Alberto Sergio Cattaneo (26 June 1967 in
Milan
Milan ( , , ; ) is a city in northern Italy, regional capital of Lombardy, the largest city in Italy by urban area and the List of cities in Italy, second-most-populous city proper in Italy after Rome. The city proper has a population of nea ...
)
is an Italian
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
and
mathematical physicist
Mathematical physics is the development of mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the development of ...
, specializing in
geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
related to
quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...
and
string theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...
.
Biography
After attending ''
Liceo scientifico
''Liceo scientifico'' (; ) is a type of secondary school in Italy. It is designed to give students the skills to progress to any university or higher educational institution.Decreto del Presidente della Repubblica 89/2010 - ''Regolamento di r ...
'' ''A. Volta'' in Milan, Cattaneo studied physics at
University of Milan
The University of Milan (; ), officially abbreviated as UNIMI, or colloquially referred to as La Statale ("the State niversity), is a public university, public research university in Milan, Italy. It is one of the largest universities in Eu ...
, 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 invariant
In the mathematical field of knot theory, a knot invariant is a quantity (in a broad sense) defined for each knot which is the same for equivalent knots. The equivalence is often given by ambient isotopy but can be given by homeomorphism. Some i ...
s), was supervised by Maurizio Martellini.
Cattaneo worked as a postdoc in 1995-1997 at
Harvard University
Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...
(with
Arthur Jaffe
Arthur Michael Jaffe (; born December 22, 1937) is an American mathematical physicist at Harvard University, where in 1985 he succeeded George Mackey as the Landon T. Clay Professor of Mathematics and Theoretical Science.
Education and career ...
) and in 1997-1998 at University of Milan (with
Paolo Cotta-Ramusino). In 1998 he moved to
University of Zurich
The University of Zurich (UZH, ) is a public university, public research university in Zurich, Switzerland. It is the largest university in Switzerland, with its 28,000 enrolled students. It was founded in 1833 from the existing colleges of the ...
'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
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU).
The Fields Medals, the IMU Abacus Medal (known before ...
in
Madrid
Madrid ( ; ) is the capital and List of largest cities in Spain, most populous municipality of Spain. It has almost 3.5 million inhabitants and a Madrid metropolitan area, metropolitan area population of approximately 7 million. It i ...
. Cattaneo was elected a Fellow of the
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
in 2013.
Research
Cattaneo's research interests include
deformation quantization
In mathematics and physics, deformation quantization roughly amounts to finding a (quantum) algebra whose classical limit is a given (classical) algebra such as a Lie algebra or a Poisson algebra.
In physics
Intuitively, a deformation of a math ...
,
symplectic and
Poisson geometry
In differential geometry, a field in mathematics, a Poisson manifold is a smooth manifold endowed with a Poisson structure. The notion of Poisson manifold generalises that of symplectic manifold, which in turn generalises the phase space from Hami ...
,
topological quantum field theories
In gauge theory and mathematical physics, a topological quantum field theory (or topological field theory or TQFT) is a quantum field theory that computes topological invariants.
While TQFTs were invented by physicists, they are also of mathemati ...
, and the mathematical aspects of perturbative quantization of
gauge theories
In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, does not change under local transformations according to certain smooth families of operations (Lie groups). Formally, t ...
.
With
Giovanni Felder he developed a
path integral interpretation of the
deformation quantization of Poisson manifolds (introduced in 2003 by
Maxim Kontsevich
Maxim Lvovich Kontsevich (, ; born 25 August 1964) is a Russian and French mathematician and mathematical physicist. He is a professor at the Institut des Hautes Études Scientifiques and a distinguished professor at the University of Miami. He ...
), as well as a description of the
symplectic groupoid integrating a
Poisson manifold
In differential geometry, a field in mathematics, a Poisson manifold is a smooth manifold endowed with a Poisson structure. The notion of Poisson manifold generalises that of symplectic manifold, which in turn generalises the phase space from Hami ...
as an infinite-dimensional
symplectic quotient In mathematics, specifically in symplectic geometry, the momentum map (or, by false etymology, moment map) is a tool associated with a Hamiltonian action of a Lie group on a symplectic manifold, used to construct conserved quantities for the action. ...
.
He supervised 14 PhD students as of 2022.
Selected publications
Articles
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Books
* with Alain Bruguières,
Bernhard Keller, Charles Torossian:
as editor
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References
External links
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{{DEFAULTSORT:Cattaneo, Alberto
20th-century Italian mathematicians
21st-century Italian mathematicians
20th-century Italian physicists
21st-century Italian physicists
Italian mathematical physicists
University of Milan alumni
Academic staff of ETH Zurich
Fellows of the American Mathematical Society
1967 births
Living people