Italian mathematician and physicist (born 1967)
Alberto Sergio Cattaneo (26 June 1967 in Milan) 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.
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. Cattaneo was elected a Fellow of the American Mathematical Society in 2013.
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.
With Giovanni Felder he developed a path integral interpretation of the deformation quantization of Poisson manifolds (introduced in 2003 by Maxim Kontsevich), as well as a description of the symplectic groupoid integrating a Poisson manifold as an infinite-dimensional symplectic quotient.
He supervised 14 PhD students as of 2022.