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RONALD J. STERN
Professor of Mathematics Department of Mathematics University of California Irvine, CA 92697-3875 Tel: (949) 824-1823 Fax: (949) 824-7993 |
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Research Interests
My primary area of research
includes low dimensional topology, particularly 4-dimensional topology,
geometry, and gauge theory. These have been dynamic fields for the past 25
years and have close ties with many other areas of research: geometric
analysis, mathematical physics, string theory, and knot theory are just a
few. |
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Recent Research Papers
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Reverse
engineering small 4-manifolds R.A. Fintushel, B.D. Park, and R.J. Stern Algebraic and Geometric Topology 7 (2007) 2103-2116. |
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Surgery on
nullhomologous tori and simply connected 4-manifolds with b^+=1 R.A. Fintushel
and R.J. Stern, Journal of Topology 1 (2008), 1-15 |
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Six Lectures on Four
4-Manifolds R.A. Fintushel
and R.J. Stern 2006 Park City
Mathematics Institute Graduate Summer School on Low Dimensional Topology |
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Will we ever classify
simply-connected smooth 4-manifolds?, Clay Mathematics Proceedings 5 (2006),
Floer Homology, Gauge Theory and Low Dimensional
Topology, CMI/AMS Book Series, 225-240. |
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Double node neighborhoods and
families of simply-connected 4-manifolds with b+=1 R.A. Fintushel
and R.J. Stern, J. Amer. Math. Soc.
19 (2006), 171-180. |
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Invariants
for Lagrangian Tori R.A. Fintushel and R.J. Stern, Geometry
and Topology 8 (2004), 949-968 |
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Tori in symplectic 4-manifolds R.A. Fintushel and R.J. Stern, Geometry
and Topology Monographs, 7 (2004), Proceedings of the Casson Fest, 311-333. |
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Families of
simply-connected 4-manifolds with the same Seiberg-Witten invariants R.A. Fintushel and R.J. Stern, Topology
43 (2004), 1449-1467 |
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Rational Surfaces and symplectic 4-manifolds with one basic class R.A. Fintushel, Jongil Park, and R.J. Stern Algebraic and Geometric Topology 2 (2002), 391-402. |
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The canonical class of
a symplectic 4-manifold R.A. Fintushel and R.J. Stern Turkish J. Math. 25 (2001), no. 1, 137--145 |
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Nonsymplectic
4-manifolds with one basic class R.A. Fintushel and R.J. Stern Pacific J. Math. 194 (2000), no. 2, 325-333. |
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Nondiffeomorphic symplectic 4-manifolds with the same Seiberg-Witten invariants R.A. Fintushel and R.J. Stern Proceedings of the Kirbyfest, Geometry and Topology Monographs 2 (1999), 103-111 |
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Symplectic
surfaces in the same homology class R.A. Fintushel and R.J. Stern Journal of Differential Geometry 52 (1999), 203-222. |
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Constructions
of Smooth 4-manifolds R.A. Fintushel and R.J. Stern Doc. Math. J. DMV Extra Volume ICM II (1998), 443-452 |
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Knots, Links, and 4-manifolds (journal version)(pdf version) R.A. Fintushel and R.J. Stern Inventiones Mathematicae 134 (1998), 363-400 |
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R.A. Fintushel and R.J. Stern Mathematical Resarch Letters 4 (1997), 907-914 |
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D. Rubermann and R.J. Stern Mathematical Resarch Letters 4 (1997), 375-378 |
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Rational blowdowns of smooth 4-manifolds (journal verson) R.A. Fintushel and R.J. Stern Journal of Differential Geometry 46 (1997), 181-235 |
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The blowup formula for Donaldson invariants R.A. Fintushel and R.J. Stern Annals of Mathematics (2)143 (1996), 529-546 |
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Immersed spheres in 4-manifolds and the immersed Thom conjecture R.A. Fintushel and R.J. Stern Turkish Journal of Mathematics 19 (1995), 145--157. |
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Donaldson invariants of 4-manifolds with simple
type R.A. Fintushel and R.J. Stern Journal of Differential Geometry 42 (1995), 577--633 |
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Slides from recent research talks
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Harvard Colloquium, April 2008
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Euler Fest,
University of Basel, June 2007
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Takao
MatumotoÕs 60th Birthday Conference, Hiroshima University February
2006
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4-dimensional
Worlds, UC Irvine February 25, 2005
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DMV
Jahrestagung, September 2004
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Videos of Conference Talks
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Some
curious symplectic and non-symplectic 4-manifolds (1998) á Pacific Northwest Geometry Conference (1996) |
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Classes I am currently Teaching
Fall 2007: Math 250A, Algebraic Topology
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Geometry and Topology,
editor
New York Journal of Mathematics,
editor
Mathematical Reviews Editorial Board
Pacific Journal of Mathematics,
President and Chair of the Board of Governors
Mathematical Sciences Publishers, Board of Directors