Ronald Alan Fintushel (born 1945) is an American mathematician, specializing in low-dimensional

geometric topology In mathematics, geometric topology is the study of manifolds and Map (mathematics)#Maps as functions, maps between them, particularly embeddings of one manifold into another. History Geometric topology as an area distinct from algebraic topo ...

(specifically of 4-

manifold In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a N ...

s) and the mathematics of

gauge theory In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, does not change under local transformations according to certain smooth families of operations (Lie groups). Formally, t ...

Education and career

Fintushel studied mathematics at

Columbia University Columbia University in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Churc ...

with a bachelor's degree in 1967 and at the

University of Illinois at Urbana–Champaign The University of Illinois Urbana-Champaign (UIUC, U of I, Illinois, or University of Illinois) is a public land-grant research university in the Champaign–Urbana metropolitan area, Illinois, United States. Established in 1867, it is the f ...

with a master's degree in 1969. In 1975 he received his Ph.D. from the

State University of New York at Binghamton The State University of New York at Binghamton (Binghamton University or SUNY Binghamton) is a public research university in Greater Binghamton, New York, United States. It is one of the four university centers in the State University of New Y ...

with thesis ''Orbit maps of local

S^1

-actions on manifolds of dimension less than five '' under the supervision of Louis McAuley. Fintushel was a professor at

Tulane University The Tulane University of Louisiana (commonly referred to as Tulane University) is a private research university in New Orleans, Louisiana, United States. Founded as the Medical College of Louisiana in 1834 by a cohort of medical doctors, it b ...

and is a professor at

Michigan State University Michigan State University (Michigan State or MSU) is a public university, public Land-grant university, land-grant research university in East Lansing, Michigan, United States. It was founded in 1855 as the Agricultural College of the State o ...

. His research deals with geometric topology, in particular of 4-manifolds (including the computation of Donaldson and Seiberg-Witten invariants) with links to gauge theory,

knot theory In topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be und ...

, and

symplectic geometry Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. Symplectic geometry has its origins in the ...

. He works closely with Ronald J. Stern. In 1998 he was an Invited Speaker, with Ronald J. Stern, with talk ''Construction of smooth 4-manifolds'' at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

in Berlin. In 1997 Fintushel received the Distinguished Faculty Award from Michigan State University. In 2016 a conference was held in his honor at Tulane University. He was elected a Fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

. Fintushel is a member of the editorial boards of ''

Geometry & Topology ''Geometry & Topology'' is a peer-refereed, international mathematics research journal devoted to geometry and topology, and their applications. It is currently based at the University of Warwick, United Kingdom, and published by Mathematical S ...

'' and the ''

Michigan Mathematical Journal The ''Michigan Mathematical Journal'' (established 1952) is published by the mathematics department at the University of Michigan. An important early editor for the Journal was George Piranian. Historically, the Journal has been published a smal ...

''.

Selected publications

*with Stern: ''Constructing lens spaces by surgery on knots'', Mathematische Zeitschrift, vol. 175, 1980, pp. 33–51 *with Stern: ''An exotic free involution of

S^4

'', Annals of Mathematics, vol. 113, 1981, pp. 357–365 *with Stern
''Pseudofree orbifolds''
Annals of Mathematics, vol. 122, 1985, pp. 335–364 *with Stern
''Instanton homology of Seifert fibred homology three spheres''
Proceedings of the London Mathematical Society, vol. 61, 1990, pp. 109–137 *with Stern: ''Immersed spheres in 4-manifolds and the immersed Thom conjecture'', Turkish Journal of Mathematics, vol. 19, 1995, pp. 145–157 *with Stern: ''Donaldson invariants of 4-manifolds with simple type'', J. Diff. Geom., vol. 42, 1995, pp. 577–633 *with Stern: ''The blowup formula for Donaldson invariants'', Annals of Mathematics, vol. 143, 1996, pp. 529–54
arXiv
*with Stern: ''Rational blowdowns of smooth 4-manifolds'', Journal of Differential Geometry, vol. 46, 1997, pp. 181–23
arXiv
*with Stern: ''Surfaces in 4-manifolds'', Math. Res. Letters, vol. 4, 1997, pp. 907–91
arXiv
*with Stern: ''Knots, links, and 4-manifolds'', Inventiones mathematicae, vol. 134, 1998, pp. 363–400
arXiv
*with Stern
''Constructions of smooth 4-manifolds.''
Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998). Doc. Math. 1998, Extra Vol. II, 443–452 *with Stern: ''Symplectic surfaces in a fixed homology class'', J. Diff. Geom., vol. 52, 2000, pp. 203–222 *with Stern: ''Families of simply connected 4-manifolds with the same Seiberg-Witten invariants'', Topology, vol. 43, 2004, pp. 1449–1467 *with Stern: ''Invariants for Lagrangian tori'', Geom. Topol., vol. 8, 2004, pp., 947-96
arXiv
*with Stern
Tori in symplectic 4-manifolds
Geometry and Topology Monographs, vol. 7, 2004, Proceedings of the Casson Fest, pp. 311–333 *with Stern, B. D. Park: ''Reverse engineering small 4-manifolds'', Algebraic & Geometric Topology, vol. 7, 2007, pp. 2103–211
arXiv
*with Stern: ''Six Lectures on Four 4-manifolds'', Low dimensional topology, IAS/Park City Math. Ser. 15, Amer. Math. Soc., Providence, RI, 2009, pp. 265–315

References

{{DEFAULTSORT:Fintushel, Ronald 1946 births Living people 20th-century American mathematicians 21st-century American mathematicians American topologists Columbia University alumni University of Illinois Urbana-Champaign alumni Binghamton University alumni Tulane University faculty Michigan State University faculty Fellows of the American Mathematical Society

Education and career

Selected publications

See also

References