American mathematician (born 1941)
Dennis Parnell Sullivan (born February 12, 1941) is an American mathematician known for his work in
algebraic topology ,
geometric topology , and
dynamical systems . He holds the Albert Einstein Chair at the
City University of New York Graduate Center and is a
distinguished professor at
Stony Brook University .
Sullivan was awarded the
Wolf Prize in Mathematics in 2010 and the
Abel Prize in 2022.
Early life and education
Sullivan was born in
Port Huron, Michigan , on February 12, 1941.
[1]
[2] His family moved to
Houston soon afterwards.
[1]
[2]
He entered
Rice University to study
chemical engineering but switched his major to mathematics in his second year after encountering a particularly motivating mathematical theorem.
[2]
[3] The change was prompted by a special case of the
uniformization theorem , according to which, in his own words:
[A]ny surface topologically like a balloon, and no matter what shape—a
banana or the
statue of David by Michelangelo —could be placed on to a perfectly round sphere so that the stretching or squeezing required at each and every point is the same in all directions at each such point.
[4]
He received his
Bachelor of Arts degree from
Rice University in 1963.
[2] He obtained his
Doctor of Philosophy from
Princeton University in 1966 with his thesis, Triangulating homotopy equivalences , under the supervision of
William Browder .
[2]
[5]
Career
Sullivan worked at the
University of Warwick on a
NATO Fellowship from 1966 to 1967.
[6] He was a
Miller Research Fellow at the
University of California, Berkeley from 1967 to 1969 and then a Sloan Fellow at
Massachusetts Institute of Technology from 1969 to 1973.
[6] He was a visiting scholar at the
Institute for Advanced Study in 1967–1968, 1968–1970, and again in 1975.
[7]
Sullivan was an associate professor at
Paris-Sud University from 1973 to 1974, and then became a permanent professor at the
Institut des Hautes Études Scientifiques (IHÉS) in 1974.
[6]
[8] In 1981, he became the Albert Einstein Chair in Science (Mathematics) at the
Graduate Center, City University of New York
[9] and reduced his duties at the IHÉS to a half-time appointment.
[1] He joined the mathematics faculty at
Stony Brook University in 1996
[6] and left the IHÉS the following year.
[6]
[8]
Sullivan was involved in the founding of the
Simons Center for Geometry and Physics and is a member of its board of trustees.
[10]
Research
Topology
Geometric topology
Along with Browder and his other students, Sullivan was an early adopter of
surgery theory , particularly for classifying high-dimensional
manifolds .
[2]
[3]
[1] His thesis work was focused on the
Hauptvermutung .
[1]
In an influential set of notes in 1970, Sullivan put forward the radical concept that, within
homotopy theory , spaces could directly "be broken into boxes"
[11] (or
localized ), a procedure hitherto applied to the algebraic constructs made from them.
[3]
[12]
The
Sullivan conjecture , proved in its original form by
Haynes Miller , states that the
classifying space BG of a
finite group G is sufficiently different from any finite
CW complex X , that it maps to such an X only 'with difficulty'; in a more formal statement, the space of all mappings BG to X , as
pointed spaces and given the
compact-open topology , is
weakly contractible .
[13] Sullivan's conjecture was also first presented in his 1970 notes.
[3]
[12]
[13]
Sullivan and
Daniel Quillen (independently) created
rational homotopy theory in the late 1960s and 1970s.
[14]
[15]
[3]
[16] It examines "rationalizations" of
simply connected
topological spaces with
homotopy groups and
singular homology groups
tensored with the
rational numbers , ignoring
torsion elements and simplifying certain calculations.
[16]
Kleinian groups
Sullivan and
William Thurston generalized
Lipman Bers '
density conjecture from singly degenerate Kleinian surface groups to all
finitely generated
Kleinian groups in the late 1970s and early 1980s.
[17]
[18] The conjecture states that every finitely generated Kleinian group is an algebraic limit of
geometrically finite Kleinian groups, and was independently proven by Ohshika and Namazi–Souto in 2011 and 2012 respectively.
[17]
[18]
Conformal and quasiconformal mappings
The
Connes–Donaldson–Sullivan–Teleman index theorem is an extension of the
Atiyah–Singer index theorem to
quasiconformal manifolds due to a joint paper by
Simon Donaldson and Sullivan in 1989 and a joint paper by
Alain Connes , Sullivan, and Nicolae Teleman in 1994.
[19]
[20]
In 1987, Sullivan and
Burton Rodin proved Thurston's conjecture about the approximation
of the
Riemann map by
circle packings .
[21]
String topology
Sullivan and Moira Chas started the field of
string topology , which examines algebraic structures on the
homology of
free loop spaces .
[22]
[23] They developed the Chas–Sullivan product to give a partial singular homology analogue of the
cup product from
singular cohomology .
[22]
[23] String topology has been used in multiple proposals to construct
topological quantum field theories in mathematical physics.
[24]
Dynamical systems
In 1975, Sullivan and
Bill Parry introduced the topological
Parry–Sullivan invariant for flows in one-dimensional dynamical systems.
[25]
[26]
In 1985, Sullivan proved the
no-wandering-domain theorem .
[3] This result was described by mathematician Anthony Philips as leading to a "revival of holomorphic dynamics after 60 years of stagnation."
[1]
Awards and honors
Personal life
Sullivan is married to fellow mathematician
Moira Chas .
[3]
[4]
See also
References
^
a
b
c
d
e
f Phillips, Anthony (2005),
"Dennis Sullivan – A Short History" , in
Lyubich, Mikhail ; Takhtadzhi͡an, Leon Armenovich (eds.), Graphs and patterns in mathematics and theoretical physics , Proceedings of Symposia in Pure Mathematics, vol. 73, Providence:
American Mathematical Society , p. xiii,
ISBN
0-8218-3666-8 ,
archived from the original on July 28, 2014, retrieved March 31, 2016 .
^
a
b
c
d
e
f
g
h
i Chang, Kenneth (March 23, 2022).
"Abel Prize for 2022 Goes to New York Mathematician" .
The New York Times .
Archived from the original on March 23, 2022. Retrieved March 23, 2022 .
^
a
b
c
d
e
f
g Cepelewicz, Jordana (March 23, 2022).
"Dennis Sullivan, Uniter of Topology and Chaos, Wins the Abel Prize" .
Quanta Magazine .
Archived from the original on March 23, 2022. Retrieved March 23, 2022 .
^
a
b Desikan, Shubashree (March 23, 2022).
"Abel prize for 2022 goes to American mathematician Dennis P. Sullivan" .
The Hindu . Retrieved March 25, 2022 .
^
Dennis Sullivan at the
Mathematics Genealogy Project
^
a
b
c
d
e
f
g
h
"Dennis Parnell Sullivan Awarded the 2022 Abel Prize for Mathematics" .
Stony Brook University . March 23, 2022.
Archived from the original on March 24, 2022. Retrieved March 23, 2022 .
^
"Dennis P. Sullivan" .
Institute for Advanced Study . December 9, 2019.
Archived from the original on March 23, 2022. Retrieved March 23, 2022 .
^
a
b
c
"Dennis Sullivan, Mathematician" .
Institut des Hautes Études Scientifiques .
Archived from the original on November 22, 2021. Retrieved March 23, 2022 .
^
"Science Faculty Spotlight: Dennis Sullivan" .
Graduate Center, CUNY . April 29, 2017.
Archived from the original on March 24, 2022. Retrieved March 23, 2022 .
^
"Dennis Sullivan Awarded the 2022 Abel Prize in Mathematics" .
Simons Center for Geometry and Physics . March 23, 2022. Retrieved March 25, 2022 .
^ Cepelewicz, Jordana (March 23, 2022).
"Dennis Sullivan, Uniter of Topology and Chaos, Wins the Abel Prize" . Quanta Magazine . Retrieved March 24, 2022 .
^
a
b
Sullivan, Dennis P. (2005).
Ranicki, Andrew (ed.).
Geometric Topology: Localization, Periodicity and Galois Symmetry: The 1970 MIT Notes (PDF) . K-Monographs in Mathematics. Dordrecht: Springer.
ISBN
1-4020-3511-X .
Archived (PDF) from the original on April 18, 2007. Retrieved October 8, 2006 .
^
a
b
Miller, Haynes (1984). "The Sullivan Conjecture on Maps from Classifying Spaces".
Annals of Mathematics . 120 (1): 39–87.
doi :
10.2307/2007071 .
JSTOR
2007071 .
^
Quillen, Daniel (1969), "Rational homotopy theory",
Annals of Mathematics , 90 (2): 205–295,
doi :
10.2307/1970725 ,
JSTOR
1970725 ,
MR
0258031
^ Sullivan, Dennis (1977).
"Infinitesimal computations in topology" .
Publications Mathématiques de l'IHÉS . 47 : 269–331.
doi :
10.1007/BF02684341 .
MR
0646078 .
S2CID
42019745 .
Archived from the original on May 3, 2007. Retrieved November 1, 2007 .
^
a
b
Hess, Kathryn (1999). "A history of rational homotopy theory". In
James, Ioan M. (ed.). History of Topology . Amsterdam: North-Holland. pp. 757–796.
doi :
10.1016/B978-044482375-5/50028-6 .
ISBN
0-444-82375-1 .
MR
1721122 .
^
a
b Namazi, Hossein; Souto, Juan (2012).
"Non-realizability and ending laminations: Proof of the density conjecture" .
Acta Mathematica . 209 (2): 323–395.
doi :
10.1007/s11511-012-0088-0 .
ISSN
0001-5962 .
S2CID
10138438 .
^
a
b Ohshika, Ken'ichi (2011).
"Realising end invariants by limits of minimally parabolic, geometrically finite groups" .
Geometry and Topology . 15 (2): 827–890.
arXiv :
math/0504546 .
doi :
10.2140/gt.2011.15.827 .
ISSN
1364-0380 .
S2CID
14463721 .
Archived from the original on May 25, 2014. Retrieved March 24, 2022 .
^
Donaldson, Simon K. ; Sullivan, Dennis (1989).
"Quasiconformal 4-manifolds" . Acta Mathematica . 163 : 181–252.
doi :
10.1007/BF02392736 .
Zbl
0704.57008 .
^
Connes, Alain ; Sullivan, Dennis; Teleman, Nicolae (1994).
"Quasiconformal mappings, operators on Hilbert space and local formulae for characteristic classes" . Topology . 33 (4): 663–681.
doi :
10.1016/0040-9383(94)90003-5 .
Zbl
0840.57013 .
^
Rodin, Burton ;
Sullivan, Dennis (1987),
"The convergence of circle packings to the Riemann mapping" , Journal of Differential Geometry , 26 (2): 349–360,
doi :
10.4310/jdg/1214441375 ,
archived from the original on October 27, 2020, retrieved March 23, 2022
^
a
b Chas, Moira;
Sullivan, Dennis (1999). "String Topology".
arXiv :
math/9911159v1 .
^
a
b
Cohen, Ralph Louis ; Jones, John D. S.; Yan, Jun (2004). "The loop homology algebra of spheres and projective spaces". In Arone, Gregory; Hubbuck, John; Levi, Ran;
Weiss, Michael (eds.). Categorical decomposition techniques in algebraic topology: International Conference in Algebraic Topology, Isle of Skye, Scotland, June 2001 .
Birkhäuser . pp. 77–92.
^ Tamanoi, Hirotaka (2010). "Loop coproducts in string topology and triviality of higher genus TQFT operations".
Journal of Pure and Applied Algebra . 214 (5): 605–615.
arXiv :
0706.1276 .
doi :
10.1016/j.jpaa.2009.07.011 .
MR
2577666 .
S2CID
2147096 .
^
Parry, Bill ; Sullivan, Dennis (1975).
"A topological invariant of flows on 1-dimensional spaces" .
Topology . 14 (4): 297–299.
doi :
10.1016/0040-9383(75)90012-9 .
^ Sullivan, Michael C. (1997).
"An invariant of basic sets of Smale flows" .
Ergodic Theory and Dynamical Systems . 17 (6): 1437–1448.
doi :
10.1017/S0143385797097617 .
S2CID
96462227 .
^
"Oswald Veblen Prize in Geometry" .
Archived from the original on January 5, 2020. Retrieved August 17, 2020 .
^
"National Academy of Sciences" .
Archived from the original on May 15, 2021. Retrieved August 17, 2020 .
^
"American Academy of Arts and Sciences" .
Archived from the original on March 24, 2022. Retrieved August 17, 2020 .
^
"Wolf Prize Winners Announced" .
Israel National News .
Archived from the original on March 24, 2022. Retrieved March 23, 2022 .
^
List of Fellows of the American Mathematical Society
Archived December 5, 2012, at
archive.today , retrieved August 5, 2013.
^ Kehoe, Elaine (January 2015).
"Sullivan Awarded Balzan Prize" . Notices of the American Mathematical Society . 62 (1): 54–55.
doi :
10.1090/noti1198 .
^
"2022: Dennis Parnell Sullivan | The Abel Prize" . abelprize.no .
Archived from the original on March 23, 2022. Retrieved March 23, 2022 .
External links
1970s 1980s 1990s 2000s 2010s 2020s
Behavioral and social science
1960s 1980s 1990s 2000s 2010s
Biological sciences
1960s 1970s 1980s 1990s 2000s 2010s
Chemistry
1960s 1980s 1990s 2000s 2010s
Engineering sciences
1960s 1970s 1980s 1990s 2000s 2010s
Mathematical, statistical, and computer sciences
1960s 1970s 1980s 1990s 2000s 2010s
Physical sciences
1960s 1970s 1980s 1990s 2000s 2010s
International National Academics People Other