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American mathematician
Curtis Tracy McMullen (born May 21, 1958) is an American mathematician who is the Cabot Professor of Mathematics at
Harvard University . He was awarded the
Fields Medal in 1998 for his work in
complex dynamics ,
hyperbolic geometry and
Teichmüller theory .
Biography
McMullen graduated as
valedictorian in 1980 from
Williams College and obtained his
PhD in 1985 from
Harvard University , supervised by
Dennis Sullivan . He held post-doctoral positions at the
Massachusetts Institute of Technology , the
Mathematical Sciences Research Institute , and the
Institute for Advanced Study , after which he was on the faculty at
Princeton University (1987–1990) and the
University of California, Berkeley (1990–1997), before joining Harvard in 1997.
McMullen was chair of the
Harvard Mathematics Department from 2017 to 2020. He was the doctoral advisor of
Maryam Mirzakhani who won the
Fields Medal as the first female in history.
Honors and awards
McMullen received the
Salem Prize in 1991 and won the
Fields Medal in 1998
[1]
[2] at the
International Congress of Mathematicians (ICM) in Berlin.
[3] At the 1990 ICM in Kyoto he was an Invited Speaker.
[4] He was awarded a
Guggenheim Fellowship in 2004, elected to the
National Academy of Sciences in 2007, and received the
Humboldt Research Award in 2011.
Major publications
McMullen, C. T. (1987),
"Families of rational maps and iterative root-finding algorithms" , Annals of Math. , 125 (3): 467–493,
doi :
10.2307/1971408 ,
JSTOR
1971408 ,
MR
0890160
McMullen, C. T. (1989),
"Amenability, Poincaré series and quasiconformal maps" , Invent. Math. , 97 : 95–127,
Bibcode :
1989InMat..97...95M ,
doi :
10.1007/BF01850656 ,
MR
0999314 ,
S2CID
15729353
McMullen, C. T. (1990), "Iteration on Teichmüller space", Invent. Math. , 99 : 207–216,
Bibcode :
1990InMat..99..425M ,
doi :
10.1007/BF01234427 ,
MR
1031909 ,
S2CID
122626150
McMullen, C. T. (1991),
"Cusps are dense" , Annals of Math. , 133 (1): 217–247,
doi :
10.2307/2944328 ,
JSTOR
2944328 ,
MR
1087348
McMullen, C. T. (2000), "From dynamics on surfaces to rational points on curves", Bull. Amer. Math. Soc. , 37 (2): 119–140,
doi :
10.1090/S0273-0979-99-00856-3 ,
MR
1713286 ,
S2CID
12036264
McMullen, C. T. (2003), "Billiards and Teichmüller curves on Hilbert modular surfaces", J. Amer. Math. Soc. , 16 (4): 857–885,
doi :
10.1090/S0894-0347-03-00432-6 ,
JSTOR
30041457 ,
MR
1992827 ,
S2CID
7678249
McMullen, C. T. (2005), "Minkowski's conjecture, well-rounded lattices and topological dimension", J. Amer. Math. Soc. , 18 (3): 711–734,
doi :
10.1090/S0894-0347-05-00483-2 ,
JSTOR
20161252 ,
MR
2138142 ,
S2CID
11777513
McMullen, C. T. (2016), "Automorphisms of projective K3 surfaces with minimum entropy", Invent. Math. , 203 (1): 179–215,
Bibcode :
2016InMat.203..179M ,
doi :
10.1007/S00222-015-0590-Z ,
S2CID
253742362 ,
Zbl
1364.37103
McMullen, C. T.; et al. (2017),
"Geodesic planes in hyperbolic 3-manifolds" , Invent. Math. , 209 (2): 425–461,
Bibcode :
2017InMat.209..425M ,
doi :
10.1007/s00222-016-0711-3 ,
MR
3674219 ,
S2CID
253747261
McMullen, C. T.; et al. (2017),
"Cubic curves and totally geodesic subvarieties of moduli space" , Annals of Math. , 185 (3): 957–990,
doi :
10.4007/annals.2017.185.3.6 ,
JSTOR
26395746 ,
MR
3664815 ,
S2CID
1658293
Books
——— (1994),
Complex Dynamics and Renormalization , Annals of Mathematics Studies, vol. 135, Princeton, NJ: Princeton University Press,
ISBN
0-691-02982-2
[5]
——— (1996),
Renormalization and 3-Manifolds which Fiber over the Circle , Annals of Mathematics Studies, vol. 142, Princeton, NJ: Princeton University Press,
ISBN
0-691-01153-2
[5]
References
^
Borcherds, Gowers, Kontsevich, and McMullen Receive Fields Medals
^ Lepowsky, James; Lindenstrauss, Joram; Manin, Yuri I.; Milnor, John (January 1999).
"The Mathematical Work of the 1998 Fields Medalists" (PDF) . Notices of the AMS . 46 (1): 17–26.
^ McMullen, Curtis T. (1998).
"Rigidity and inflexibility in conformal dynamics" . Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. II . pp. 841–855.
^ McMullen, Curtis T. (1991). "Rational maps and Kleinian groups". In Satake, Ichiro (ed.). Proceedings of the International Congress of Mathematicians, August 21-29, 1990, Kyoto, Japan . Tokyo: Springer. pp. 889–900.
^
a
b
Lyubich, Mikhail (1999).
"Review of Complex dynamics and renormalization and Renormalization and 3-manifolds which fiber over the circle " (PDF) . Bull. Amer. Math. Soc. (N.S.) . 36 (1): 103–107.
doi :
10.1090/s0273-0979-99-00770-3 .
External links
International National Academics Other