Albert Marden
{{short description|American mathematician}}
{{Infobox scientist
| name = Albert Marden
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| birth_date = {{birth date and age |1934|11|18|df=yes}}
| birth_place = Milwaukee
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| nationality = American
| fields = Mathematics
| workplaces = University of Minnesota
| alma_mater = Harvard University
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| doctoral_advisor = Lars Ahlfors
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Albert Marden (born 18 November 1934) is an American mathematician, specializing in complex analysis and hyperbolic geometry.
Education and career
Marden received his PhD in 1962 from Harvard University with thesis advisor Lars Ahlfors.{{MathGenealogy|id = 8304}} 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.{{cite web|title=Albert Marden|website=IAS (ias.edu)|date=9 December 2019|url=http://www.ias.edu/scholars/albert-marden}}
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,{{Citation | last1=Marden | first1=Albert | title=The geometry of finitely generated kleinian groups | jstor=1971059 | mr=0349992 | zbl = 0282.30014 | year=1974 | journal=Annals of Mathematics | series = Second Series | issn=0003-486X | volume=99 | issue=3 | pages=383–462 | doi = 10.2307/1971059 }} which was proved in 2004 by Ian Agol and independently by a collaborative effort of Danny Calegari and David Gabai.{{cite arXiv|author=Canary, Richard D.|authorlink=Richard Canary|title=Marden's Tameness Conjecture: history and applications|year=2010|eprint=1008.0118|class=math.GT}}
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=
- {{cite journal|title=The geometry of finite generated kleinian groups|journal=Ann. of Math.|volume=99|issue=3|year=1974|pages=383–462|doi=10.2307/1971059|jstor=1971059|last1=Marden|first1=Albert}}
- with David B. A. Epstein: {{cite book|chapter=Convex hulls in hyperbolic space, a theorem of Sullivan, and measured pleated surfaces|title=In: Analytical and geometric aspects of hyperbolic space (Warwick and Durham, 1984)|pages=113–253|series=London Math. Soc. Lecture Note Series, 111|publisher=Cambridge Univ. Press|location=Cambridge|year=1987|chapter-url=https://books.google.com/books?id=OPA6AAAAIAAJ&pg=PA113|isbn=9780521339063}}
- with Troels Jørgensen: {{cite journal|title=Algebraic and geometric convergence of Kleinian groups|journal=Mathematica Scandinavica|year=1990|volume=66|issue=1|pages=47–72|jstor=24492023|last1=Jørgensen|first1=T|last2=Marden|first2=A|doi=10.7146/math.scand.a-12292|doi-access=free}}
- with Burt Rodin: {{cite book|chapter=On Thurston's formulation and proof of Andreev's theorem|title=In: Computational methods and function theory|volume=1435|year=1990|pages=103–115|publisher=Springer|series=Lecture Notes in Mathematics|doi=10.1007/BFb0087901|last1=Marden|first1=Al|last2=Rodin|first2=Burt|isbn=978-3-540-52768-8}}
- with Daniel Gallo and Michael Kapovich: {{cite journal|title=The monodromy groups of Schwarzian equations on closed Riemann surfaces|journal=Annals of Mathematics|year=2000|volume=151|issue=2|pages=625–704|url=http://emis.de/journals/Annals/151_2/marden.pdf|doi=10.2307/121044|jstor=121044|last1=Gallo|first1=Daniel|last2=Kapovich|first2=Michael|last3=Marden|first3=Albert|arxiv=math/9511213|s2cid=8077145}}
- with D. B. A. Epstein and V. Markovic: {{cite journal|title=Quasiconformal homeomorphisms and the convex hull boundary|journal=Ann. of Math.|issue=2|volume=159 (2004), no. 1|pages=305–336|jstor=3597252|last1=Epstein|first1=D. B. A|last2=Marden|first2=A|last3=Markovic|first3=V|year=2004|doi=10.4007/annals.2004.159.305|doi-access=free}}
=Books=
- with Richard Canary and David B. A. Epstein (editors): {{cite book|title=Fundamentals of hyperbolic geometry: selected exposures|publisher=Cambridge University Press|year=2006|url=https://books.google.com/books?id=MyvZ4ygF7poC|isbn=9780521615587}}
- {{cite book|url=https://books.google.com/books?id=w0IYCTiXOm4C|title=Outer Circles. An introduction to hyperbolic 3 manifolds|publisher=Cambridge University Press|year=2007|isbn=9781139463768}}{{cite web|title=Review of Outer Circles. An Introduction to Hyperbolic 3-Manifolds by Albert Marden|date=15 June 2011|website=European Mathematical Society|url=http://euro-math-soc.eu/review/outer-circles-introduction-hyperbolic-3-manifolds}}
- {{cite book|title=Hyperbolic manifolds: an introduction in 2 and 3 dimensions|publisher=Cambridge University Press|year=2016|url=https://books.google.com/books?id=g5bsDAAAQBAJ|isbn=9781316432525}}{{cite web|author=Das, Tushar|date=1 July 2017|title=Review of Hyperbolic Manifolds: An Introduction in 2 and 3 Dimensions by Albert Marden|website=MAA Reviews, Mathematical Association of America|url=https://www.maa.org/press/maa-reviews/hyperbolic-manifolds-an-introduction-in-2-and-3-dimensions}}
References
External links
- [http://www.math.umn.edu/~am/ Homepage]
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Category:20th-century American mathematicians
Category:21st-century American mathematicians
Category:Harvard University alumni
Category:University of Minnesota faculty