Alberto Cattaneo

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.{{Cite web |title=Alberto Cattaneo - The Mathematics Genealogy Project |url=https://www.genealogy.math.ndsu.nodak.edu/id.php?id=120224 |access-date=2022-06-18 |website=www.genealogy.math.ndsu.nodak.edu}}

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.

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.{{Cite book |url=https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM2006.2/ICM2006.2.ocr.pdf |title=Proceedings of the International Congress of Mathematician 2006 |publisher=European Mathematical Society |year=2007 |editor-last=Sanz-Solé |editor-first=Marta |editor-link=Marta Sanz-Solé |location=Madrid |pages=339 |editor-last2=Soria |editor-first2=Javier |editor-last3=Varona |editor-first3=Juan Luis |editor-last4=Verdera |editor-first4=Joan}} Cattaneo was elected a Fellow of the American Mathematical Society in 2013.{{Cite web |title=Fellows of the American Mathematical Society |url=https://www.ams.org/cgi-bin/fellows/fellows.cgi |access-date=2022-06-18 |website=American Mathematical Society |language=en}}

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.

With Giovanni Felder he developed a path integral interpretation of the deformation quantization of Poisson manifolds (introduced in 2003 by Maxim Kontsevich),{{cite journal |last1=Cattaneo |first1=Alberto |last2=Felder |first2=Giovanni |author-link2=Giovanni Felder |year=2000 |title=A Path Integral Approach to the Kontsevich Quantization Formula |journal=Communications in Mathematical Physics |volume=212 |issue=3 |pages=591–611 |arxiv=math/9902090 |bibcode=2000CMaPh.212..591C |doi=10.1007/s002200000229 |s2cid=8510811}} as well as a description of the symplectic groupoid integrating a Poisson manifold as an infinite-dimensional symplectic quotient.{{Cite book |last1=Cattaneo |first1=Alberto S. |last2=Felder |first2=Giovanni |chapter=Poisson sigma models and symplectic groupoids |author-link2=Giovanni Felder |date=2001 |title=Quantization of Singular Symplectic Quotients |chapter-url=https://link.springer.com/chapter/10.1007/978-3-0348-8364-1_4 |language=en |location=Basel |publisher=Birkhäuser |pages=61–93 |doi=10.1007/978-3-0348-8364-1_4 |isbn=978-3-0348-8364-1|s2cid=10248666 |arxiv=math/0003023 }}

He supervised 14 PhD students as of 2022.

• {{cite journal|url=https://aip.scitation.org/doi/abs/10.1063/1.531238|doi=10.1063/1.531238|title=Topological BF theories in 3 and 4 dimensions|year=1995|last1=Cattaneo|first1=Alberto S.|last2=Cotta-Ramusino|first2=Paolo|last3=Fröhlich|first3=Jürg|last4=Martellini|first4=Maurizio|journal=Journal of Mathematical Physics|volume=36|issue=11|pages=6137–6160|arxiv=hep-th/9505027|bibcode=1995JMP....36.6137C|s2cid=166350}}
• {{cite journal|url=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|arxiv=math/0012228| doi=10.1215/S0012-7094-02-11524-5|title=From local to global deformation quantization of Poisson manifolds|year=2002|last1=Cattaneo|first1=Alberto S.|last2=Felder|first2=Giovanni|last3=Tomassini|first3=Lorenzo|journal=Duke Mathematical Journal|volume=115|issue=2|s2cid=10201285}}
• {{cite book|arxiv=math/0403135|doi=10.5167/uzh-21691|year=2005|last1=Cattaneo|first1=A. S.|last2=Indelicato|first2=D.|title=Formality and star products|volume=323|pages=79–144|isbn=9780521615051|s2cid=17250747}}
• {{cite journal| arxiv=math/0501540 | doi=10.1016/j.aim.2006.03.010|doi-access=free|title=Relative formality theorem and quantisation of coisotropic submanifolds|year=2007|last1=Cattaneo|first1=Alberto S.|last2=Felder|first2=Giovanni|journal=Advances in Mathematics|volume=208|issue=2|pages=521–548|s2cid=10469717}}
• {{cite journal|arxiv=math/0701378|doi=10.5167/uzh-6703|year=2008|last1=Cattaneo|first1=A. S.|title=Deformation quantization and reduction|journal=Cont. Math.|volume=450|pages=79–101|s2cid=218971990}}
• {{cite journal|arxiv=0905.3574|doi=10.4310/JSG.2010.v8.n2.a4|title=Symplectic microgeometry I: Micromorphisms|year=2010|last1=Cattaneo|first1=Alberto S.|last2=Dherin|first2=Benoit|last3=Weinstein|first3=Alan|author-link3=Alan Weinstein|journal=Journal of Symplectic Geometry|volume=8|issue=2|pages=205–223|s2cid=50308861}}
• {{cite journal|arxiv=1103.0672|doi=10.1007/s00574-011-0027-2|title=Symplectic microgeometry II: Generating functions|year=2011|last1=Cattaneo|first1=Alberto S.|last2=Dherin|first2=Benoît|last3=Weinstein|first3=Alan|journal=Bulletin of the Brazilian Mathematical Society |series=New Series|volume=42|issue=4|pages=507–536|s2cid=44023383}}
• {{cite book |isbn=978-3-0348-8364-1 |chapter=Poisson sigma models and symplectic groupoids by A. Cattaneo and G. Felder |author-link3=Martin Schlichenmaier |title=Quantization of Singular Symplectic Quotients, eds. Landsman, Pflaum, & Schlichenmaier |year=2012 |chapter-url=https://books.google.com/books?id=TiPyBwAAQBAJ&pg=PA61 |pages=61–94 |last1=Landsman |first1=N. P. |last2=Pflaum |first2=Markus |last3=Schlichenmaier |first3=Martin|publisher=Birkhäuser }}
• {{cite book|arxiv=1207.0239|last1=Cattaneo|first1=Alberto S.|last2=Mnev|first2=Pavel|last3=Reshetikhin|first3=Nicolai|title=Proceedings of Proceedings of the Corfu Summer Institute 2011 — PoS(CORFU2011)|chapter=Classical and Quantum Lagrangian Field Theories with Boundary |year=2012|page=044 |doi=10.22323/1.155.0044 |doi-access=free }}
• {{cite journal|arxiv=1109.4789|doi=10.4310/JSG.2013.v11.n3.a1|title=Symplectic microgeometry III: Monoids|year=2013|last1=Cattaneo|first1=Alberto S.|last2=Dherin|first2=Benoit|last3=Weinstein|first3=Alan|journal=Journal of Symplectic Geometry|volume=11|issue=3|pages=319–341|s2cid=50637248}}
• {{cite arXiv|eprint=1602.00741|last1=Cattaneo|first1=Alberto S.|last2=Mnev|first2=Pavel|last3=Reshetikhin|first3=Nicolai|title=Perturbative BV theories with Segal-like gluing|year=2016|class=math-ph}}
• {{cite journal|arxiv=1607.02412|doi=10.1007/s11005-016-0907-x|title=On Time|year=2017|last1=Cattaneo|first1=Alberto S.|last2=Schiavina|first2=Michele|journal=Letters in Mathematical Physics|volume=107|issue=2|pages=375–408|bibcode=2017LMaPh.107..375C|s2cid=119145820}}
• {{cite journal|arxiv=1507.01221|doi=10.1007/s00220-017-3031-6|title=Perturbative Quantum Gauge Theories on Manifolds with Boundary|year=2018|last1=Cattaneo|first1=Alberto S.|last2=Mnev|first2=Pavel|last3=Reshetikhin|first3=Nicolai|journal=Communications in Mathematical Physics|volume=357|issue=2|pages=631–730|bibcode=2018CMaPh.357..631C|hdl=21.11116/0000-0004-0613-0|s2cid=119640108}}
• {{cite journal|arxiv=1807.11782|doi=10.1007/s00220-019-03591-5|title=Globalization for Perturbative Quantization of Nonlinear Split AKSZ Sigma Models on Manifolds with Boundary|year=2019|last1=Cattaneo|first1=Alberto S.|last2=Moshayedi|first2=Nima|last3=Wernli|first3=Konstantin|journal=Communications in Mathematical Physics|volume=372|issue=1|pages=213–260|bibcode=2019CMaPh.372..213C|s2cid=119605584}}
• {{cite journal|arxiv=2007.08167|last1=Cattaneo|first1=Alberto S.|last2=Dherin|first2=Benoit|last3=Weinstein|first3=Alan|title=Symplectic microgeometry, IV: Quantization|journal=Pacific Journal of Mathematics|year=2021|volume=312|issue=2|pages=355–399|doi=10.2140/pjm.2021.312.355|s2cid=220546201}}

• with Alain Bruguières, Bernhard Keller, Charles Torossian: {{cite book|title=Déformation, quantification, théorie de Lie|url=https://books.google.com/books?id=ieDuAAAAMAAJ|year=2005|series=Panoramas et Synthèse, tome 20|publisher=Société Mathématique de France|isbn=978-2-85629-183-2}}{{cite web|title=Déformation, Quantification, Théorie de Lie|website=AMS Bookstore|url=https://bookstore.ams.org/pasy-20}}

• {{cite book|url=https://books.google.com/books?id=Co51gW-04lkC|title = Higher Structures in Geometry and Physics: In Honor of Murray Gerstenhaber and Jim Stasheff|isbn = 9780817647353|editor1 = Cattaneo, Alberto S.|editor2 = Giaquinto, Anthony|editor3 = Xu, Ping|date = 25 November 2010| publisher=Springer }}

• {{cite web|title=Alberto Cattaneo, Lecture 1|date=October 17, 2013|publisher=CGI-Geometry of Strings and Fields|website=YouTube|url=https://www.youtube.com/watch?v=9pnipvJbUIs}}
• {{cite web|title=Alberto Cattaneo, Lecture 2|date=October 17, 2013|publisher=CGI-Geometry of Strings and Fields|website=YouTube|url=https://www.youtube.com/watch?v=c-K4s3djCGI}}
• {{cite web|title=Alberto Cattaneo: An introduction to the BV-BFV Formalism|date=June 22, 2018|publisher=Centre International de Rencontres Mathématiques|website=YouTube|url=https://www.youtube.com/watch?v=0dqS_NYMml0}}
• {{cite web|title=Alberto Cattaneo {{!}} The BV-BFV Formalism|date=April 24, 2020|publisher=Nikita Nikolaev|website=YouTube|url=https://www.youtube.com/watch?v=vF5h1j67uTc}}
• {{cite web|title=Alberto Cattaneo - AKSZ for General Relativity|date=December 2, 2020|publisher=Prague Mathematical Physics Seminar|website=YouTube|url=https://www.youtube.com/watch?v=Q4GzSDMJrrs}}

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Category:20th-century Italian mathematicians

Category:21st-century Italian mathematicians

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Category:21st-century Italian physicists

Category:Italian mathematical physicists

Category:University of Milan alumni

Category:Academic staff of ETH Zurich

Category:Fellows of the American Mathematical Society

Category:1967 births

Category:Living people