Claudio Bartocci
Informazioni generali e contatti
Dipartimento: DIMAUfficio: 808Orario di ricevimento: Su appuntamento (preferibilmente via email)Telefono: 010-3536808Email: Questo indirizzo e-mail è protetto dallo spam bot. Abilita Javascript per vederlo. Homepage: http://fermat.dima.unige.it/~bartocci/Insegnamenti
- Geometria Differenziale (A.A. 2019/2020) (3° LT)
- Metodi Geometrici in Fisica Matematica (A.A. 2019/2020) (1°, 2° LM)
- Storia della Matematica (A.A. 2019/2020) (3° LT; 1°, 2° LM)
Insegnamenti precedenti
A.A 2018/2019
- Geometria Differenziale (A.A. 2018/2019) (3° LT)
- Metodi Geometrici in Fisica Matematica (A.A. 2018/2019) (1°, 2° LM)
- Storia della Matematica (A.A. 2018/2019) (3° LT; 1°, 2° LM)
Curriculum
Claudio Bartocci teaches geometry, mathematical physics and history of mathematics at the Università di Genova (Italy). He received his Dottorato in matematica (1990) from the Università di Milano and his Ph.D. in mathematics (1993) from the University of Warwick.
His recent research interests are the in the following areas:
• Geometry and mathematical physics: moduli spaces of sheaves on complex surfaces; quiver varieties; Fourier-Mukai and Nahm transforms;
geometry of integrable systems; bi-Hamiltonian structures; special-Kähler geometry; applications to gauge theory and to string theories.
• History of mathematics in the 19th and 20th centuries; philosophical aspects of the relationship between geometry and physics;
• Connections between mathematics and literature in the 20th century (in particular, Musil, Valéry, Queneau, Perec, Gadda, Sinisgalli).
He also writes for the general public.
For a detailed cv click here
Pubblicazioni
Books
M1. C.B., U. Bruzzo, D. Hernández Ruipérez, The geometry of supermanifolds, Mathematics and its applications vol. 71, Kluwer Academic Publishers, Dordrecht/ Boston/London 1991.
M2. C.B., U. Bruzzo, D. Hernández Ruipérez, Fourier-Mukai and Nahm transforms in geometry and mathematical physics, Progress in Mathematics vol. 276, Birkhäuser, Boston 2009.
M3. C.B., Una piramide di problemi. Storie di geometria da Gauss a Hilbert, [A pyramid of problems. Stories about geometry from Gauss to Hilbert], Raffaello Cortina, Milano 2012; English revised edition, Birkhäuser, Boston, forthcoming.
M4. C.B., Dimostrare l’impossibile [Proving what is impossible], Raffaello Cortina, Milano 2014 (finalist for the 2015 “Premio Galileo”).
M5. C.B., P. Martin, A. Tagliapietra, Zerologia. Sullo zero, il vuoto e il nulla, il Mulino, Bologna 2016.
Proceedings
P1. Proceedings of the XIX International Conference on Differential Geometric Methods in Theoretical Physics (Rapallo, 19-24/VI/1990), ed. by C.B., U. Bruzzo, R. Cianci, “Lectures Notes in Physics", 375, Springer-Verlag, Berlin 1991.
P2. New trends in geometry, and its role in natural and living sciences, ed. by C.B., L. Boi, C. Sinigaglia, Imperial College Press, London 2011 [cf. S22].
Exhibition catalogue
E1. C.B. & L. Civalleri, Numeri [Numbers], Codice, Torino 2014.
Edited books
O1. H. Poincaré, Geometria e caso: scritti scientifici [Geometry and chance: scientific writings], ed. by C.B., Bollati Boringhieri, Torino 1995 (reprinted 2005, 2009) [cf. S1].
O2. AA VV, Racconti matematici [Mathematical tales], ed. by C.B., Einaudi, Torino 2006 [cf. S11].
O3. T. Kuhn, La tensione essenziale e altri saggi [The essential tension and other essays], ed. by C.B. and G. Giorello, Einaudi, Torino 2006 [cf. S9].
O4. C.B., R. Betti, A. Guerraggio e R. Lucchetti (eds), Vite matematiche. Protagonisti del '900 da Hilbert a Wiles, Springer, Milano 2007; English translation: Mathematical lives. Protagonists of the Twentieth Century Form Hilbert to Wiles, Springer, Berlin-Heidelberg 2010 [cf. S6, S13, S14].
O5-O8. C.B. e P. Odifreddi (general eds), La matematica [Mathematics], advisory board: Sir Michael Atiyah, A. Connes, F. Dyson, Yu. Manin, D. Mumford, H. Putnam, S. Smale:
O5. Vol 1. I luoghi e i tempi [Places and times], Einaudi, Torino 2007; French translation: La mathématique. Les lieux et les temps, CNRS Éditions, Paris 2009;
O6. Vol 2. Problemi e teoremi [Problems and theorems], ed. by C.B., Einaudi, Torino 2008;
O7. Vol. 3. Suoni, forme parole [Suonds, shapes, words], ed. by C.B.,,Einaudi, Torino, 2011;
O8. Vol. 4. Pensare il mondo [Thinking the world], ed. by C.B., Einaudi, Torino, 2010.
Edited Journal Issues
J1. Gödel (ed. by C.B. & R. Lucchetti), Lettera Matematica Pristem, 62-63 (2007).
J2. Henri Poincaré (ed. by C.B.), Lettera Matematica Pristem, 84-85 (2013).
Research articles in mathematics (geometry, mathematical physics)
A1. C.B., U. Bruzzo, Cohomology of supermanifolds, Journal of Mathematical Physics, 28 (1987), 2363-2368.
A2. C.B., U. Bruzzo, Some remarks on the differential-geometric approach to supermanifolds, Journal of Geometry and Physics, 4 (1987), 391-404.
A3. C.B., U. Bruzzo, Cohomology of the structure sheaf of real and complex supermanifolds, Journal of Mathematical Physics, 29 (1988), 1789-1795 (Erratum, Journal of Mathematical Physics, 30 (1989), 1951).
A4. C.B., U. Bruzzo, Cohomological methods in supermanifold theory, in: Group theoretical methods in physics (Varna, 1987), Lecture Notes in Phys. 313, H.D. Doebner, J.D. Hennig and T.D. Palev eds, Springer-Verlag, Berlin, 1988, pp. 109-115.
A5. C.B., Foundations of super vector bundles, in: Proceedings of the conference on differential geometry and its applications (Dubrovnik, 26/6 - 3/7/1988), E. Bolkan et al. eds, University of Novi Sad, Novi Sad, 1989, pp. 15-21.
A6. C.B., U. Bruzzo, Existence of connections on superbundles, Letters in Mathematical Physics, 17 (1989), 61-68.
A7. C.B., U. Bruzzo, Super line bundles, Letters in Mathematical Physics, 17 (1989), 263-274.
A8. C.B., U. Bruzzo, D. Hernández Ruipérez, A remark on a new category of supermanifolds, Journal of Geometry and Physics, 6 (1989), 509-516.
A9. C.B., U. Bruzzo, G. Landi, Geometry of standard constraints and Weil triviality in supersymmetric gauge theories, Letters in Mathematical Physics, 18 (1989), 235-245.
A10. C.B., U. Bruzzo, On DeWitt supermanifolds and their Picard variety, Comptes Rendus de l'Académie des Sciences Sér. I Mathématiques, 309 (1989),75-80.
A11. C.B., Some topics in the theory of super line bundles, in: Proceedings of the 8th Italian conference on general relativity and gravitational physics (Cavalese,1988), M. Cerdonio et al. eds, World Scientific 1989, pp. 582-588.
A12. C.B., U. Bruzzo, G. Landi, Cohomology of supermanifolds, standard constraints and quantum anomalies, in: Proceedings of the XVIIth International Conference on Differential-Geometric Methods in Theoretical Physics (Chester,12-19/8/1988), A.I. Solomon ed., World Scienti c 1989, pp. 185-196.
A13. C.B., U. Bruzzo, G. Landi, Chern-Simons forms on principal super fibre bundles, Journal of Mathematical Physics, 31 (1990), 45-54.
A14. C.B., U. Bruzzo, D. Hernández Ruipérez, Some results on line bundles over SUSY-curves, in: Differential geometric methods in theoretical physics (Proceedings, Tahoe City 1989), L.L. Chau and W. Nahm eds, Plenum Publ. Corp., New York, 1990, pp. 667-672.
A15. C.B., U. Bruzzo, D. Hernández Ruipérez, Products and vector bundles in the category of G-supermanifolds, Siberian mathematical Journal, 34 (1992), 1-9 [originally published in Russian: Proizvedeniya i vektornye rassloeniya v kategorii G-supermnogoobrazi, Sibirskii Matematicheskii Zhurnal, 34 (1991)].
A16. C.B., U. Bruzzo, D. Hernández Ruipérez, V.G. Pestov, An axiomatic approach to supermanifolds, Soviet Math. Doklady, 44 (1992), 744-747 [originally published in Russian: Ob aksiomaticheskom podhode k supermnogoobraziyam, Doklady Math. Akademii Nauk SSSR, 321 (1991), 649-652].
A17. C.B., U. Bruzzo, D. Hernández Ruipérez e V.G. Pestov, Foundations of supermanifold theory: the axiomatic approach, Differential Geometry and Its Applications, 3 (1993), 135-155.
A18. C.B., Instantons on K3 surfaces, in: Proceedings of the XIXth International Colloquium on Group Theoretical Methods in Physics, Anales de Física (Monografías), M.A. del Olmo et al. eds, Madrid 1993, vol. II, pp. 64-67.
A19. C.B., U. Bruzzo, D. Hernández Ruipérez, Fourier-Mukai transform and index theory, Manuscripta Mathematica, 85 (1994), 141-163.
A21. C.B., Mukai-Nahm transform on K3 surfaces, in: Proceedings of the 10th Italian conference on general relativity and gravitational physics (Bardonecchia, 1992), M. Francaviglia et al. eds, World Scienti c 1994, pp. 29-35.
A22. C.B., U. Bruzzo, M. Carfora, A. Marzuoli, Entropy of random coverings and 4-D quantum gravity, Journal of Geometry and Physics, 18 (1996), 247-294.
A23. C.B., U. Bruzzo, D. Hernández Ruipérez, A novel approach to the study of moduli spaces of instantons on K3 surfaces, in: Proceedings of the 11th Italian conference on general relativity and gravitational physics (Trieste, 26-30/IX/1994), M. Carfora et al. eds, World Scienti c 1996, pp. 73-87.
A24. C.B., U. Bruzzo, D. Hernández Ruipérez, V.G. Pestov, Supermanifold theory: towards a unifying approach, in: Proceedings of the IV Workshop de Outono: Xeometría diferencial e as suas aplicacións (Santiago de Campostela, 18-20/IX/1995), Anales de Física - Monografías 3, 1996, pp. 1-17.
A25. C.B., U. Bruzzo, D. Hernández Ruipérez, A Fourier-Mukai transform for stable bundles on K3 surfaces, Journal für die reine und angewandte Mathematik, 486 (1997), 1-16.
A26. C.B., U. Bruzzo, D. Hernández Ruipérez, Moduli of reflexive K3 surfaces, in: Complex Analysis and Geometry (Trento 1995), V. Ancona et al. eds, Pitman Research Notes in Mathematics 366, Longman, Harlow 1997, pp. 60-68.
A27. C.B., U. Bruzzo, D. Hernández Ruipérez, V.G. Pestov, Quotient supermanifolds, Bulletin of the Australian Mathematical Society, 58 (1998), 107-120.
A28. C.B., U. Bruzzo, D. Hernández Ruipérez, Existence of µ-stable bundles on K3 surfaces and the Fourier-Mukai transform, in: Algebraic Geometry (Catania 1993/Barcelona 1994), P. Newstead ed., Lecture Notes in Pure and Appl. Math. 200, M. Dekker, New York 1998, pp. 245-257.
A29. C.B., U. Bruzzo, D. Hernández Ruipérez, A hyperkähler Fourier transform, Differential Geometry and its Applications, 8 (1998), 239-249.
A30. C.B., U. Bruzzo, D. Hernández Ruipérez, J. Muñoz Porras, Mirror symmetry on K3 surfaces via Fourier-Mukai transform, Communications in Mathematical Physics, 195 (1998), 79-93.
A31. C.B., U. Bruzzo, G. Sanguinetti, Categorial mirror symmetry for K3 surfaces, Communications in Mathematical Physics, 206 (1999), 265-272.
A32. C.B., I. Biswas, Higgs bundles and the Fourier-Mukai transform, Southeast Asian Bulletin of Mathematics, 25 (2001), 201-207.
A33. C.B., U. Bruzzo, D. Hernández Ruipérez, J. Muñoz Porras, Relatively stable bundles over elliptic fibrations, Mathematische Nachrichten, 238 (2002), 23-36.
A34. C.B., La geometria dei sistemi integrabili, Lettera Matematica Pristem, 44, giugno 2002, pp. 22-28.
A35. C.B., M. Jardim, A Nahm transform for instantons over ALE spaces, in: Clifford Algebras: Applications to Mathematics, Physics, and Engineering, R. Ablamowicz, ed., Progress in Mathematical Physics, Birkhäuser, Boston, 2003, 155-166.
A36. C.B., I. Mencattini, Hyper-symplectic structures on integrable systems, Journal of Geometry and Physics, 50 (2004), 339-444.
A37. C.B., M. Jardim, Hyperkähler Nahm transforms, in: Algebraic structures and moduli spaces, H. Nakajima and E. Markman eds., CRM Proceedings & Lectures Notes, AMS, 2004, pp. 150-159.
A38. C.B., G. Falqui, M. Pedroni, A geometric interpretation of the separability of the Neumann-Rosochatius system, Differential Geometry and its Applications, 21 (2004), 349-360.
A39. C.B., E. Macrì, Classification of Poisson surfaces, Communications in Contemporary Mathematics, 7 (2005), 1-7.
A40. C.B., I. Mencattini, Some remarks on special Kähler manifolds, Journal of Geometry and Physics, 59 (2009), 755-763.
A41. C.B., G. Falqui, I. Mencattini, G. Ortenzi, M. Pedroni, On the geometric origin of the bi-hamiltonian structure of the Calogero-Moser system, International Mathematical Research Notices, International Mathematics Research Notices, (2010) 2010, 279-296.
A42. C.B., U. Bruzzo, C. Rava, Moduli spaces of framed sheaves on Hirzebruch surfaces, Advances in Geometry, 15 (2015), 55-76.
A43. C.B., U. Bruzzo, V. Lanza, C. Rava, ADHM data for the Hilbert scheme of points of the total space of , arXiv:1403.0460 (2014).
A44. C.B., U. Bruzzo, V. Lanza, C. Rava, Hilbert scheme of as quiver varieties, arXiv:1504.02987 (2015).
A45. C.B., A. Tacchella, Poisson-Nijenhuis structures on quiver path algebras, arXiv:1604.02012 (2016).
A46. C.B., U. Bruzzo, C. Rava, Erratum to “Monads for framed sheaves on Hirzebruch surfaces”, Advances in Geometry (2016), to appear (4 pp.).
A47. C.B., V. Lanza, C. Rava, Moduli spaces of framed sheaves and quiver varieties (2016).
Other articles and essays (history of mathematics, philosophy of science, literature and mathematics, expository papers, and miscellanea)
S1. C.B., Equazioni e orbite celesti [Equations and celestial orbits], introduction to: H. Poincaré, Geometria e caso: scritti scientifici [Geometry and chance: scientific writings], ed. by C. Bartocci, Bollati Boringhieri, Torino 1995, pp. I-L
S2. C.B. La geometria del sapere [The geometry of knowledge], preface to: H. Poincaré, Scienza e metodo [Science and method], ed. by C. Bartocci, Einaudi, Torino 1997, pp. 1-15.
S3. C.B., Ricordo di André Weil [A souvenir of André Weil], Lettera matematica Pristem, 36, 2000, p. 57.
S4. C.B., L’ombra negata. Dimostrazioni matematiche e immaginazione visiva [The shadow denied. Mathematical proofs and visual imagination], in: Il pensiero visivo, Atti del convegno (Villa Reale, Monza, 15-17 marzo 2001), ed. by G. Di Napoli, Istituto statale d'Arte, Monza 2002, pp. 129-147
S5. C.B., Il mondo è matematico? [Is the world mathematical?], in AA. VV. La matematica della natura, Erga edizioni, Genova 2004, pp. 17-38
S6. C.B., L’audacia dell'intelligenza. L'immaginario matematico dell’ Uomo senza qualità, Lettera Matematica Pristem, 50-51, 2004, 32-39; revised version in: Vite matematiche. Protagonisti del '900 da Hilbert a Wiles, a cura di C.B., R. Betti, A. Guerraggio e R. Lucchetti, Springer, Milano 2007, pp. 111-127; Engl. translation, Robert Musil. The Audacity of Intelligence, in: Mathematical lives. Protagonists of the Twentieth Century Form Hilbert to Wiles, Springer, Berlin-Heidelberg 2010, pp. 79-90.
S7. C.B., Alle origini del mito di Einstein [At the origins of Einstein’s myth], preface to: A. Einstein, Il lato umano, ed. by H. Dukas and B. Hoffmann, Einaudi, Torino 2005, pp. VII-XIV.
S8. C.B., Geometria e fisica nell’Ottocento. Gauss, Riemann, Helmholtz [Geometry and physics in the 19th century, Gauss, Riemann, Helmholtz], in: La scienza, vol. XI, directed by E. Bellone, Utet-La Repubblica, 2005, pp. 507-525.
S9. C.B. e G. Giorello, Tradizione e iconoclastia [Tradition and iconoclasm], introduction to: T. Kuhn, La tensione essenziale e altri saggi, Einaudi, Torino 2006, pp. VII-XXXI.
S10. C.B., Laicità e ricerca scientifica [Secularism and scientific research], in: Laicità, ed. by G. Boniolo, Einaudi, Torino 2006, pp. 97-113.
S11. C.B., Introduction to Racconti matematici, Einaudi, Torino 2006, pp. I - XXVII.
S12. C.B. e L. Guzzardi, L’irrealtà del tempo: Kant, Einstein e gli universi rotanti di Kurt Gödel [The irreality of time: Kant, Einstein, and Kurt Gödel’s rotating universes], Lettera Matematica Pristem, 62-63, 2007, pp. 69-78.
S13. C.B., Michael F. Atiyah: le ragioni profonde della matematica, in: Vite matematiche. Protagonisti del '900 da Hilbert a Wiles, a cura di C.B., R. Betti, A. Guerraggio e R. Lucchetti, Springer, Milano 2007, pp. 275-291; Engl. translation, Michael F. Atiyah. Mathematics’ deep reasons, in: Mathematical lives. Protagonists of the Twentieth Century Form Hilbert to Wiles, Springer, Berlin-Heidelberg 2010, pp. 197-208.
S14. C.B., Interview with Andrew Wiles, in Mathematical lives. Protagonists of the Twentieth Century Form Hilbert to Wiles, Springer, Berlin-Heidelberg 2010, pp. 231-235.
S15. C.B., Comunicare la scienza [Communicating science], in: Matematici al lavoro, E. Del Prete, A. Russo e G. Anzellotti, Sironi, Milano 2008, pp. 65-69.
S16. C.B., Il tempo cosmico da Einstein a Gödel [Cosmic time from Einstein to Gödel], in: Manca qualche passaggio? Sei lezioni su Einstein e Lucrezio, ed. by G. Martufi, Cafoscarina, Venezia 2008, pp. 97-121.
S17. C.B., Chi crede ancora nell’unità della natura? [Who still believes in Nature’s unity?], in: Idea di natura, ed. by E. Cadelo, Marsilio, Venezia 2008, pp. 49-58.
S18. C.B., L’anima dell’esattezza: intrecci tra matematica e letteratura [The soul of precision: intertwinings between mathematics and literature], SissaNews, luglio 2008, pp. 11-12.
S19. C.B., Sinisgalli e la civiltà delle macchine [Sinisgalli and the “civiltà delle macchine”], Lettera Matematica Pristem, 69 (2008), pp. 68-69.
S20. C.B., La chiocciola e la spirale [The snail shell and the spiral], in Un “Leonardo” del Novecento: Leonardo Sinisgalli (1908-1981), G.I. Bischi and P. Nastasi eds., Pristem Storia 23-24, 2009, pp. 127-140.
S21. C.B., Raccontare mondi possibili: letteratura e matematica [Tales about possible worlds: literature and mathematics], in: Cavalcare la luce. Scienza e letteratura. Atti del Convegno Internazionale, Alessandria 23-25 maggio 2007, ed. by G. Ioli, Interlinea Edizioni, Novara 2009, pp. 141-146.
S21. C.B., La dimensione più misteriosa, in: Gino De Dominicis. L’immortale (Catalogue of an exhibition held at the MAXXI, Museo nazionale delle arti del XXI secolo, Rome, Italy, May 30-Nov. 7, 2010), a cura di A. Bonito Oliva, Electa, Milano 2010, pp. 63-67; Engl. translation, The most mysterious dimension, in: Gino De Dominicis. The Immortal, ed. by A. Bonito Oliva, Electa, Milan 2010.
S22. C.B., “Dimenticare differenze” [“Forgetting differences”], in: Maria Morganti, Un diario tira l’altro. Condivisione, Corraini, Mantova 2010, pp. 23-25.
S23. C.B. and U. Bruzzo, The emergence of algebraic geometry in contemporary physics, in: New trends in geometry, and its role in natural and living sciences, edited by C.B., L. Boi, C. Sinigaglia, Imperial College Press, London 2011.
S24. C.B., Geometrie vittoriane [Victorian geometries], introduction to a: Edwin A. Abbott, Flatlandia, translated by F. Oddera, Einaudi, Torino 2011, pp. V-XXXI.
S25. C.B., Scienza e filosofia: un divorzio italiano [Science and philosophy: an Italian divorce], in: Atlante della letteratura italiana, a cura di S. Luzzatto e G. Pedullà, vol. III. Dal Romanticismo a oggi, a cura di D. Scarpa, Einaudi, Torino 2012, pp. 448-453.
S26. C.B., “Ragionare bene su figure disegnate male”: la nascita della topologia algebrica, Lettera Matematica, 84-85 (2013), pp. 22-31; Engl. transl. “Reasoning well from badly drawn figures”: the birth of algebraic topology, Lettera Matematica International Edition, 1 (2013), pp. 13-22.
S27. C.B. and G. Giorello, “Il Grande Compagno è morto” [“The Great Companion is dead”], introduction to: W.K. Clifford, Etica, scienza e fede, Bollati Boringhieri, Torino 2013, pp. 7-43.
S28. L. Barbieri Viale and C.B., Il potere dell’innocenza [The power of innocence], in: Matematica ribelle. Le due vite di Alexander Grothendieck, Corriere della Sera Grandi Saggi, Milano 2014, pp. 49-62.
S29. C.B., Analogy and invention. Some remarks on Poincaré’s Analysis situs papers, in: Proceedings of the International Colloquium “The Philosophers and Mathematics” (Lisboa, October 29-30, 2014), Springer, to appear.