università di Perugia, Perugia, 1/X/2010

• “The Calogero-Moser integrable system and bi-hamiltonian geometry”, Department of Mathematics, Columbia University, New York, 11/III/2011

• “OmegaN-manifolds and Calogero-Mosero system”, Department of Mathematics, University of Pennsylvania, Philadelphia, 29/III/2011

• “The bi-hamiltonian structure of the Calogero-Moser system”, SISSA, Trieste, 22/IX/2011

• “Il punto: storia e teoria di un concetto matematico”, Facoltà di Design e Arti, Iuav, Venezia, 19/III/2012

• “Spazi musicali”, Conservatorio “G. Verdi”, Como, 28/III/2012

• “Moduli spaces of framed sheaves on Hirzebruch surfaces”, Dipartimento di Matematica, Politecnico di Torino, 11/IV/2012

• “Lo zero: storia e teoria di un concetto matematico”, Facoltà di Design e Arti, Iuav, Venezia, 16/IV/2012

• “Hilbert e i fondamenti della geometria”, Dipartimento di Matematica, Università di Milano, 8/V/2012

• “Pyramiden, Probleme und Fluchtwege”, invited lecture (with Piergiorgio Odifreddi), Istituto Italiano di Cultura, Hamburg, 19/X/2012

• “Hilbert e la rifondazione della geometria”, Colloquia Patavina, Dipartimento di Matematica, Università di Padova, 30/X/2012

• “Poincaré’s century”, lectio magistralis, SISSA, Trieste, 20/IX/2012

• “Le geometrie del possibile”, Dipartimento di Scienze Umanistiche, Università di Catania, 11/I/2013

• “Pas de géométrie sans la parole”, Scuola di Architettura e Società, Politecnico di Milano, Milano, 18/I/2013

• “Problemi e congetture: gli sviluppi della geometria in Hilbert e Poincaré”, Dipartimento di Matematica, Università di Udine, 15/II/2013

• “Letteratura e matematica”, Università degli Studi di Salerno, Fisciano, 5/III/2013

• “Clifford’s geometry of the universe and the ‘duty of inquiry’”, IMT, Lucca, 23/I/2014

• “Poincaré’s Creation of Algebraic Topology: ‘Reasoning Well from Badly Drawn Figures’”, Colloquium Research Group “Modern Geometry and the Concept of Space”, Max Planck Institute for the History of Science, Berlin, 11/III/2014

• Talk at the Colloquium Day “Séminaire Grothendieck”, Dipartimento di Matematica, Università degli Studi di Milano, 23/III/2015 (other speakers: Laurent Lafforgue, Winfried Scharlau, Pierre Lochak, Giulio Giorello, and Leila Schneps)

• “Does geometry needs foundations?”, invited lecture, Dottorato di Filosofia, Università di Milano, 26/V/2015

• “Poisson quiver varieties and Hilbert schemes of points of ”, IMECC, Universidade Estadual de Campinas (Brazil), 26/VIII/2015

• “Freedom and imagination: the subversive power of mathematics”, invited address, Colloquium Generale, Universität Bern, 14/X/2015

• “Instantons, fibrés encadrés, variétés de représentations de carquois”, Séminaire de physique mathématique, Université Paris Diderot, 29/I/2016

• “Aux origines de la théorie des connexions : les contributions de Weyl et de Cartan à la croisée de la géométrie et de la physique (1918-1925)”, Séminaire d’histoire et philosophie de la physique, Laboratoire SPHERE, Université Paris Diderot, 2/II/2016

• “Quiver varieties and Hilbert schemes of points of ”, Séminaire de physique mathématique et de topologie algébrique, Université d’Angers, 3/II/2016

• “The early age of connections: at the intersection of geometry & physics”, Seminar of Historical Epistemology, Dipartimento di Filosofia, Università di Milano, 2/V/2016

• “Freedom and creativity in mathematics”, Sissa Colloquium, SISSA, Trieste, 25/V/2016

• “NP structures on quiver path algebras”, Geometry & Mathematical Physics Seminar, SISSA, Trieste, 26/V/2016

• “The emergence of the theory of connections and fibre bundles: at the crossroad between geometry and physics”, Scuola Normale Superiore, Pisa, 7/III/2017

• “Dalla classe nulla all’insieme vuoto”, Dottorato di ricerca in filosofia, Università Vita-Salute San Raffaele, Milano, 11/V/2017

• “Quiver varieties and moduli spaces of framed sheaves on projective surfaces”, Institut de Mathématiques de Bourgogne, Université de Bourgogne, Dijon (France), 10/XI/2017

• “Associative geometry and integrable systems”, The Algebra, Geometry and Topology Seminar, School of Mathematics, University of Kent, Canterbury (UK), 26/I/2018

• “Ladders of sets and isomorphisms”, Lezioni Enriques - Seminario di Storia e Filosofia della Matematica, Dipartimento di Matematica, Università degli Studi di Milano, 12/XI/2019

• "Relative algebraic geometry and F₁-geometry”, Departamento de Matemáticas, Universidad de Salamanca, 28/IX/2022

• "Entre intuition et heuristique: aux origines de la conjecture de Poincaré", Séminaire d'Histoire et Philosophie des Sciences, Laboratoire J. Dieudonné, Université Côte d'Azur, Nice, 22/11/2022

Fellowship grants

• Consiglio Nazionale delle Ricerche Grant for Undergraduate students (1986)

• Pre-Doctoral Fellowship Grant, Istituto Nazionale di Alta Matematica “F. Severi” (XI/1986 -III/1987)

• Doctoral Fellowship Grant, Ministero dell’Università e della Ricerca (IV/1987 - IV/1990)

• Research Fellowship Grant, Consiglio Nazionale delle Ricerche (IV/1990 - IV/1991)

• Research Fellowship Grant, Consiglio Nazionale delle Ricerche (II/1994 - X/1994)

• CNR-NATO Senior Grant (V/1996 - VI/1996)

• Fellowship Grant, The Italian Academy, Columbia University, New York (spring semester 2011)

Research grants

• “Methods of algebraic geometry in gauge theory and string theory”, research project funded by the Università di Genova: principal investigator (1998)

• “Algebraically integrable systems: moduli spaces of geometric structure and generalized Fourier-Mukai transforms”, research team of the Università di Genova of the PRIN “Geometry of integrable systems” (national coordinator: B. Dubrovin): scientific coordinator (1999-2001)

• “Geometry of integrable systems and string theory”, research project funded by the Università di Genova: principal investigator (2000)

• Unità di ricerca dell’Università di Genova “Algebraically integrable systems: separation of variables and Poisson structures on moduli spaces of sheaves on complex surfaces”, research team of the Università di Genova of the PRIN “Geometry of integrable systems” (national coordinator: B. Dubrovin): scientific coordinator (2001-2003)

• “Algebraically integrable systems: special Kähler geometry and Poisson structures”, research team of the Università di Genova of the PRIN “Geometry of integrable systems” (national coordinator: B. Dubrovin): scientific coordinator (2004-2006)

• “Adelic Grassmannian and Weyl algebra”, research project funded by the Università di Genova: principal investigator (2008)

• “Theory of integrable systems: tt*-geometry and twistor methods”, research project funded by the Fondazione CARIGE: scientific coordinator (2008)

• “Aspetti matematici nello studio delle interazioni fondamentali: dalle algebre di operatori alla geometria non-commutativa”, FRA 2017, research project funded by the Università di Genova: scientific coordinator (2017-2018)

• “Wall and chamber structure for moduli spaces of framed sheaves", FRA 2022, research project funded by the Università di Genova: scientific coordinator (2022-2023)

Participation in research projects (excluded those listed above)

• “Europroj”, funded by the EC (1993-1997)

• “Gruppo Nazionale per le Strutture Algebriche e geometriche e loro Applicazioni (GNSAGA)”, funded by the Consiglio Nazionale delle Ricerche (CNR) and later by the Istituto Nazionale di Alta Matematica (INDAM) (1994- )

• “Azione Integrata SISSA (Trieste) - Universidad de Salamanca: Sheaves on Calabi-Yau manifolds and applications to integrable systems and string theory”, funded by the Italian “Ministero dell'Istruzione, dell'Università e della Ricerca” and the Spanish “Ministerio de Educación, Ciencia y Tecnología” (2002-2003)

• “Algebraic varieties of dimension >2, algebraic cycles, K-theory and motives” (national coordinator A. Verra), PRIN funded by the Italian “Ministero dell'Istruzione, dell'Università e della Ricerca” (2003-2004)

• “Marie Curie Research Training Network ENIGMA - European Network in Geometry, Mathematical Physics and Applications”, funded by the EC (FP6, 2004-2007)

• “The Theory of Nonlinear Integrable Systems and Applications”, funded by E.I.N.S.T.E.I.N. Consortium and Russian Foundation for Basic Research (2006-2008)

• “Azione Integrata SISSA (Trieste) - Universidad de Salamanca: Moduli spaces of coherent sheaves, triangulated categories and applications in mathematical physics”, funded by the Italian “Ministero dell'Istruzione, dell'Università e della Ricerca” and the Spanish “Ministerio de Educación, Ciencia y Tecnología” (2007-2008)

• “Geometric methods in the theory of nonlinear waves and applications” (national coordinator B. Dubrovin), PRIN funded by the Italian “Ministero dell'Istruzione, dell'Università e della Ricerca” (2007- 2009)

• “Geometric, analytic and numerical methods in the theory of nonlinear waves and applications” (national coordinator B. Dubrovin), PRIN funded by the Italian “Ministero dell'Istruzione, dell'Università e della Ricerca” (2010-2012)

• “Geometry of algebraic varieties” (national coordinator A. Verra), PRIN funded by the Italian “Ministero dell'Istruzione, dell'Università e della Ricerca” (2012-2014)

• “Analytical and geometric methods in mathematical physics and probability”, research project funded by the Università di Genova, 2012

• “Mathematical aspects in the theory of interacting fields”, research project funded by the Università di Genova, 2013

• “Mathematical aspects in the theory of interacting fields and quantization deformation”, research project funded by the Università di Genova, 2014 & 2015

• “Tensors: Algebra and Geometry”, (national coordinator L. Chiantini), PRIN funded by the Italian “Ministero dell'Istruzione, dell'Università e della Ricerca” (2017-2019)

• “Metodi di geometria e di analisi funzionale nella teoria delle interazioni fondamentali”, research project funded by the Università di Genova, 2019 & 2020

(Co)-organization of conferences, workshops, and schools

• XIXth International Conference on Differential Geometric Methods in Theoretical Physics, Rapallo (Genova),19-24/VI/1990

• Summer Workshop on Algebraic Geometry and Physics, Medina del Campo (Spain) 15-20/IX/1997

• Summer School on Algebraic Geometry and Physics, Luminy, Marseille, 6-14/IX/1999

• RIcerca e FORmazione in Matematica, Genova, 12-15/VI/2000

• Matematica e cultura 2001, Venezia, 30-31/III/2001

• Matematica e cultura 2002, Venezia, 22-24/III/2002

• Workshop on Algebraic Geometry and Physics (WAGP) – K-theory, derived categories and strings, Dipartimento di Matematica, Università di Genova, Genova, 18-21/VI/2002

• Matematica e cultura 2003, Venezia, 28-29/III/2003

• 2003 School and Workshop on Algebraic Geometry and Physics (School on Fourier-Mukai functors and Nahm transforms; Workshop on Geometric Integral Transforms and Applications), Departamento de Matemática Pura y Aplicada, Universidad de Salamanca, 18-23/VI/2003

• More geometrico: ruolo e significato del pensiero geometrico nelle scienze contemporanee, Università degli Studi di Milano, Milano, 3-4/V/2005

• International workshop Moduli spaces, enumerative problems, and integrable systems, Dipartimento di Matematica, Università di Genova, Genova, 25-28/V/2008

• More geometrico: An interdisciplinary conference on geometry, cognition, space and movement, SISSA, Trieste, 6-8/X/2009

• Moduli spaces and Integrable Systems (Christmas Workshop), international workshop, Dipartimento di Matematica, Università di Genova, 19-21/XII/2012

• Ideas of point: an elusive concept in mathematics and physics throughout history, international conference, SISSA, Trieste, 14-16/XI/2013

• Prevedere il passato: matematica e astronomia nelle ricerche storiche di A.C. Garibaldi (1932-2013), international workshop co-organized with Observatoire de Paris – Histoire des sciences et de l’astronomie, Dipartimento di Matematica, Università di Genova, 12/IX/2014

• Moduli spaces and Integrable Systems (2nd Christmas Workshop), international workshop, Dipartimento di Matematica, Università di Genova, 18-20/XII/2014

• Quivers, Moduli spaces and Integrable Systems (3rd Christmas Workshop), international workshop, Dipartimento di Matematica, Università di Genova, 19-21/XII/2016

• Quiver varieties, Moduli spaces, and Applications to mathematical physics (4th Christmas Workshop), international workshop, Dipartimento di Matematica, Università di Genova, 19-21/XII/2018

(Co)-organization of departmental seminars and colloquia

• Colloquium Mathematicum, Dipartimento di Matematica, Università di Genova, 1996-1998

• Seminario di Geometria & Fisica, Dipartimento di Matematica, Università di Genova (1998-2003)

Postdoc supervision

• Igor Mencattini, 2008

Ph.D. supervision

• Edoardo Provenzi, “A mathematical overview of canonical and covariant loop quantum algebra”, Dottorato di ricerca in Matematica e Applicazioni, Università di Genova, 2002-2004

• Alberto Tacchella, “A multicomponent generalization of the KP/CM correspondence”, Dottorato di ricerca in Matematica e Applicazioni, Università di Genova, 2006-2010

• Claudio Rava, “ADHM data for framed sheaves on Hirzebruch surfaces”, Dottorato di ricerca in Fisica Matematica, Sissa, Trieste, 2008-2012 (joint supervision with U. Bruzzo)

• Valeriano Lanza, “Hilbert schemes of points of the total space of O_P¹ (–n) as quiver varieties”, Dottorato di ricerca in Matematica e Applicazioni, Università di Genova, 2011-2015

• Andrea Gentili, “A first order deformation theory for linear quasi-categories”, Dottorato di ricerca in Matematica e Applicazioni, Università di Genova, 2011-2015

• Andrea Gandolfo, “The genesis of the theory of connections: H. Weyl and É. Cartan, Dottorato di ricerca in Matematica e Applicazioni, Università di Genova, 2011-2016 (joint supervision with U. Bruzzo)

• Giovanni Filocamo, “Forme della conoscenza matematica: visualizzazione, rappresentazione non simbolica, intuizione”, Dottorato di ricerca in Matematica e Applicazioni, Università di Genova, 2012-2017

• Flavio Baracco, “Weyl’s phenomenological background”, Dottorato di ricerca in Filosofia e Scienze dell’Uomo, Università degli Studi di Milano, 2017-2019 (joint supervision with M. D’Agostino)

“Tesi di laurea” supervision

• Supervision of about 40 theses in mathematics (1991-2021), mainly on the following topics: gauge theory; Frobenius manifolds; hyper-Kähler manifolds; algebraic geometry of integrable systems; Poisson complex surfaces; GBV algebras; spin structures; projective structures and opers; generalized complex geometry; Hilbert’s 5^th problem; history of 19^th century mathematics (“pathological functions” in analysis; Clifford’s geometric algebras; pseudospherical surfaces from Dini to Bäcklund); general relativity (Gödel’s universes; spacetime causal structures); history of cartography and differential geometry (18^th-19^th centuries)); Hilbert’s 3^th problem; Seiberg-Witten invariants; quiver representations

• Joint supervision of 1 thesis in philosophy (2014; topic: formal mereology)

– At the University of Genova, if not otherwise specified

Laurea quadriennale (in matematica if not otherwise specified)

• “Esercitazioni di Istituzioni di Fisica Matematica” [continuum mechanics] (1990-91; 1991-1992; 1992-93)

• “Esercitazioni di Meccanica Razionale” [analytical mechanics & special relativity] ](1990-91, Ingegneria; 1991-1992, Matematica; 1992-93, Fisica; 1994-95, Fisica; 1995-96, Fisica; 1996-97, Fisica)

• “Istituzioni di Fisica Matematica, I modulo, indirizzo generale” [special and general relativity; dynamical systems] (1993-94; 1994-95; 1995-96)

• “Istituzioni di Fisica Matematica, I modulo, indirizzo applicativo” [fluid mechanics] (1994-1995)

• “Istituzioni di Fisica Matematica, I modulo” [special and general relativity] (1996-1997; 1997-1998; 1998-99; 2000-2001)

• “Analisi I, II modulo” [calculus] (1998-1999, Polo universitario G. Marconi, La Spezia)

• “Istituzioni di Fisica Matematica, II modulo” [Hamiltonian mechanics & symplectic geometry] (1998-99; 1999-2000, 2002-2003)

• “Meccanica Razionale” [analytical mechanics] (2001-2002)

• “Fisica Matematica, I modulo” [gauge theory] (2003-2004)

Laurea triennale in matematica

• “Sistemi dinamici e meccanica analitica” [dynamical systems & analytical mechanics] (2002-2003; 2003-2004; 2004-2005, 2005-2006)

• “Istituzioni di Fisica Matematica I” [Hamiltonian mechanics & symplectic geometry] (2006-2007, 2008-2009, 2009-2010; 2010-2011; 2011-2012; 2012-2013; 2013-2014; 2014-2015; 2015-2016; 2016-2017)

• “Storia della matematica” [history of mathematics] (2016-2017; 2017-2018; 2018-2019; 2019-2020, 2020-2021, 2021-22)

• “Geometria differenziale” [differential geometry] (2016-2017; 2017-2018; 2018-2019; 2019-2020, 2020-2021, 2021-22)

Laurea triennale in filosofia

• “Storia della scienza, I modulo (Scienze matematiche e fisiche)” [history of exact sciences] (Università Vita & Salute - San Raffaele, Milano, per affidamento, 2017-2018)

Laurea magistrale in fisica

• “Fisica Matematica” [differential geometric methods in physics and gauge theory] (2008-2009)

Laurea magistrale in matematica

• “Fisica Matematica II” [gauge theory] (2004-2005)

• “Complementi di storia della matematica” [history of mathematics] (2008-2009; 2009-2010; 2010-2011; 2011-2012; 2012-2013; 2013-2014; 2014-2015: 2015-2016)

• “Introduzione alle superfici di Riemann” [Riemann surfaces] (minicourse, 2011-2012)

• “Metodi geometrici in fisica matematica” [general relativity or gauge theory] (a.a. 2005-2006; 2008-2009; 2009-2010, 2010-2011; 2011-2012; 2012-2013; 2013-2014; 2014-2015; 2015-2016; 2016-2017; 2017-2018; 2018-2019; 2019-2020; 2021-22)

• “Coomologia dei fasci” [sheaf cohomology] (minicourse, 2018-2019)

Graduate courses

• “Mukai transform on complex surfaces” (with U. Bruzzo), Dottorato in Fisica Matematica, SISSA, 1993

• “Seiberg-Witten invariants and geometry of Kähler surfaces”, Dottorato in Matematica, Genova-Torino, 1999

• “Classical decomposition of semisimple Lie groups” (with F. De Mari), Dottorato in Matematica, Genova, 2001, 2002, 2005, 2006

• “Gauge theory: an introduction”, Dottorato in Matematica, Università di Genova, 2002, 2003, 2005, 2006; Dottorato in Fisica Matematica, SISSA, 2007

• “Representations of compact Lie groups”, Dottorato in Matematica, Università di Genova, 2016

• “Spacetime Geometries”, Dottorato di ricerca in Filosofia e Scienze dell’Uomo, Università degli Studi di Milano, March 2017

Other teaching activities

• “La matematica nella storia del pensiero”, 5 two-hour lectures for high-school teachers, Liceo Colombo, Genova, January-March 2018

• “Giunta del Dipartimento”, Dipartimento di Matematica, Università di Genova (member, 2004-2013 and 2017- 2018)

• “Commissione scientifica di Area 01 [Mathematics & Computer science]”, Università di Genova (member, 2007-2011)

• “Commissione scientifica del Dipartimento di Matematica”, Università di Genova (member, 2013- )

• Scientific committee of the “Biblioteca of the Scuola di Scienze Matematiche, Fisiche e Naturali, Università di Genova” (member, 2014-2016)

• Graduate Admissions Committee, Dipartimento di Matematica, Università di Genova (member, 2000, 2001 and 2016 - )

• “Collegio dei docenti” of the doctoral school in Mathematics, Università di Genova (member, 1999-2014 / coordinator, 2004-207 )

• “Collegio dei docenti” of the doctoral school in Philosophy and Human Sciences, Università degli Studi di Milano (member, 2016- 2017; 2019- 2020)

• Member of Ph.D. thesis committees in Italy (Università di Genova, 2003, 2007; SISSA, Trieste, 2008, 2019); Spain (Universidad de Salamanca, 2009), France (Université de Nice, 2009)

• Referee for the following international journals: International Mathematical Research Notes; Advances in Mathematics; Journal of Geometry and Physics; Foundations of Science; Journal of Mathematical Physics; Journal of High Energy Physics (JHEP); Nuovo Cimento B; Canadian Mathematical Bulletin; Publicacions Matemàtiques; European Journal for Philosophy of Science; SIGMA; Rivista di filosofia

• Remote Evaluator for NEST Programme (European Commission, 2003, 2004, 2005)

• “Reviewer for NSA proposals” (NSA/AMS, USA, 2008)

• Member of the editorial board of the journal Lettera Matematica Pristem (2003-2019)

• Reviewer for Mathematical Reviews (1988- ) and Zentralblatt MATH (2003- )

• Consultant for a major Italian publishing house (1997- )

• Curator of the exhibitions: “Numeri”, Palazzo delle Esposizioni, Rome, 14/X/2014 -3/VI/2015; “Numeri nel tempo. Contare, misurare, calcolare”, Metaponto (part of the project “Matera Capitale Europea della Cultura 2019”), 21/VI - 30/XI/2019

• Invited speaker at many events intended for the general public: e.g. Salone internazionale del libro, Torino (2002, 2006, 2007, 2011, 2012); Festival della scienza, Genova (2003, 2004, 2005, 2006, 2007, 2008, 2010, 2012, 2013, 2016, 2019); Festival della matematica, Roma (2007, 2008, 2009); Fiera internazionale dell’editoria scientifica, Trieste (2007); Festival dei saperi, Pavia (2008); Festival della letteratura, Mantova (2008, 2012, 2019); MathFestival, Italian Academy, Columbia University, New York (2009); Milano Scienza, Milano Mondo 2009; Festival PordenoneLegge, Pordenone (2010); Festival BergamoScienza, Bergamo (2011); La Milanesiana, Milano (2012, 2013) BookCity Filosofia, Milano (2013, 2020); Festival della comunicazione, Camogli (2015, 2016); Festivalscienza, Cagliari (2015); Festival della mente, Sarzana (2016, 2017); Festival jonico della filosofia, Savoca (2017); Festival della politica, Mestre (2019); Festival delle scienze, Roma (2020).