Alberto 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.

Alberto Sergio Cattaneo
Alberto Cattaneo (right) with Ping Xu, Oberwolfach 2003
Born26 June 1967
Milan
NationalityItalian
Alma materUniversità degli Studi di Milano
Scientific career
FieldsMathematical Physics
InstitutionsUniversity of Zurich
ThesisTeorie topologiche di tipo BF ed invarianti dei nodi (1995)
Doctoral advisorMaurizio Martellini
Doctoral studentsThomas Willwacher
Websitehttps://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 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

Books

as editor

References
  1. "Prof. Alberto S. Cattaneo". Institut für Mathematik, Universität Zürich.
  2. "Alberto Cattaneo - The Mathematics Genealogy Project". www.genealogy.math.ndsu.nodak.edu. Retrieved 2022-06-18.
  3. 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.
  4. "Fellows of the American Mathematical Society". American Mathematical Society. Retrieved 2022-06-18.
  5. 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.
  6. Cattaneo, Alberto S.; Felder, Giovanni (2001). "Poisson sigma models and symplectic groupoids". Quantization of Singular Symplectic Quotients. Basel: Birkhäuser: 61–93. doi:10.1007/978-3-0348-8364-1_4. ISBN 978-3-0348-8364-1. S2CID 10248666.
  7. "Déformation, Quantification, Théorie de Lie". AMS Bookstore.
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