Giovanni Felder (18 November 1958 in

Aarau Aarau (, ) is a List of towns in Switzerland, town, a Municipalities of Switzerland, municipality, and the capital of the northern Swiss Cantons of Switzerland, canton of Aargau. The List of towns in Switzerland, town is also the capital of the dis ...

) is a Swiss mathematical physicist and mathematician, working at ETH Zurich. He specializes in algebraic and geometric properties of

integrable In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first i ...

models of

statistical mechanics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic be ...

and

quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...

Education and career

Felder attended school in

Lugano Lugano (, , ; lmo, label=Ticinese dialect, Ticinese, Lugan ) is a city and municipality in Switzerland, part of the Lugano District in the canton of Ticino. It is the largest city of both Ticino and the Italian-speaking southern Switzerland. Luga ...

and Willisau District. He studied physics at

ETH Zurich (colloquially) , former_name = eidgenössische polytechnische Schule , image = ETHZ.JPG , image_size = , established = , type = Public , budget = CHF 1.896 billion (2021) , rector = Günther Dissertori , president = Joël Mesot , ac ...

, where he graduated with M.Sc. in 1982 and with Ph.D. in 1986. His doctoral dissertation, entitled ''Renormalization Group, Tree Expansion, and Non-renormalizable Quantum Field Theories'', was supervised by

Jürg Fröhlich Jürg Martin Fröhlich (born 4 July 1946 in Schaffhausen) is a Swiss mathematician and theoretical physicist. He is best known for introducing rigorous techniques for the analysis of statistical mechanics models, in particular continuous symmetry ...

(and

Konrad Osterwalder Konrad Osterwalder (born June 3, 1942) is a Swiss mathematician and physicist, former Undersecretary-General of the United Nations, former Rector of the United Nations University (UNU), and Rector Emeritus of the Swiss Federal Institute of Techn ...

). Felder held postdoctoral positions from 1986 to 1988 at IHES, from 1988 to 1989 at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

, and from 1989 to 1991 at the Institute of Theoretical Physics, ETH Zurich. From 1991 to 1994 he became an assistant professor of mathematics at ETH Zurich. From 1994 to 1996 he worked as professor of mathematics at the

University of North Carolina The University of North Carolina is the multi-campus public university system for the state of North Carolina. Overseeing the state's 16 public universities and the NC School of Science and Mathematics, it is commonly referred to as the UNC Sy ...

. In 1996 he returned at ETH Zurich as professor of mathematics. Since 2013 he is the director of the Institute for Theoretical Studies at ETH Zurich. In 1994 Felder was an invited speaker 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 Nevanlinna Prize (to be rename ...

in Zurich. He was elected member of the

Academia Europaea The Academia Europaea is a pan-European Academy of Humanities, Letters, Law, and Sciences. The Academia was founded in 1988 as a functioning Europe-wide Academy that encompasses all fields of scholarly inquiry. It acts as co-ordinator of Europea ...

in 2012 and 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

Felder's research involves mathematical problems motivated by physical ideas. In the late 1980s Felder did research with Krzysztof Gawedzki and

Antti Kupiainen Antti Kupiainen (born 23 June 1954, Varkaus, Finland) is a Finnish mathematical physicist. Education and career Kupiainen completed his undergraduate education in 1976 at the Technical University of Helsinki and received his Ph.D. in 1979 from Pri ...

on the geometry of the Wess-Zumino-Witten model in

conformal field theory A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometimes ...

. In 1989 he introduced a BRST approach to the "minimal two-dimensional conformal invariant models of Belavin,

Polyakov Polyakov or Poliakov, (russian: Поляко́в, uk, Поляко́в, he, פוליאקוב‎, be, Палякоў, Paliakoŭ), or Polyakova, Paliakova (feminine; ) is a Slavs, Slavic surname. It may be transliterated as ''Poliakoff''. Nota ...

and Zamolodchikov." With

Alexander Varchenko Alexander Nikolaevich Varchenko (russian: Александр Николаевич Варченко, born February 6, 1949) is a Soviet and Russian mathematician working in geometry, topology, combinatorics and mathematical physics. Education and c ...

and Vitaly Tarasov, Felder did research on various

models in

and

and resulting

special functions Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications. The term is defined by ...

(such as the

elliptic gamma function In mathematics, the elliptic gamma function is a generalization of the q-gamma function, which is itself the q-analog of the ordinary gamma function. It is closely related to a function studied by , and can be expressed in terms of the triple gamma ...

, elliptic

quantum groups In mathematics and theoretical physics, the term quantum group denotes one of a few different kinds of noncommutative algebras with additional structure. These include Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebras) ...

, and elliptic

Macdonald polynomials In mathematics, Macdonald polynomials ''P''λ(''x''; ''t'',''q'') are a family of orthogonal symmetric polynomials in several variables, introduced by Macdonald in 1987. He later introduced a non-symmetric generalization in 1995. Macdonald origi ...

). With Alberto Cattaneo in 2000 he gave a path integral interpretation of Kontsevich's deformation quantization of Poisson manifolds as well as a description of the

symplectic groupoid In differential geometry, a Poisson structure on a smooth manifold M is a Lie bracket \ (called a Poisson bracket in this special case) on the algebra (M) of smooth functions on M , subject to the Product rule, Leibniz rule : \ = \h + g \ . ...

integrating a

Poisson manifold In differential geometry, a Poisson structure on a smooth manifold M is a Lie bracket \ (called a Poisson bracket in this special case) on the algebra (M) of smooth functions on M , subject to the Leibniz rule : \ = \h + g \ . Equivalentl ...

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 ac ...

. He supervised 22 doctoral students as of 2022, including

Thomas Willwacher Thomas Hans Willwacher (born 12 April 1983) is a German mathematician and mathematical physicist working as a Professor at the Institute of Mathematics, ETH Zurich. Biography Willwacher completed his PhD at ETH Zurich in 2009 with a thesis on "C ...

References

External links

* * * {{DEFAULTSORT:Felder, Giovanni 20th-century Swiss mathematicians 21st-century Swiss mathematicians 20th-century Swiss physicists 21st-century Swiss physicists Mathematical physicists ETH Zurich alumni Academic staff of ETH Zurich Members of Academia Europaea Fellows of the American Mathematical Society 1958 births Living people