Alberto Sergio Cattaneo (26 June 1967 in Milan)[1] is an Italian mathematician and mathematical physicist, specializing in geometry related to quantum field theory and string theory.
Alberto Sergio Cattaneo | |
|---|---|
 Alberto Cattaneo (right) with Ping Xu, Oberwolfach 2003 | |
| Born | 26 June 1967 Milan |
| Nationality | Italian |
| Alma mater | Università degli Studi di Milano |
| Scientific career | |
| Fields | Mathematical Physics |
| Institutions | University of Zurich |
| Thesis | Teorie topologiche di tipo BF ed invarianti dei nodi (1995) |
| Doctoral advisor | Maurizio Martellini |
| Doctoral students | Thomas Willwacher |
| Website | https://www.math.uzh.ch/cattaneo/ |
Biography
editAfter attending Liceo scientifico A. Volta in Milan, Cattaneo studied physics at University of Milan, graduating in 1991. In 1995 he obtained a PhD in theoretical physics at the same university; his thesis, entitled Teorie topologiche di tipo BF ed invarianti dei nodi (Topological BF theories and knot invariants), was supervised by Maurizio Martellini.[2]
Cattaneo worked as a postdoc in 1995-1997 at Harvard University (with Arthur Jaffe) and in 1997-1998 at University of Milan (with Paolo Cotta-Ramusino). In 1998 he moved to University of Zurich's mathematics department as assistant professor and he become full professor in 2003.[1]
In 2006 he was an invited speaker, with the talk From topological field theory to deformation quantization and reduction, at the International Congress of Mathematicians in Madrid.[3] Cattaneo was elected a Fellow of the American Mathematical Society in 2013.[4]
Research
editCattaneo's research interests include deformation quantization, symplectic and Poisson geometry, topological quantum field theories, and the mathematical aspects of perturbative quantization of gauge theories.[1]
With Giovanni Felder he developed a path integral interpretation of the deformation quantization of Poisson manifolds (introduced in 2003 by Maxim Kontsevich),[5] as well as a description of the symplectic groupoid integrating a Poisson manifold as an infinite-dimensional symplectic quotient.[6]
He supervised 14 PhD students as of 2022.[2]
Selected publications
editArticles
edit- Cattaneo, Alberto S.; Cotta-Ramusino, Paolo; Fröhlich, Jürg; Martellini, Maurizio (1995). "Topological BF theories in 3 and 4 dimensions". Journal of Mathematical Physics. 36 (11): 6137–6160. arXiv:hep-th/9505027. Bibcode:1995JMP....36.6137C. doi:10.1063/1.531238. S2CID 166350.
- Cattaneo, Alberto S.; Felder, Giovanni; Tomassini, Lorenzo (2002). "From local to global deformation quantization of Poisson manifolds". Duke Mathematical Journal. 115 (2). arXiv:math/0012228. doi:10.1215/S0012-7094-02-11524-5. S2CID 10201285.
- Cattaneo, A. S.; Indelicato, D. (2005). Formality and star products. Vol. 323. pp. 79–144. arXiv:math/0403135. doi:10.5167/uzh-21691. ISBN 9780521615051. S2CID 17250747.
- Cattaneo, Alberto S.; Felder, Giovanni (2007). "Relative formality theorem and quantisation of coisotropic submanifolds". Advances in Mathematics. 208 (2): 521–548. arXiv:math/0501540. doi:10.1016/j.aim.2006.03.010. S2CID 10469717.
- Cattaneo, A. S. (2008). "Deformation quantization and reduction". Cont. Math. 450: 79–101. arXiv:math/0701378. doi:10.5167/uzh-6703. S2CID 218971990.
- Cattaneo, Alberto S.; Dherin, Benoit; Weinstein, Alan (2010). "Symplectic microgeometry I: Micromorphisms". Journal of Symplectic Geometry. 8 (2): 205–223. arXiv:0905.3574. doi:10.4310/JSG.2010.v8.n2.a4. S2CID 50308861.
- Cattaneo, Alberto S.; Dherin, Benoît; Weinstein, Alan (2011). "Symplectic microgeometry II: Generating functions". Bulletin of the Brazilian Mathematical Society. New Series. 42 (4): 507–536. arXiv:1103.0672. doi:10.1007/s00574-011-0027-2. S2CID 44023383.
- Landsman, N. P.; Pflaum, Markus; Schlichenmaier, Martin (2012). "Poisson sigma models and symplectic groupoids by A. Cattaneo and G. Felder". Quantization of Singular Symplectic Quotients, eds. Landsman, Pflaum, & Schlichenmaier. Birkhäuser. pp. 61–94. ISBN 978-3-0348-8364-1.
- Cattaneo, Alberto S.; Mnev, Pavel; Reshetikhin, Nicolai (2012). "Classical and Quantum Lagrangian Field Theories with Boundary". Proceedings of Proceedings of the Corfu Summer Institute 2011 — PoS(CORFU2011). p. 044. arXiv:1207.0239. doi:10.22323/1.155.0044.
- Cattaneo, Alberto S.; Dherin, Benoit; Weinstein, Alan (2013). "Symplectic microgeometry III: Monoids". Journal of Symplectic Geometry. 11 (3): 319–341. arXiv:1109.4789. doi:10.4310/JSG.2013.v11.n3.a1. S2CID 50637248.
- Cattaneo, Alberto S.; Mnev, Pavel; Reshetikhin, Nicolai (2016). "Perturbative BV theories with Segal-like gluing". arXiv:1602.00741 [math-ph].
- Cattaneo, Alberto S.; Schiavina, Michele (2017). "On Time". Letters in Mathematical Physics. 107 (2): 375–408. arXiv:1607.02412. Bibcode:2017LMaPh.107..375C. doi:10.1007/s11005-016-0907-x. S2CID 119145820.
- Cattaneo, Alberto S.; Mnev, Pavel; Reshetikhin, Nicolai (2018). "Perturbative Quantum Gauge Theories on Manifolds with Boundary". Communications in Mathematical Physics. 357 (2): 631–730. arXiv:1507.01221. Bibcode:2018CMaPh.357..631C. doi:10.1007/s00220-017-3031-6. hdl:21.11116/0000-0004-0613-0. S2CID 119640108.
- Cattaneo, Alberto S.; Moshayedi, Nima; Wernli, Konstantin (2019). "Globalization for Perturbative Quantization of Nonlinear Split AKSZ Sigma Models on Manifolds with Boundary". Communications in Mathematical Physics. 372 (1): 213–260. arXiv:1807.11782. Bibcode:2019CMaPh.372..213C. doi:10.1007/s00220-019-03591-5. S2CID 119605584.
- Cattaneo, Alberto S.; Dherin, Benoit; Weinstein, Alan (2021). "Symplectic microgeometry, IV: Quantization". Pacific Journal of Mathematics. 312 (2): 355–399. arXiv:2007.08167. doi:10.2140/pjm.2021.312.355. S2CID 220546201.
Books
edit- with Alain Bruguières, Bernhard Keller, Charles Torossian: Déformation, quantification, théorie de Lie. Panoramas et Synthèse, tome 20. Société Mathématique de France. 2005. ISBN 978-2-85629-183-2.[7]
as editor
edit- Cattaneo, Alberto S.; Giaquinto, Anthony; Xu, Ping, eds. (25 November 2010). Higher Structures in Geometry and Physics: In Honor of Murray Gerstenhaber and Jim Stasheff. Springer. ISBN 9780817647353.
References
edit- ^ a b c "Prof. Alberto S. Cattaneo". Institut für Mathematik, Universität Zürich.
- ^ a b "Alberto Cattaneo - The Mathematics Genealogy Project". www.genealogy.math.ndsu.nodak.edu. Retrieved 2022-06-18.
- ^ Sanz-Solé, Marta; Soria, Javier; Varona, Juan Luis; Verdera, Joan, eds. (2007). Proceedings of the International Congress of Mathematician 2006 (PDF). Madrid: European Mathematical Society. p. 339.
- ^ "Fellows of the American Mathematical Society". American Mathematical Society. Retrieved 2022-06-18.
- ^ Cattaneo, Alberto; Felder, Giovanni (2000). "A Path Integral Approach to the Kontsevich Quantization Formula". Communications in Mathematical Physics. 212 (3): 591–611. arXiv:math/9902090. Bibcode:2000CMaPh.212..591C. doi:10.1007/s002200000229. S2CID 8510811.
- ^ Cattaneo, Alberto S.; Felder, Giovanni (2001). "Poisson sigma models and symplectic groupoids". Quantization of Singular Symplectic Quotients. Basel: Birkhäuser. pp. 61–93. arXiv:math/0003023. doi:10.1007/978-3-0348-8364-1_4. ISBN 978-3-0348-8364-1. S2CID 10248666.
- ^ "Déformation, Quantification, Théorie de Lie". AMS Bookstore.
External links
edit- "Alberto Cattaneo, Lecture 1". YouTube. CGI-Geometry of Strings and Fields. October 17, 2013.
- "Alberto Cattaneo, Lecture 2". YouTube. CGI-Geometry of Strings and Fields. October 17, 2013.
- "Alberto Cattaneo: An introduction to the BV-BFV Formalism". YouTube. Centre International de Rencontres Mathématiques. June 22, 2018.
- "Alberto Cattaneo | The BV-BFV Formalism". YouTube. Nikita Nikolaev. April 24, 2020.
- "Alberto Cattaneo - AKSZ for General Relativity". YouTube. Prague Mathematical Physics Seminar. December 2, 2020.