Alberto Cattaneo
Italian mathematician and physicist (born 1967)
From Wikipedia, the free encyclopedia
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 |
| 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
After 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 the University of Milan (with Paolo Cotta-Ramusino). In 1998, he moved to University of Zurich's mathematics department as an assistant professor, and he became a 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
Cattaneo'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
Articles
- 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
- 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
- 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.