Dennis Sullivan

{{Infobox scientist

| name = Dennis Sullivan

| image = Dennis_Sullivan_(1968).jpg

| caption = Sullivan in 1968

| birth_name = Dennis Parnell Sullivan

| birth_date = {{birth date and age|1941|2|12}}

| birth_place = Port Huron, Michigan, U.S.

| death_date =

| death_place =

| fields = Topology

| workplaces = Stony Brook University
City University of New York

| education = Rice University (BA)
Princeton University (MA, PhD)

| doctoral_advisor = William Browder

| thesis_title = Triangulating Homotopy Equivalences

| thesis_url = https://www.proquest.com/openview/c2ea4b8706d151cbd744eb8faa49938b/

| thesis_year = 1966

| doctoral_students = Harold Abelson
Curtis T. McMullen

| known_for = {{plainlist|

| awards = {{plainlist|

Oswald Veblen Prize in Geometry (1971)
National Medal of Science (2004)
Leroy P. Steele Prize (2006)
Wolf Prize (2010)
Balzan Prize (2014)
Abel Prize (2022){{cite book|editor=Holden, Helge|editor2=Piene, Ragni|publisher=Springer-Verlag|chapter=Dennis Sullivan's Work on Dynamics by Edson de Faria and Sebastian van Strien |date=2024 |title=The Abel Prize 2018-2022 }} [https://arxiv.org/abs/2306.06290 arXiv preprint]}}

}}

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 Graduate Center of the City University of New York 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.{{Citation |chapter=Dennis Sullivan – A Short History |chapter-url=https://books.google.com/books?id=yuGic0WClQ4C&pg=PR13 |title=Graphs and patterns in mathematics and theoretical physics |first=Anthony |last=Phillips |page=xiii |editor1-first=Mikhail |editor1-last=Lyubich |editor1-link=Mikhail Lyubich |editor2-first=Leon Armenovich |editor2-last=Takhtadzhi͡an |location=Providence |publisher=American Mathematical Society |year=2005 |series=Proceedings of Symposia in Pure Mathematics |volume=73 |isbn=0-8218-3666-8 |access-date=March 31, 2016 |archive-date=July 28, 2014 |archive-url=https://web.archive.org/web/20140728180508/http://books.google.com/books?id=yuGic0WClQ4C&pg=PR13 |url-status=live }}. His family moved to Houston soon afterwards.{{cite news |url=https://www.nytimes.com/2022/03/23/science/abel-prize-mathematics.html |title=Abel Prize for 2022 Goes to New York Mathematician |first=Kenneth |last=Chang |work=The New York Times |date=March 23, 2022 |access-date=March 23, 2022 |archive-date=March 23, 2022 |archive-url=https://web.archive.org/web/20220323110725/https://www.nytimes.com/2022/03/23/science/abel-prize-mathematics.html |url-status=live}}

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. The change was prompted by a special case of the uniformization theorem, according to which, in his own words:

{{blockquote|[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.{{Cite news |url=https://www.thehindu.com/sci-tech/science/abel-prize-for-2022-goes-to-american-mathematician-dennis-p-sullivan/article65251992.ece |title=Abel prize for 2022 goes to American mathematician Dennis P. Sullivan |first=Shubashree |last=Desikan |date=March 23, 2022 |work=The Hindu |access-date=March 25, 2022}}}}

He received his Bachelor of Arts degree from Rice University in 1963. He obtained his Doctor of Philosophy from Princeton University in 1966 with his thesis, Triangulating homotopy equivalences, under the supervision of William Browder.{{MathGenealogy|id=1472|title=Dennis Sullivan}}

Career

Sullivan worked at the University of Warwick on a NATO Fellowship from 1966 to 1967. 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. He was a visiting scholar at the Institute for Advanced Study in 1967–1968, 1968–1970, and again in 1975.{{cite web|url=https://www.ias.edu/scholars/dennis-p-sullivan|title=Dennis P. Sullivan|website=Institute for Advanced Study|date=December 9, 2019|access-date=March 23, 2022|archive-date=March 23, 2022|archive-url=https://web.archive.org/web/20220323205305/https://www.ias.edu/scholars/dennis-p-sullivan|url-status=live}}

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.{{cite web|url=https://www.ihes.fr/en/professeur/dennis-sullivan-2/|title=Dennis Sullivan, Mathematician|website=Institut des Hautes Études Scientifiques|access-date=March 23, 2022|archive-date=November 22, 2021|archive-url=https://web.archive.org/web/20211122204026/https://www.ihes.fr/en/professeur/dennis-sullivan-2/|url-status=live}} In 1981, he became the Albert Einstein Chair in Science (Mathematics) at the Graduate Center of the City University of New York{{cite web |url=https://www.gc.cuny.edu/news/science-faculty-spotlight-dennis-sullivan |title=Science Faculty Spotlight: Dennis Sullivan |website=CUNY Graduate Center |date=April 29, 2017 |access-date=March 23, 2022 |archive-date=March 24, 2022 |archive-url=https://web.archive.org/web/20220324160540/https://www.gc.cuny.edu/news/science-faculty-spotlight-dennis-sullivan |url-status=live}} and reduced his duties at the IHÉS to a half-time appointment. He joined the mathematics faculty at Stony Brook University in 1996{{cite web |url=https://news.stonybrook.edu/university/dennis-parnell-sullivan-awarded-the-2022-abel-prize-for-mathematics/ |title=Dennis Parnell Sullivan Awarded the 2022 Abel Prize for Mathematics |website=Stony Brook University |date=March 23, 2022 |access-date=March 23, 2022 |archive-date=March 24, 2022 |archive-url=https://web.archive.org/web/20220324003919/https://news.stonybrook.edu/university/dennis-parnell-sullivan-awarded-the-2022-abel-prize-for-mathematics/ |url-status=live}} and left the IHÉS the following year.

Sullivan was involved in the founding of the Simons Center for Geometry and Physics and is a member of its board of trustees.{{cite web |url=https://scgp.stonybrook.edu/archives/36854 |title=Dennis Sullivan Awarded the 2022 Abel Prize in Mathematics |website=Simons Center for Geometry and Physics |date=March 23, 2022 |access-date=March 25, 2022}}

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. His thesis work was focused on the Hauptvermutung.

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"{{Cite web |last=Cepelewicz |first=Jordana |date=March 23, 2022 |title=Dennis Sullivan, Uniter of Topology and Chaos, Wins the Abel Prize |url=https://www.quantamagazine.org/dennis-sullivan-uniter-of-topology-and-chaos-wins-the-abel-prize-20220323/ |access-date=March 24, 2022 |website=Quanta Magazine |language=en}} (or localized), a procedure hitherto applied to the algebraic constructs made from them.{{cite book|title=Geometric Topology: Localization, Periodicity and Galois Symmetry: The 1970 MIT Notes|series=K-Monographs in Mathematics|first=Dennis P.|last=Sullivan|authorlink=Dennis Sullivan|editor-first=Andrew|editor-last=Ranicki|editor-link=Andrew Ranicki|isbn=1-4020-3511-X|year=2005|url=http://www.maths.ed.ac.uk/~aar/surgery/gtop.pdf|publisher=Springer|location=Dordrecht|access-date=October 8, 2006|archive-date=April 18, 2007|archive-url=https://web.archive.org/web/20070418041907/http://www.maths.ed.ac.uk/~aar/surgery/gtop.pdf|url-status=live}}

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.{{cite journal |first=Haynes |last=Miller |authorlink=Haynes Miller |title=The Sullivan Conjecture on Maps from Classifying Spaces |journal=Annals of Mathematics |volume=120 |issue=1 |year=1984 |pages=39–87 |doi=10.2307/2007071|jstor=2007071}} Sullivan's conjecture was also first presented in his 1970 notes.

Sullivan and Daniel Quillen (independently) created rational homotopy theory in the late 1960s and 1970s.{{citation|author1-first=Daniel|author1-last=Quillen|author1-link=Daniel Quillen|title=Rational homotopy theory|journal=Annals of Mathematics|volume=90|year=1969|pages=205–295|doi=10.2307/1970725|issue=2|mr=0258031|jstor=1970725}}{{cite journal|last=Sullivan|first=Dennis|title=Infinitesimal computations in topology|year=1977|journal=Publications Mathématiques de l'IHÉS|volume=47|pages=269–331|doi=10.1007/BF02684341|url=http://www.numdam.org/item?id=PMIHES_1977__47__269_0|mr=0646078|s2cid=42019745|access-date=November 1, 2007|archive-date=May 3, 2007|archive-url=https://web.archive.org/web/20070503003045/http://www.numdam.org/item?id=PMIHES_1977__47__269_0|url-status=live}}{{cite news |url=https://www.quantamagazine.org/dennis-sullivan-uniter-of-topology-and-chaos-wins-the-abel-prize-20220323/ |title=Dennis Sullivan, Uniter of Topology and Chaos, Wins the Abel Prize |first=Jordana |last=Cepelewicz |work=Quanta Magazine |date=March 23, 2022 |access-date=March 23, 2022 |archive-date=March 23, 2022 |archive-url=https://web.archive.org/web/20220323123752/https://www.quantamagazine.org/dennis-sullivan-uniter-of-topology-and-chaos-wins-the-abel-prize-20220323/ |url-status=live }}{{cite book|author1-last=Hess|author1-first=Kathryn|author1-link=Kathryn Hess|chapter=A history of rational homotopy theory|title= History of Topology|pages=757–796|publisher= North-Holland |location=Amsterdam|year= 1999|editor-first=Ioan M.|editor-last= James| editor-link=Ioan James|isbn=0-444-82375-1|mr=1721122|doi=10.1016/B978-044482375-5/50028-6}} 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.

==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. 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.{{cite journal |last1=Namazi |first1=Hossein |last2=Souto |first2=Juan |title=Non-realizability and ending laminations: Proof of the density conjecture |year=2012 |journal=Acta Mathematica |volume=209 |issue=2 |pages=323–395 |doi=10.1007/s11511-012-0088-0 |s2cid=10138438 |issn=0001-5962 |doi-access=free }}{{cite journal | last1=Ohshika | first1=Ken'ichi | title=Realising end invariants by limits of minimally parabolic, geometrically finite groups | url=http://www.msp.warwick.ac.uk/gt/2011/15-02/p023.xhtml | year=2011 | journal=Geometry and Topology | issn=1364-0380 | volume=15 | issue=2 | pages=827–890 | doi=10.2140/gt.2011.15.827 | arxiv=math/0504546 | s2cid=14463721 | access-date=March 24, 2022 | archive-date=May 25, 2014 | archive-url=https://web.archive.org/web/20140525195019/http://www.msp.warwick.ac.uk/gt/2011/15-02/p023.xhtml | url-status=live }}

==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.{{cite journal|first1=Simon K.|last1=Donaldson|author1-link=Simon Donaldson|first2=Dennis|last2=Sullivan|title=Quasiconformal 4-manifolds|journal=Acta Mathematica|volume=163|year=1989|pages=181–252|doi=10.1007/BF02392736|zbl=0704.57008|doi-access=free}}{{cite journal|first1=Alain|last1=Connes|author1-link=Alain Connes|first2=Dennis|last2=Sullivan|first3=Nicolae|last3=Teleman|title=Quasiconformal mappings, operators on Hilbert space and local formulae for characteristic classes|journal=Topology|volume=33|issue=4|year=1994|pages=663–681|zbl=0840.57013|doi=10.1016/0040-9383(94)90003-5|doi-access=free}}

In 1987, Sullivan and Burton Rodin proved Thurston's conjecture about the approximation

of the Riemann map by circle packings.{{citation

| last1 = Rodin

| first1 = Burton

| author1-link = Burton Rodin

| last2 = Sullivan

| first2 = Dennis

| author2-link = Dennis Sullivan

| issue = 2

| journal = Journal of Differential Geometry

| pages = 349–360

| title = The convergence of circle packings to the Riemann mapping

| url = http://projecteuclid.org/euclid.jdg/1214441375

| volume = 26

| year = 1987

| doi = 10.4310/jdg/1214441375

| doi-access = free

| access-date = March 23, 2022

| archive-date = October 27, 2020

| archive-url = https://web.archive.org/web/20201027071914/https://projecteuclid.org/euclid.jdg/1214441375

| url-status = live}}

==String topology==

Sullivan and Moira Chas started the field of string topology, which examines algebraic structures on the homology of free loop spaces. They developed the Chas–Sullivan product to give a partial singular homology analogue of the cup product from singular cohomology.{{cite arXiv |last1=Chas |first1=Moira|last2=Sullivan|first2=Dennis|authorlink2= Dennis Sullivan|date=1999 |title=String Topology |eprint=math/9911159v1}}{{cite book |first1=Ralph Louis |last1=Cohen |authorlink=Ralph Louis Cohen |first2=John D. S. |last2=Jones |first3=Jun |last3=Yan |chapter=The loop homology algebra of spheres and projective spaces |title=Categorical decomposition techniques in algebraic topology: International Conference in Algebraic Topology, Isle of Skye, Scotland, June 2001 |editor1-first=Gregory |editor1-last=Arone |editor2-first=John |editor2-last=Hubbuck |editor3-first=Ran |editor3-last=Levi |editor4-first=Michael |editor4-last=Weiss |editor4-link=Michael Weiss (mathematician) |publisher=Birkhäuser |pages=77–92 |year=2004}} String topology has been used in multiple proposals to construct topological quantum field theories in mathematical physics.{{Cite journal|first=Hirotaka|last=Tamanoi|title=Loop coproducts in string topology and triviality of higher genus TQFT operations|journal= Journal of Pure and Applied Algebra|volume= 214|issue=5|pages=605–615|year=2010|mr=2577666 |doi=10.1016/j.jpaa.2009.07.011|arxiv=0706.1276|s2cid=2147096}}

=Dynamical systems=

In 1975, Sullivan and Bill Parry introduced the topological Parry–Sullivan invariant for flows in one-dimensional dynamical systems.{{cite journal |first1=Bill |last1=Parry |author1-link=Bill Parry (mathematician) |first2=Dennis |last2=Sullivan |title=A topological invariant of flows on 1-dimensional spaces | journal=Topology | volume=14 |issue=4 |year=1975 |pages=297–299 |doi=10.1016/0040-9383(75)90012-9|doi-access=free }}{{cite journal |title=An invariant of basic sets of Smale flows |first=Michael C. |last=Sullivan |journal=Ergodic Theory and Dynamical Systems |volume=17 |issue=6 |pages=1437–1448 |year=1997 |doi=10.1017/S0143385797097617|s2cid=96462227 |url=https://opensiuc.lib.siu.edu/math_articles/70 }}

In 1985, Sullivan proved the no-wandering-domain theorem. This result was described by mathematician Anthony Philips as leading to a "revival of holomorphic dynamics after 60 years of stagnation."

Awards and honors

1971 Oswald Veblen Prize in Geometry{{cite web|url=https://www.ams.org/prizes-awards/pabrowse.cgi?parent_id=34|title=Oswald Veblen Prize in Geometry|access-date=August 17, 2020|archive-date=January 5, 2020|archive-url=https://web.archive.org/web/20200105064133/http://www.ams.org/prizes-awards/pabrowse.cgi?parent_id=34|url-status=live}}
1981 Prix Élie Cartan, French Academy of Sciences
1983 Member, National Academy of Sciences{{cite web|url=http://www.nasonline.org/member-directory/members/49958.html|title=National Academy of Sciences|access-date=August 17, 2020|archive-date=May 15, 2021|archive-url=https://web.archive.org/web/20210515183249/http://www.nasonline.org/member-directory/members/49958.html|url-status=live}}
1991 Member, American Academy of Arts and Sciences{{cite web|url=https://www.amacad.org/person/dennis-parnell-sullivan|title=American Academy of Arts and Sciences|access-date=August 17, 2020|archive-date=March 24, 2022|archive-url=https://web.archive.org/web/20220324160540/https://www.amacad.org/person/dennis-parnell-sullivan|url-status=live}}
1994 King Faisal International Prize for Science
2004 National Medal of Science
2006 Steele Prize for lifetime achievement
2010 Wolf Prize in Mathematics, for "his contributions to algebraic topology and conformal dynamics"{{Cite web |title=Wolf Prize Winners Announced |url=https://www.israelnationalnews.com/news/135820 |access-date=March 23, 2022 |website=Israel National News |language=en |archive-date=March 24, 2022 |archive-url=https://web.archive.org/web/20220324160541/https://www.israelnationalnews.com/news/135820 |url-status=live}}
2012 Fellow of the American Mathematical Society[https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society] {{Webarchive|url=https://archive.today/20121205081942/http://www.ams.org/profession/fellows-list |date=December 5, 2012}}, retrieved August 5, 2013.
2014 Balzan Prize in Mathematics (pure or applied){{Cite journal |date=January 2015 |title=Sullivan Awarded Balzan Prize |journal=Notices of the American Mathematical Society |volume=62 |issue=1 |pages=54–55 |doi=10.1090/noti1198 |doi-access=free|last1=Kehoe |first1=Elaine }}
2022 Abel Prize{{Cite web |title=2022: Dennis Parnell Sullivan {{!}} The Abel Prize |url=https://abelprize.no/abel-prize-laureates/2022 |access-date=March 23, 2022 |website=abelprize.no |archive-date=March 23, 2022 |archive-url=https://web.archive.org/web/20220323111559/https://abelprize.no/abel-prize-laureates/2022 |url-status=live}}

Personal life

Sullivan is married to fellow mathematician Moira Chas.

References

External links

{{MacTutor Biography|id=Sullivan}}
{{MathGenealogy |id=1472}}
[https://www.gc.cuny.edu/people/dennis-sullivan Sullivan's homepage at the City University of New York]
[http://www.math.stonybrook.edu/~dennis/ Sullivan's homepage at Stony Brook University]
[http://www.balzan.org/en/prizewinners/dennis-parnell-sullivan Dennis Sullivan] {{Webarchive|url=https://web.archive.org/web/20180528082926/http://www.balzan.org/en/prizewinners/dennis-parnell-sullivan |date=May 28, 2018}} International Balzan Prize Foundation