Michael Aizenman
Encyclopedia
Michael Aizenman is a mathematician
and a physicist
at Princeton University
working in the fields of mathematical physics
, statistical mechanics
, functional analysis
and probability theory
.
The highlights of his work include: the triviality
of a class of scalar
quantum field theories
in more than four dimensions; a description of the phase transition
in the Ising model
in three and more dimensions; the sharpness of the phase transition
in percolation theory
; a method for the study of spectral and dynamical localization for random Schrödinger operators; and insights concerning conformal invariance
in two-dimensional percolation.
M. Aizenman has been awarded several honors. Among them is the Norbert Wiener Prize (1990) of the Amer. Math. Soc.
and SIAM
for "his outstanding contribution of original and non-perturbative mathematical methods in statistical mechanics
by means of which he was able to solve several long open important problems concerning critical phenomena, phase transitions, and quantum field theory
.", and the
Dannie Heineman Prize in Mathematical Physics (2010), awarded by the APS and the AIP
.
He is also the recipient of the Brouwer Medal (2002) of the Dutch Math. Soc. and the Royal Dutch Acad. Sc.
, and of an honorary degree of the Université de Cergy-Pontoise
(2009). He is a member of the National Academy of Sciences
since 1997, and the editor-in-chief of the journal Communications in Mathematical Physics
since 2001.
Aizenman was an undergraduate at the Hebrew University of Jerusalem
. He was awarded his PhD in 1975 at Yeshiva University
(Belfer Graduate School of Science), New York
, with advisor Joel Lebowitz
. After postdoctoral appointments at the Courant Institute of Mathematical Sciences
of New York University
(1974–75), and Princeton University (1975–1977), with Elliott H. Lieb
, he was appointed Assistant Professor at Princeton. In 1982 he moved to Rutgers University
as Associate Professor and then full Professor. In 1987 he moved to the Courant Institute and in 1990 returned to Princeton
as Professor of Mathematics and Physics.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and a physicist
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...
at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
working in the fields of mathematical physics
Mathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...
, statistical mechanics
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
, functional analysis
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
and probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
.
The highlights of his work include: the triviality
Quantum triviality
In a quantum field theory, charge screening can restrict the value of the observable "renormalized" charge of a classical theory. Ifthe only allowed value of the renormalized charge is zero, the theory is said to be "trivial" or noninteracting...
of a class of scalar
Scalar (physics)
In physics, a scalar is a simple physical quantity that is not changed by coordinate system rotations or translations , or by Lorentz transformations or space-time translations . This is in contrast to a vector...
quantum field theories
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
in more than four dimensions; a description of the phase transition
Phase transition
A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....
in the Ising model
Ising model
The Ising model is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables called spins that can be in one of two states . The spins are arranged in a graph , and each spin interacts with its nearest neighbors...
in three and more dimensions; the sharpness of the phase transition
Phase transition
A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....
in percolation theory
Percolation theory
In mathematics, percolation theory describes the behavior of connected clusters in a random graph. The applications of percolation theory to materials science and other domains are discussed in the article percolation.-Introduction:...
; a method for the study of spectral and dynamical localization for random Schrödinger operators; and insights concerning conformal invariance
Riemann surface
In mathematics, particularly in complex analysis, a Riemann surface, first studied by and named after Bernhard Riemann, is a one-dimensional complex manifold. Riemann surfaces can be thought of as "deformed versions" of the complex plane: locally near every point they look like patches of the...
in two-dimensional percolation.
M. Aizenman has been awarded several honors. Among them is the Norbert Wiener Prize (1990) of the Amer. Math. Soc.
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
and SIAM
Society for Industrial and Applied Mathematics
The Society for Industrial and Applied Mathematics was founded by a small group of mathematicians from academia and industry who met in Philadelphia in 1951 to start an organization whose members would meet periodically to exchange ideas about the uses of mathematics in industry. This meeting led...
for "his outstanding contribution of original and non-perturbative mathematical methods in statistical mechanics
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
by means of which he was able to solve several long open important problems concerning critical phenomena, phase transitions, and quantum field theory
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
.", and the
Dannie Heineman Prize in Mathematical Physics (2010), awarded by the APS and the AIP
American Institute of Physics
The American Institute of Physics promotes science, the profession of physics, publishes physics journals, and produces publications for scientific and engineering societies. The AIP is made up of various member societies...
.
He is also the recipient of the Brouwer Medal (2002) of the Dutch Math. Soc. and the Royal Dutch Acad. Sc.
Royal Netherlands Academy of Arts and Sciences
The Royal Netherlands Academy of Arts and Sciences is an organisation dedicated to the advancement of science and literature in the Netherlands...
, and of an honorary degree of the Université de Cergy-Pontoise
Cergy-Pontoise University
Cergy-Pontoise University is a French university, in the Academy of Versailles.Cergy-Pontoise University is a public university and a leading centre of teaching and research, which welcomes 17,700 students and 1,500 international students interested in studying abroad.The university is ideally...
(2009). He is a member of the National Academy of Sciences
United States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
since 1997, and the editor-in-chief of the journal Communications in Mathematical Physics
Communications in Mathematical Physics
Communications in Mathematical Physics is a peer-reviewed academic journal published by Springer. The journal publishes papers in all fields of mathematical physics, but focuses particularly in Analysis related to condensed matter physics, statistical mechanics and quantum field theory, and in...
since 2001.
Aizenman was an undergraduate at the Hebrew University of Jerusalem
Hebrew University of Jerusalem
The Hebrew University of Jerusalem ; ; abbreviated HUJI) is Israel's second-oldest university, after the Technion – Israel Institute of Technology. The Hebrew University has three campuses in Jerusalem and one in Rehovot. The world's largest Jewish studies library is located on its Edmond J...
. He was awarded his PhD in 1975 at Yeshiva University
Yeshiva University
Yeshiva University is a private university in New York City, with six campuses in New York and one in Israel. Founded in 1886, it is a research university ranked as 45th in the US among national universities by U.S. News & World Report in 2012...
(Belfer Graduate School of Science), New York
New York
New York is a state in the Northeastern region of the United States. It is the nation's third most populous state. New York is bordered by New Jersey and Pennsylvania to the south, and by Connecticut, Massachusetts and Vermont to the east...
, with advisor Joel Lebowitz
Joel Lebowitz
Joel L. Lebowitz is a mathematical physicist widely acknowledged for his outstanding contributions to statistical physics, statistical mechanics and many other fields of Mathematics and Physics...
. After postdoctoral appointments at the Courant Institute of Mathematical Sciences
Courant Institute of Mathematical Sciences
The Courant Institute of Mathematical Sciences is an independent division of New York University under the Faculty of Arts & Science that serves as a center for research and advanced training in computer science and mathematics...
of New York University
New York University
New York University is a private, nonsectarian research university based in New York City. NYU's main campus is situated in the Greenwich Village section of Manhattan...
(1974–75), and Princeton University (1975–1977), with Elliott H. Lieb
Elliott H. Lieb
Elliott H. Lieb is an eminent American mathematical physicist and professor of mathematics and physics at Princeton University who specializes in statistical mechanics, condensed matter theory, and functional analysis....
, he was appointed Assistant Professor at Princeton. In 1982 he moved to Rutgers University
Rutgers University
Rutgers, The State University of New Jersey , is the largest institution for higher education in New Jersey, United States. It was originally chartered as Queen's College in 1766. It is the eighth-oldest college in the United States and one of the nine Colonial colleges founded before the American...
as Associate Professor and then full Professor. In 1987 he moved to the Courant Institute and in 1990 returned to Princeton
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
as Professor of Mathematics and Physics.