Brian Marcus
Brian Marcus is a mathematician, 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)[1], and a fellow of the AMS[2]. He was the Department Head of Mathematics at UBC from 2002 to 2007 [3] and the Deputy Director of PIMS from 2006 to 2008[1].
Education and academic career
Marcus earned his Ph.D. in 1971 from the University of California at Berkeley, under the supervision of Rufus Bowen [4]. He then worked as an IBM Watson Postdoctoral Fellow, an Associate Professor of Mathematics at UNC Chapel Hill and a Research Staff Member at IBM Research – Almaden. Also, he held visiting associate professor positions at UC Berkeley, UC Santa Cruz and Stanford University [1]. From 2016 to 2018, he was the Deputy Director of the PIMS [1], where currently he is the UBC Site Director. [5]. Also, he is one the representatives of the Pacific Rim Mathematical Association [6].
His main areas of research are ergodic theory, symbolic dynamics and information theory. In particular, he has published important contributions in the theory of Horocycle flows and Entropy. Marcus has written over seventy research papers, some of them published in the three most prestigious mathematics journals (Annals of Mathematics, Inventiones Mathematicae and Journal of the AMS). His collaborators include, Wolfgang Krieger, Roy Adler, Rufus Bowen, Dominique Perrin, Jack Wolf, Yuval Peres and Sheldon Newhouse [7], and he has supervised ten Ph.D. students [8]. Marcus (with Doug Lind) wrote the book An Introduction to Symbolic Dynamics and Coding [9] (currently with more than 3,000 citations on Google Scholar), and (with Susan Williams) the Scholarpedia article on Symbolic dynamics[10].
In 1993, Marcus was awarded the Leonard J. Abraham Prize Paper award of the IEEE [11]. In 2018, he was named a fellow of the American Mathematical Society [2].
Books
- 1995: (with Doug Lind) An Introduction to Symbolic Dynamics and Coding, Cambridge University Press doi:10.1017/CBO9780511626302.
Selected publications
- Ergodic properties of horocycle flows for surfaces of negative curvature, Annals of Mathematics 105 (1977), 81-105 doi:10.2307/1971026.
- with Rufus Bowen: Unique ergodicity of horocycle foliations, Israel Journal of Mathematics 26 (1977) 43-67 doi:10.1007/BF03007655.
- The horocycle flow is mixing of all degrees, Inventiones Mathematicae 46 (1978)201-209 doi:10.1007/BF01390274
- with Roy Adler: Topological entropy and equivalence of dynamical systems, Memoirs of the American Mathematical Society 219 (1979) doi:10.1090/memo/0219.
- Topological conjugacy of horocycle flows, American Journal of Mathematics (1983) 623-632 doi:10.2307/2374316
- with Selim Tuncel: Matrices of polynomials, positivity, and finite equivalence of Markov chains, Journal of the American Mathematical Society 6 (1993), 131- 147 doi:10.1090/S0894-0347-1993-1168959-X .
- with Selim Tuncel: Entropy at a weight-per-symbol and an imbedding theorem for Markov chains, Inventiones Mathematicae 102 (1990), 235-266 doi:10.1007/BF01233428 .
References
- ↑ 1.0 1.1 1.2 1.3 "PIMS Board of Directors". Retrieved August 15, 2019. Cite error: Invalid
<ref>tag; name "pims" defined multiple times with different content - ↑ 2.0 2.1 "2018 Fellows of the AMS" (PDF). Retrieved August 15, 2019.
- ↑ "Annual Canadian meeting of chairs" (PDF). Retrieved August 15, 2019.
- ↑ "Geneaology of Rufus Bowen". Retrieved August 15, 2019.
- ↑ "PIMS Board of Directors". Retrieved August 15, 2019.
- ↑ "PRIMA Representatives". Retrieved August 15, 2019.
- ↑ "Publication list of Brian Marcus" (PDF). Retrieved August 15, 2019.
- ↑ "Geneaology of Brian Marcus". Retrieved August 15, 2019.
- ↑ "Symbolic Dynamics book". Retrieved August 15, 2019.
- ↑ "Scholarpedia: Symbolic Dynamics". Retrieved August 15, 2019.
- ↑ "Leonard G. Abraham Prize". Retrieved October 18 2019. Check date values in:
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