American mathematician (born 1941)
Dennis Parnell Sullivan (born February 12, 1941) is an American mathematician known for his work inalgebraic topology ,geometric topology , anddynamical systems . He holds the Albert Einstein Chair at theGraduate Center of the City University of New York and is adistinguished professor atStony Brook University .
Sullivan was awarded theWolf Prize in Mathematics in 2010 and theAbel Prize in 2022.
Early life and education [ edit ] Sullivan was born inPort Huron, Michigan , on February 12, 1941.[ 2] [ 3] Houston soon afterwards.[ 2] [ 3]
He enteredRice University to studychemical engineering but switched his major to mathematics in his second year after encountering a particularly motivating mathematical theorem.[ 3] [ 4] uniformization theorem , according to which, in his own words:
[A]ny surface topologically like a balloon, and no matter what shape—a banana or thestatue 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.[ 5]
He received hisBachelor of Arts degree fromRice University in 1963.[ 3] Doctor of Philosophy fromPrinceton University in 1966 with his thesis,Triangulating homotopy equivalences , under the supervision ofWilliam Browder .[ 3] [ 6]
Sullivan worked at theUniversity of Warwick on aNATO Fellowship from 1966 to 1967.[ 7] Miller Research Fellow at theUniversity of California, Berkeley from 1967 to 1969 and then a Sloan Fellow atMassachusetts Institute of Technology from 1969 to 1973.[ 7] Institute for Advanced Study in 1967–1968, 1968–1970, and again in 1975.[ 8]
Sullivan was an associate professor atParis-Sud University from 1973 to 1974, and then became a permanent professor at theInstitut des Hautes Études Scientifiques (IHÉS) in 1974.[ 7] [ 9] [ 10] [ 2] Stony Brook University in 1996[ 7] [ 7] [ 9]
Sullivan was involved in the founding of theSimons Center for Geometry and Physics and is a member of its board of trustees.[ 11]
Along with Browder and his other students, Sullivan was an early adopter ofsurgery theory , particularly for classifying high-dimensionalmanifolds .[ 3] [ 4] [ 2] Hauptvermutung [ 2]
In an influential set of notes in 1970, Sullivan put forward the radical concept that, withinhomotopy theory , spaces could directly "be broken into boxes"[ 12] localized [ 4] [ 13]
TheSullivan conjecture , proved in its original form byHaynes Miller , states that theclassifying space BG of afinite group G is sufficiently different from any finiteCW complex X , that it maps to such anX only 'with difficulty'; in a more formal statement, the space of all mappingsBG toX , aspointed spaces and given thecompact-open topology , isweakly contractible .[ 14] [ 4] [ 13] [ 14]
Sullivan andDaniel Quillen (independently) createdrational homotopy theory in the late 1960s and 1970s.[ 15] [ 16] [ 4] [ 17] simply connected topological spaces withhomotopy groups andsingular homology groupstensored with therational numbers , ignoringtorsion elements and simplifying certain calculations.[ 17]
Sullivan andWilliam Thurston generalizedLipman Bers 'density conjecture from singly degenerate Kleinian surface groups to allfinitely generated Kleinian groups in the late 1970s and early 1980s.[ 18] [ 19] geometrically finite Kleinian groups, and was independently proven by Ohshika and Namazi–Souto in 2011 and 2012 respectively.[ 18] [ 19]
Conformal and quasiconformal mappings [ edit ] TheConnes–Donaldson–Sullivan–Teleman index theorem is an extension of theAtiyah–Singer index theorem toquasiconformal manifolds due to a joint paper bySimon Donaldson and Sullivan in 1989 and a joint paper byAlain Connes , Sullivan, and Nicolae Teleman in 1994.[ 20] [ 21]
In 1987, Sullivan andBurton Rodin proved Thurston's conjecture about the approximationof theRiemann map bycircle packings .[ 22]
Sullivan and Moira Chas started the field ofstring topology , which examines algebraic structures on thehomology offree loop spaces .[ 23] [ 24] cup product fromsingular cohomology .[ 23] [ 24] topological quantum field theories in mathematical physics.[ 25]
In 1975, Sullivan andBill Parry introduced the topologicalParry–Sullivan invariant for flows in one-dimensional dynamical systems.[ 26] [ 27]
In 1985, Sullivan proved theno-wandering-domain theorem .[ 4] [ 2]
Sullivan is married to fellow mathematicianMoira Chas .[ 4] [ 5]
^ Holden, Helge; Piene, Ragni, eds. (2024). "Dennis Sullivan's Work on Dynamics by Edson de Faria and Sebastian van Strien".The Abel Prize 2018-2022 . Springer-Verlag. arXiv preprint ^a b c d e f Phillips, Anthony (2005),"Dennis Sullivan – A Short History" , inLyubich, 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, retrievedMarch 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. RetrievedMarch 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. RetrievedMarch 23, 2022 . ^a b Desikan, Shubashree (March 23, 2022)."Abel prize for 2022 goes to American mathematician Dennis P. Sullivan" .The Hindu . RetrievedMarch 25, 2022 . ^ Dennis Sullivan at theMathematics Genealogy Project ^a b c d e f g h "Dennis Parnell Sullivan Awarded the 2022 Abel Prize for Mathematics" .Stony Brook University Archived from the original on March 24, 2022. RetrievedMarch 23, 2022 .^ "Dennis P. Sullivan" .Institute for Advanced Study Archived from the original on March 23, 2022. RetrievedMarch 23, 2022 .^a b c "Dennis Sullivan, Mathematician" .Institut des Hautes Études Scientifiques Archived from the original on November 22, 2021. RetrievedMarch 23, 2022 .^ "Science Faculty Spotlight: Dennis Sullivan" .CUNY Graduate Center . April 29, 2017.Archived from the original on March 24, 2022. RetrievedMarch 23, 2022 .^ "Dennis Sullivan Awarded the 2022 Abel Prize in Mathematics" .Simons Center for Geometry and Physics . RetrievedMarch 25, 2022 .^ Cepelewicz, Jordana (March 23, 2022)."Dennis Sullivan, Uniter of Topology and Chaos, Wins the Abel Prize" .Quanta Magazine . RetrievedMarch 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. RetrievedOctober 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. RetrievedNovember 1, 2007 . ^a b Hess, Kathryn (1999). "A history of rational homotopy theory". InJames, 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. RetrievedMarch 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, retrievedMarch 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. RetrievedAugust 17, 2020 .^ "National Academy of Sciences" .Archived from the original on May 15, 2021. RetrievedAugust 17, 2020 .^ "American Academy of Arts and Sciences" .Archived from the original on March 24, 2022. RetrievedAugust 17, 2020 .^ "Wolf Prize Winners Announced" .Israel National News Archived from the original on March 24, 2022. RetrievedMarch 23, 2022 .^ List of Fellows of the American Mathematical Society Archived December 5, 2012, atarchive.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. RetrievedMarch 23, 2022 .
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