Benjamin Weiss ( he, בנימין ווייס; born 1941) is an American-Israeli mathematician known for his contributions
to
ergodic theory
Ergodic theory (Greek: ' "work", ' "way") is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, statistical properties means properties which are expres ...
,
topological dynamics In mathematics, topological dynamics is a branch of the theory of dynamical systems in which qualitative, asymptotic properties of dynamical systems are studied from the viewpoint of general topology.
Scope
The central object of study in topol ...
,
probability theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...
,
game theory
Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...
, and
descriptive set theory
In mathematical logic, descriptive set theory (DST) is the study of certain classes of "well-behaved" subsets of the real line and other Polish spaces. As well as being one of the primary areas of research in set theory, it has applications to ot ...
.
Biography
Benjamin ("Benjy") Weiss was born in New York City. In 1962 he received B.A. from
Yeshiva University
Yeshiva University is a private Orthodox Jewish university with four campuses in New York City.["About YU]
on the Yeshiva Universit ...
and M.A. from the Graduate School of Science,
Yeshiva University
Yeshiva University is a private Orthodox Jewish university with four campuses in New York City.["About YU]
on the Yeshiva Universit ...
. In 1965, he received his Ph.D. from
Princeton
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 ni ...
under the supervision of
William Feller
William "Vilim" Feller (July 7, 1906 – January 14, 1970), born Vilibald Srećko Feller, was a Croatian- American mathematician specializing in probability theory.
Early life and education
Feller was born in Zagreb to Ida Oemichen-Perc, a Cro ...
.
Academic career
Between 1965 and 1967, Weiss worked at the
IBM Research
IBM Research is the research and development division for IBM, an American multinational information technology company headquartered in Armonk, New York, with operations in over 170 countries. IBM Research is the largest industrial research org ...
. In 1967, he joined the faculty of the
Hebrew University of Jerusalem
The Hebrew University of Jerusalem (HUJI; he, הַאוּנִיבֶרְסִיטָה הַעִבְרִית בִּירוּשָׁלַיִם) is a public research university based in Jerusalem, Israel. Co-founded by Albert Einstein and Dr. Chaim Weiz ...
; and since 1990 occupied the Miriam and Julius Vinik Chair in Mathematics (Emeritus since 2009). Weiss held visiting positions at
Stanford
Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is considere ...
,
MSRI, and
IBM Research
IBM Research is the research and development division for IBM, an American multinational information technology company headquartered in Armonk, New York, with operations in over 170 countries. IBM Research is the largest industrial research org ...
Center.
Weiss published over 180 papers in
ergodic theory
Ergodic theory (Greek: ' "work", ' "way") is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, statistical properties means properties which are expres ...
,
topological dynamics In mathematics, topological dynamics is a branch of the theory of dynamical systems in which qualitative, asymptotic properties of dynamical systems are studied from the viewpoint of general topology.
Scope
The central object of study in topol ...
,
orbit equivalence,
probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...
,
information theory
Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist a ...
,
game theory
Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...
,
descriptive set theory
In mathematical logic, descriptive set theory (DST) is the study of certain classes of "well-behaved" subsets of the real line and other Polish spaces. As well as being one of the primary areas of research in set theory, it has applications to ot ...
; with notable contributions including introduction of
Markov partition
A Markov partition in mathematics is a tool used in dynamical systems theory, allowing the methods of symbolic dynamics to be applied to the study of hyperbolic dynamics. By using a Markov partition, the system can be made to resemble a discrete ...
s (with Roy Adler), development of ergodic theory of
amenable group
In mathematics, an amenable group is a locally compact topological group ''G'' carrying a kind of averaging operation on bounded functions that is invariant under translation by group elements. The original definition, in terms of a finitely addit ...
s (with Don Ornstein),
mean dimension (with Elon Lindenstrauss), introduction of
sofic subshifts and
sofic groups. The
road coloring conjecture In graph theory the road coloring theorem, known previously as the road coloring conjecture, deals with Synchronization, synchronized instructions. The issue involves whether by using such instructions, one can reach or locate an object or destinati ...
was also posed by Weiss with
Roy Adler.
One of Weiss's students is
Elon Lindenstrauss
Elon Lindenstrauss ( he, אילון לינדנשטראוס, born August 1, 1970) is an Israeli mathematician, and a winner of the 2010 Fields Medal.
Since 2004, he has been a professor at Princeton University. In 2009, he was appointed to Profess ...
, a 2010 recipient of the
Fields Medal
The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award ho ...
.
Awards and recognition
Weiss gave an invited address 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 ...
1974,
was twice the main speaker at a
Conference Board of Mathematical Sciences (1979 and 1995),
gave the M.B.Porter Distinguished Lecture Series at
Rice University
William Marsh Rice University (Rice University) is a Private university, private research university in Houston, Houston, Texas. It is on a 300-acre campus near the Houston Museum District and adjacent to the Texas Medical Center. Rice is ranke ...
(1998).
In 2000 Weiss was elected as a Foreign Honorary Member of the
American Academy of Arts and Sciences
The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and ...
.
In 2006 he was awarded the
Rothschild Prize
Yad Hanadiv (The Rothschild Foundation) is a Rothschild family philanthropic foundation in Israel.
Goals and objectives
Yad Hanadiv defines its mission as: Dedicated to creating resources for advancing Israel as a healthy, vibrant, democratic s ...
in Mathematics.
In 2012 Weiss 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, ...
.
List of Fellows of the American Mathematical Society
retrieved 2013-09-01.
See also
* Daniel Rudolph
Daniel Jay Rudolph (1949–2010) was a mathematician who was considered a leader in ergodic theory and dynamical systems. He studied at Caltech and Stanford and taught postgraduate mathematics at Stanford University, the University of Mary ...
- contemporary of and academic collaborator with Weiss
References
{{DEFAULTSORT:Weiss, Benjamin
Living people
Israeli mathematicians
Dynamical systems theorists
Princeton University alumni
Hebrew University of Jerusalem faculty
Fellows of the American Mathematical Society
1941 births