Biography:Alberto Cattaneo
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/ |
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.
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 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
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. doi:10.1063/1.531238. Bibcode: 1995JMP....36.6137C. https://aip.scitation.org/doi/abs/10.1063/1.531238.
- Cattaneo, Alberto S.; Felder, Giovanni; Tomassini, Lorenzo (2002). "From local to global deformation quantization of Poisson manifolds". Duke Mathematical Journal 115 (2). doi:10.1215/S0012-7094-02-11524-5. https://projecteuclid.org/journals/duke-mathematical-journal/volume-115/issue-2/From-local-to-global-deformation-quantization-of-Poisson-manifolds/10.1215/S0012-7094-02-11524-5.short.
- Cattaneo, A. S.; Indelicato, D. (2005). Formality and star products. 323. pp. 79–144. doi:10.5167/uzh-21691. ISBN 9780521615051.
- Cattaneo, Alberto S.; Felder, Giovanni (2007). "Relative formality theorem and quantisation of coisotropic submanifolds". Advances in Mathematics 208 (2): 521–548. doi:10.1016/j.aim.2006.03.010.
- Cattaneo, A. S. (2008). "Deformation quantization and reduction". Cont. Math. 450: 79–101. doi:10.5167/uzh-6703.
- Cattaneo, Alberto S.; Dherin, Benoit; Weinstein, Alan (2010). "Symplectic microgeometry I: Micromorphisms". Journal of Symplectic Geometry 8 (2): 205–223. doi:10.4310/JSG.2010.v8.n2.a4.
- 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. doi:10.1007/s00574-011-0027-2.
- 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. pp. 61–94. ISBN 978-3-0348-8364-1. https://books.google.com/books?id=TiPyBwAAQBAJ&pg=PA61.
- Cattaneo, Alberto S.; Mnev, Pavel; Reshetikhin, Nicolai (2012). "Classical and quantum Lagrangian field theories with boundary". arXiv:1207.0239 [math-ph].
- Cattaneo, Alberto S.; Dherin, Benoit; Weinstein, Alan (2013). "Symplectic microgeometry III: Monoids". Journal of Symplectic Geometry 11 (3): 319–341. doi:10.4310/JSG.2013.v11.n3.a1.
- 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. doi:10.1007/s11005-016-0907-x. Bibcode: 2017LMaPh.107..375C.
- Cattaneo, Alberto S.; Mnev, Pavel; Reshetikhin, Nicolai (2018). "Perturbative Quantum Gauge Theories on Manifolds with Boundary". Communications in Mathematical Physics 357 (2): 631–730. doi:10.1007/s00220-017-3031-6. Bibcode: 2018CMaPh.357..631C.
- 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. doi:10.1007/s00220-019-03591-5. Bibcode: 2019CMaPh.372..213C.
- Cattaneo, Alberto S.; Dherin, Benoit; Weinstein, Alan (2021). "Symplectic microgeometry, IV: Quantization". Pacific Journal of Mathematics 312 (2): 355–399. doi:10.2140/pjm.2021.312.355.
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. https://books.google.com/books?id=ieDuAAAAMAAJ.[7]
as editor
- Higher Structures in Geometry and Physics: In Honor of Murray Gerstenhaber and Jim Stasheff. 25 November 2010. ISBN 9780817647353. https://books.google.com/books?id=Co51gW-04lkC.
References
- ↑ 1.0 1.1 1.2 "Prof. Alberto S. Cattaneo". http://user.math.uzh.ch/cattaneo/.
- ↑ 2.0 2.1 "Alberto Cattaneo - The Mathematics Genealogy Project". https://www.genealogy.math.ndsu.nodak.edu/id.php?id=120224.
- ↑ Sanz-Solé, Marta, ed (2007). Proceedings of the International Congress of Mathematician 2006. Madrid: European Mathematical Society. pp. 339. https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM2006.2/ICM2006.2.ocr.pdf.
- ↑ "Fellows of the American Mathematical Society" (in en). https://www.ams.org/cgi-bin/fellows/fellows.cgi.
- ↑ Cattaneo, Alberto; Felder, Giovanni (2000). "A Path Integral Approach to the Kontsevich Quantization Formula". Communications in Mathematical Physics 212 (3): 591–611. doi:10.1007/s002200000229. Bibcode: 2000CMaPh.212..591C.
- ↑ Cattaneo, Alberto S.; Felder, Giovanni (2001). "Poisson sigma models and symplectic groupoids" (in en). Quantization of Singular Symplectic Quotients (Basel: Birkhäuser): 61–93. doi:10.1007/978-3-0348-8364-1_4. ISBN 978-3-0348-8364-1. https://link.springer.com/chapter/10.1007/978-3-0348-8364-1_4.
- ↑ "Déformation, Quantification, Théorie de Lie". https://bookstore.ams.org/pasy-20.
External links
- "Alberto Cattaneo, Lecture 1". CGI-Geometry of Strings and Fields. October 17, 2013. https://www.youtube.com/watch?v=9pnipvJbUIs.
- "Alberto Cattaneo, Lecture 2". CGI-Geometry of Strings and Fields. October 17, 2013. https://www.youtube.com/watch?v=c-K4s3djCGI.
- "Alberto Cattaneo: An introduction to the BV-BFV Formalism". Centre International de Rencontres Mathématiques. June 22, 2018. https://www.youtube.com/watch?v=0dqS_NYMml0.
- "Alberto Cattaneo | The BV-BFV Formalism". Nikita Nikolaev. April 24, 2020. https://www.youtube.com/watch?v=vF5h1j67uTc.
- "Alberto Cattaneo - AKSZ for General Relativity". Prague Mathematical Physics Seminar. December 2, 2020. https://www.youtube.com/watch?v=Q4GzSDMJrrs.
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