Albert Marden

Short description: American mathematician

Albert Marden

Born|  (1934-11-18) 18 November 1934 (age 91)

Milwaukee

Nationality| United States
Alma mater| Harvard University
Scientific career
Fields| Mathematics
Institutions| University of Minnesota
Doctoral advisor| Lars Ahlfors

Albert Marden (born 18 November 1934) is an American mathematician, specializing in complex analysis and hyperbolic geometry.

## Contents

* 1 Education and career
* 2 Selected publications
* 2.1 Articles
* 2.2 Books
* 3 References
* 4 External links

## 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.
* 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. https://books.google.com/books?id=OPA6AAAAIAAJ&pg=PA113.
* 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.
* 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. 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". Annals of Mathematics 151 (2): 625–704. doi:10.2307/121044. http://emis.de/journals/Annals/151_2/marden.pdf.
* 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.

### Books

* with Richard Canary and David B. A. Epstein (editors):  Fundamentals of hyperbolic geometry: selected exposures. Cambridge University Press. 2006. ISBN 9780521615587. https://books.google.com/books?id=MyvZ4ygF7poC.
* Outer Circles. An introduction to hyperbolic 3 manifolds. Cambridge University Press. 2007. ISBN 9781139463768. https://books.google.com/books?id=w0IYCTiXOm4C. [5]
* Hyperbolic manifolds: an introduction in 2 and 3 dimensions. Cambridge University Press. 2016. ISBN 9781316432525. https://books.google.com/books?id=g5bsDAAAQBAJ. [6]

## References

1. ↑ Albert Marden at the Mathematics Genealogy Project
2. ↑ "Albert Marden". 9 December 2019. http://www.ias.edu/scholars/albert-marden.
3. ↑ Marden, Albert (1974), "The geometry of finitely generated kleinian groups", Annals of Mathematics, Second Series 99 (3): 383–462, doi:10.2307/1971059, ISSN 0003-486X
4. ↑ Canary, Richard D. (2010). "Marden's Tameness Conjecture: history and applications". arXiv:1008.0118 [math.GT].
5. ↑ "Review of Outer Circles. An Introduction to Hyperbolic 3-Manifolds by Albert Marden". 15 June 2011. http://euro-math-soc.eu/review/outer-circles-introduction-hyperbolic-3-manifolds.
6. ↑ Das, Tushar (1 July 2017). "Review of Hyperbolic Manifolds: An Introduction in 2 and 3 Dimensions by Albert Marden". https://www.maa.org/press/maa-reviews/hyperbolic-manifolds-an-introduction-in-2-and-3-dimensions.

## External links

* Homepage

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