Jürg Martin Fröhlich (born 4 July 1946 in
Schaffhausen
Schaffhausen (; gsw, Schafuuse; french: Schaffhouse; it, Sciaffusa; rm, Schaffusa; en, Shaffhouse) is a town with historic roots, a municipality in northern Switzerland, and the capital of the canton of the same name; it has an estimate ...
) is a Swiss
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, structure, space, models, and change.
History
On ...
and
theoretical physicist
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experime ...
. He is best known for introducing rigorous techniques for the analysis of statistical mechanics models, in particular continuous symmetry breaking (infrared bounds), and for pioneering the study of topological phases of matter using low-energy effective field theories.
Biography
In 1965 Fröhlich began to study mathematics and physics at
Eidgenössischen Technischen Hochschule Zürich. In 1969, under
Klaus Hepp and Robert Schrader, he attained the
Diplom (“Dressing Transformations in Quantum Field Theory”), and in 1972 he earned a PhD from the same institution under Klaus Hepp. After postdoctoral visits to the
University of Geneva
The University of Geneva (French: ''Université de Genève'') is a public research university located in Geneva, Switzerland. It was founded in 1559 by John Calvin as a theological seminary. It remained focused on theology until the 17th centur ...
and
Harvard University
Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of high ...
(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 ...
), he took an assistant professorship in 1974 in the mathematics department of
Princeton University
Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ...
. From 1978 until 1982 he was a professor at
Institut des Hautes Études Scientifiques
The Institut des hautes études scientifiques (IHÉS; English: Institute of Advanced Scientific Studies) is a French research institute supporting advanced research in mathematics and theoretical physics. It is located in Bures-sur-Yvette, jus ...
in
Bures-sur-Yvette
Bures-sur-Yvette (, literally ''Bures on Yvette'') is a commune in the Essonne department in Île-de-France in northern France.
Geography
Bures-sur-Yvette is located in the Vallée de Chevreuse on the river Yvette, along which the RER line&nb ...
in Paris, and since 1982 he has been a professor for theoretical physics at ETH, where he founded the Center for Theoretical Studies.
Over the course of his career, Fröhlich has worked on
quantum field theory (including
axiomatic quantum field theory Axiomatic quantum field theory is a mathematical discipline which aims to describe quantum field theory in terms of rigorous axioms. It is strongly associated with functional analysis and operator algebras, but has also been studied in recent years ...
,
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 sometime ...
, and
topological quantum field theory
In gauge theory and mathematical physics, a topological quantum field theory (or topological field theory or TQFT) is a quantum field theory which computes topological invariants.
Although TQFTs were invented by physicists, they are also of mathe ...
), on the precise mathematical treatment of models of
statistical mechanics, on theories of
phase transition
In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states o ...
, on the
fractional quantum Hall effect
The fractional quantum Hall effect (FQHE) is a physical phenomenon in which the Hall conductance of 2-dimensional (2D) electrons shows precisely quantized plateaus at fractional values of e^2/h. It is a property of a collective state in which elec ...
, and on
non-commutative geometry.
Honors and awards
In 1991 he received with
Thomas Spencer the
Dannie Heineman prize, in 1997 he received the
Marcel Benoist Prize
The Marcel Benoist Prize, offered by the Marcel Benoist Foundation, is a monetary prize that has been offered annually since 1920 to a scientist of Swiss nationality or residency who has made the most useful scientific discovery. Emphasis is p ...
, in 2001 he won the
Max Planck Medal
The Max Planck medal is the highest award of the German Physical Society , the world's largest organization of physicists, for extraordinary achievements in theoretical physics. The prize has been awarded annually since 1929, with few exceptions, ...
of the Deutschen Physikalischen Gesellschaft, and in 2009 he was awarded the
Henri Poincaré Prize. He is a 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 ...
and the
Berlin-Brandenburg Academy of Sciences and Humanities
The Berlin-Brandenburg Academy of Sciences and Humanities (german: Berlin-Brandenburgische Akademie der Wissenschaften), abbreviated BBAW, is the official academic society for the natural sciences and humanities for the German states of Berlin a ...
. In 2012 he became 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 1978, Fröhlich gave an invited address to the
International Congress of Mathematicians in
Helsinki
Helsinki ( or ; ; sv, Helsingfors, ) is the capital, primate, and most populous city of Finland. Located on the shore of the Gulf of Finland, it is the seat of the region of Uusimaa in southern Finland, and has a population of . The city ...
(“On the mathematics of phase transitions”) and in 1994 at the plenary talk of the ICM in Zurich (“The
FQHE,
Chern–Simons Theory and Integral Lattices”). He also co-authored a book on
quantum triviality
In a quantum field theory, charge screening can restrict the value of the observable "renormalized" charge of a classical theory. If
the only resulting value of the renormalized charge is zero, the theory is said to be "trivial" or noninteracting. ...
. In 2020, he was elected international member of the
National Academy of Sciences.
Selected works
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See also
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Chern–Simons theory
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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 sometime ...
*
Fractional quantum Hall effect
The fractional quantum Hall effect (FQHE) is a physical phenomenon in which the Hall conductance of 2-dimensional (2D) electrons shows precisely quantized plateaus at fractional values of e^2/h. It is a property of a collective state in which elec ...
*
Local quantum physics
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Noncommutative geometry
Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of ''spaces'' that are locally presented by noncommutative algebras of functions (possibly in some g ...
*
Quantum field theory
*
Quantum triviality
In a quantum field theory, charge screening can restrict the value of the observable "renormalized" charge of a classical theory. If
the only resulting value of the renormalized charge is zero, the theory is said to be "trivial" or noninteracting. ...
*
Topological quantum field theory
In gauge theory and mathematical physics, a topological quantum field theory (or topological field theory or TQFT) is a quantum field theory which computes topological invariants.
Although TQFTs were invented by physicists, they are also of mathe ...
References
External links
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{{DEFAULTSORT:Frohlich, Jurg
Swiss physicists
1946 births
Living people
Members of Academia Europaea
Fellows of the American Mathematical Society
Theoretical physicists
ETH Zurich alumni
ETH Zurich faculty
People from Schaffhausen
Foreign associates of the National Academy of Sciences
Winners of the Max Planck Medal
Swiss mathematicians