Brian Marcus is an American-born

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 ...

who works in Canada. He is a professor in the department of mathematics at the University of British Columbia (UBC), where he is the site director of the Pacific Institute for the Mathematical Sciences (PIMS), a fellow of the AMS and the

IEEE The Institute of Electrical and Electronics Engineers (IEEE) is an American 501(c)(3) organization, 501(c)(3) public charity professional organization for electrical engineering, electronics engineering, and other related disciplines. The IEEE ...

. He was the department head of mathematics at

UBC The University of British Columbia (UBC) is a Public university, public research university with campuses near University of British Columbia Vancouver, Vancouver and University of British Columbia Okanagan, Kelowna, in British Columbia, Canada ...

from 2002 to 2007 and the deputy director of PIMS from 2016 to 2018.

Education and academic career

Marcus earned his Ph.D. in 1975 from the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

(UC Berkeley); his supervisor was

Rufus Bowen Robert Edward "Rufus" Bowen (February 23, 1947 – July 30, 1978) was an American internationally known professor in the Department of Mathematics at the University of California, Berkeley, who specialized in dynamical systems theory. Bowen's wo ...

. He then worked as an

IBM International Business Machines Corporation (using the trademark IBM), nicknamed Big Blue, is an American Multinational corporation, multinational technology company headquartered in Armonk, New York, and present in over 175 countries. It is ...

Watson Postdoctoral Fellow, an associate professor at

UNC Chapel Hill The University of North Carolina at Chapel Hill (UNC, UNC–Chapel Hill, or simply Carolina) is a public research university in Chapel Hill, North Carolina, United States. Chartered in 1789, the university first began enrolling students in 1795 ...

and a researcher at IBM Research – Almaden. He additionally held visiting associate professor positions at UC Berkeley,

University of California, Santa Cruz The University of California, Santa Cruz (UC Santa Cruz or UCSC) is a public university, public Land-grant university, land-grant research university in Santa Cruz, California, United States. It is one of the ten campuses in the University of C ...

, and

Stanford University Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...

. From 2016 to 2018, he was the deputy director of the Pacific Institute for the Mathematical Sciences, where, as of 2019, he is the

Site Director. He is one of the representatives of the Pacific Rim Mathematical Association. His main areas of research are

ergodic theory Ergodic theory is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, "statistical properties" refers to properties which are expressed through the behav ...

symbolic dynamics In mathematics, symbolic dynamics is the study of dynamical systems defined on a discrete space consisting of infinite sequences of abstract symbols. The evolution of the dynamical system is defined as a simple shift of the sequence. Because of t ...

and

information theory Information theory is the mathematical study of the quantification (science), quantification, Data storage, storage, and telecommunications, communication of information. The field was established and formalized by Claude Shannon in the 1940s, ...

. He has published contributions in the theory of

horocycle In hyperbolic geometry, a horocycle ( from Greek roots meaning "boundary circle"), sometimes called an oricycle or limit circle, is a curve of constant curvature where all the perpendicular geodesics ( normals) through a point on a horocycle are ...

flows and

entropy Entropy is a scientific concept, most commonly associated with states of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the micros ...

. Marcus has written over seventy research papers, some of them published in ''

Annals of Mathematics The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as t ...

'', ''

Inventiones Mathematicae ''Inventiones Mathematicae'' is a mathematical journal published monthly by Springer Science+Business Media. It was established in 1966 and is regarded as one of the most prestigious mathematics journals in the world. The current (2023) managing ...

'' and '' Journal of the AMS''. His collaborators include Wolfgang Krieger,

Roy Adler Roy Lee Adler (February 22, 1931 – July 26, 2016) was an American mathematician. Adler earned his Ph.D. in 1961 from Yale University under the supervision of Shizuo Kakutani (''On some algebraic aspects of measure preserving transformations'') ...

Dominique Perrin Dominique Pierre Perrin (b. 1946) is a French mathematician and theoretical computer scientist known for his contributions to coding theory and to combinatorics on words. He is a professor of the University of Marne-la-Vallée and currently serv ...

Jack Wolf Jack Keil Wolf (March 14, 1935 – May 12, 2011) was an American researcher in information theory and coding theory. Biography Wolf was born in 1935 in Newark, New Jersey, and graduated from Weequahic High School in 1952. He received his unde ...

Yuval Peres Yuval Peres (; born 5 October 1963) is an Israeli mathematician best known for his research in probability theory, ergodic theory, mathematical analysis, theoretical computer science, and in particular for topics such as fractals and Hausdorff m ...

and Sheldon Newhouse. Marcus (with Doug Lind) wrote the book ''An Introduction to Symbolic Dynamics and Coding'' (currently with more than 3,000 citations on

Google Scholar Google Scholar is a freely accessible web search engine that indexes the full text or metadata of Academic publishing, scholarly literature across an array of publishing formats and disciplines. Released in Beta release, beta in November 2004, th ...

), and (with Susan Williams) the

Scholarpedia ''Scholarpedia'' is an English-language wiki-based online encyclopedia with features commonly associated with Open access (publishing), open-access online academic journals, which aims to have quality content in science and medicine. ''Scholarpe ...

article on

. In 1993, Marcus was awarded the Leonard J. Abraham Prize Paper award of the

. In 1999, he was elected as a fellow of the

. He was named 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 2018; the citation was "For contributions to dynamical systems, symbolic dynamics and applications to data storage problems, and service to the profession."

Selected publications

Books

* 1995: (with Doug Lind) ''An Introduction to Symbolic Dynamics and Coding'', Cambridge University Press .

Research papers

*Ergodic properties of horocycle flows for surfaces of negative curvature,

105 (1977), 81-105 . *with

: Unique ergodicity of horocycle foliations,

Israel Journal of Mathematics '' Israel Journal of Mathematics'' is a peer-reviewed mathematics journal published by the Hebrew University of Jerusalem ( Magnes Press). History Founded in 1963, as a continuation of the ''Bulletin of the Research Council of Israel'' (Section ...

26 (1977) 43-67 . *The horocycle flow is mixing of all degrees,

46 (1978)201-209 *with

: Topological entropy and equivalence of dynamical systems,

Memoirs of the American Mathematical Society ''Memoirs of the American Mathematical Society'' is a mathematical journal published by the American Mathematical Society and intended to carry peer-reviewed book-length research publications (monographs). As such, it has been described as havin ...

219 (1979) . *Topological conjugacy of horocycle flows,

American Journal of Mathematics The ''American Journal of Mathematics'' is a bimonthly mathematics journal published by the Johns Hopkins University Press. History The ''American Journal of Mathematics'' is the oldest continuously published mathematical journal in the United S ...

(1983) 623-632 *with Selim Tuncel: Entropy at a weight-per-symbol and an imbedding theorem for Markov chains,

102 (1990), 235-266 . *with Selim Tuncel: Matrices of polynomials, positivity, and finite equivalence of Markov chains,

Journal of the American Mathematical Society The ''Journal of the American Mathematical Society'' (''JAMS''), is a quarterly peer-reviewed mathematical journal published by the American Mathematical Society. It was established in January 1988. Abstracting and indexing This journal is abs ...

6 (1993), 131- 147 .

References

{{DEFAULTSORT:Marcus, Brian Living people 21st-century American mathematicians 20th-century American mathematicians Canadian mathematicians Fellows of the American Mathematical Society University of California, Berkeley alumni Academic staff of the University of British Columbia Fellows of the IEEE Year of birth missing (living people)

Education and academic career

Selected publications

Books

Research papers

See also

References