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, structure, space, models, and change. History On ...

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 a 501(c)(3) professional association for electronic engineering and electrical engineering (and associated disciplines) with its corporate office in New York City and its operation ...

. He was the department head of mathematics at UBC 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 land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

(UC Berkeley); his supervisor was

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

. He then worked as an IBM Watson Postdoctoral Fellow, an associate professor at UNC Chapel Hill and a researcher at

IBM Research – Almaden IBM Research is the research and development division for IBM, an American Multinational corporation, multinational information technology company headquartered in Armonk, New York, with operations in over 170 countries. IBM Research is the larges ...

. 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. It is one of the ten campuses in the University of California syste ...

, and

Stanford University 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 consider ...

. From 2016 to 2018, he was the deputy director of the

Pacific Institute for the Mathematical Sciences The Pacific Institute for the Mathematical Sciences (PIMS) is a mathematical institute created in 1996 by universities in Western Canada and the Northwestern United States to promote research and excellence in all areas of the mathematical science ...

, where, as of 2019, he is the UBC Site Director. He is one of the representatives of the Pacific Rim Mathematical Association. His main areas of research are

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 ...

, symbolic dynamics 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 ...

. He has published contributions in the theory of

horocycle In hyperbolic geometry, a horocycle (), sometimes called an oricycle, oricircle, or limit circle, is a curve whose normal or perpendicular geodesics all converge asymptotically in the same direction. It is the two-dimensional case of a horosphere ...

flows and

entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...

. 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 the ...

'', ''

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 managing editors ...

'' and ''

Journal of the AMS 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 abstr ...

''. 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 science, 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 ...

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 under ...

Yuval Peres Yuval Peres ( he, יובל פרס; born 5 October 1963) is a mathematician known for his research in probability theory, ergodic theory, mathematical analysis, theoretical computer science, and in particular for topics such as fractals and Hausdo ...

and Sheldon Newhouse. Marcus (with

Doug Lind Doug Lind is an American mathematician specializing in ergodic theory and dynamical systems. He is a professor emeritus at the University of Washington. Lind was named as one of the inaugural fellows of the American Mathematical Society in 2013 ...

) 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 scholarly literature across an array of publishing formats and disciplines. Released in beta in November 2004, the Google Scholar index includes p ...

), and (with Susan Williams) the

Scholarpedia ''Scholarpedia'' is an English-language wiki-based online encyclopedia with features commonly associated with open-access online academic journals, which aims to have quality content in science and medicine. ''Scholarpedia'' articles are written ...

article on symbolic dynamics. 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

) ''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). Founded in 1963, as a continuation of the ''Bulletin of the Research Council of Israel'' (Section F), the jou ...

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 in six volumes per year, totalling approximately 33 individually bound numbers, by the American Mathematical Society. It is intended to carry papers on new mathema ...

219 (1979) . *Topological conjugacy of horocycle flows, American Journal of Mathematics (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 abstr ...

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 Fellow Members of the IEEE Year of birth missing (living people)

Education and academic career

Selected publications

Books

Research papers

See also

References