Albert Marden
American mathematician
From Wikipedia, the free encyclopedia
Albert Marden (born 18 November 1934) is an American mathematician, specializing in complex analysis and hyperbolic geometry. He is a son of another prominent mathematician, Morris Marden.
Albert Marden | |
|---|---|
| Born | 18 November 1934 Milwaukee, United States |
| Alma mater | Harvard University |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of Minnesota |
| Doctoral advisor | Lars Ahlfors |
Education and career
Marden received his PhD in 1962 from Harvard University with thesis advisor Lars Ahlfors.[1] Marden has been a professor at the University of Minnesota since the 1970s, where he is now professor emeritus. He was a member of the Institute for Advanced Study (IAS) in the academic year 1969–70, Fall 1978, and Fall 1987.[2]
His research deals with Riemann surfaces, quadratic differentials, Teichmüller spaces, hyperbolic geometry of surfaces and 3-manifolds, Fuchsian groups, Kleinian groups, complex dynamics, and low-dimensional geometric analysis.
Concerning properties of hyperbolic 3-manifolds, Marden formulated in 1974 the tameness conjecture,[3] which was proved in 2004 by Ian Agol and independently by a collaborative effort of Danny Calegari and David Gabai.[4]
In 1962, he gave a talk (as an approved speaker but not an invited speaker) on A sufficient condition for the bilinear relation on open Riemann surfaces at the International Congress of Mathematicians in Stockholm. In 2012 he was elected a Fellow of the American Mathematical Society. His doctoral students include Howard Masur.
Selected publications
Articles
- Marden, Albert (1974). "The geometry of finite generated kleinian groups". Ann. of Math. 99 (3): 383–462. doi:10.2307/1971059. JSTOR 1971059.
- with David B. A. Epstein: "Convex hulls in hyperbolic space, a theorem of Sullivan, and measured pleated surfaces". In: Analytical and geometric aspects of hyperbolic space (Warwick and Durham, 1984). London Math. Soc. Lecture Note Series, 111. Cambridge: Cambridge Univ. Press. 1987. pp. 113–253. ISBN 9780521339063.
- with Troels Jørgensen: Jørgensen, T; Marden, A (1990). "Algebraic and geometric convergence of Kleinian groups". Mathematica Scandinavica. 66 (1): 47–72. doi:10.7146/math.scand.a-12292. JSTOR 24492023.
- with Burt Rodin: Marden, Al; Rodin, Burt (1990). "On Thurston's formulation and proof of Andreev's theorem". In: Computational methods and function theory. Lecture Notes in Mathematics. Vol. 1435. Springer. pp. 103–115. doi:10.1007/BFb0087901. ISBN 978-3-540-52768-8.
- with Daniel Gallo and Michael Kapovich: Gallo, Daniel; Kapovich, Michael; Marden, Albert (2000). "The monodromy groups of Schwarzian equations on closed Riemann surfaces" (PDF). Annals of Mathematics. 151 (2): 625–704. arXiv:math/9511213. doi:10.2307/121044. JSTOR 121044. S2CID 8077145.
- with D. B. A. Epstein and V. Markovic: Epstein, D. B. A; Marden, A; Markovic, V (2004). "Quasiconformal homeomorphisms and the convex hull boundary". Ann. of Math. 159 (2004), no. 1 (2): 305–336. doi:10.4007/annals.2004.159.305. JSTOR 3597252.
Books
- with Richard Canary and David B. A. Epstein (editors): Fundamentals of hyperbolic geometry: selected exposures. Cambridge University Press. 2006. ISBN 9780521615587.
- Outer Circles. An introduction to hyperbolic 3 manifolds. Cambridge University Press. 2007. ISBN 9781139463768.[5]
- Hyperbolic manifolds: an introduction in 2 and 3 dimensions. Cambridge University Press. 2016. ISBN 9781316432525.[6]