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RONALD J. STERN
Professor of
Mathematics Department of
Mathematics University of
California Irvine, CA
92697-3875 Email:
rstern@uci.edu 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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Exotic group actions on simply-connected smooth 4-manifolds, R.A. Fintushel, R.J. Stern, and N. Sunukjian, preprint |
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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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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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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
á Oberwolfach,
September 2008
á MSRI,
August 2008
á Harvard
Colloquium, April 2008
á Euler Fest, University of
Basel, June 2007
á Takao Matumoto's 60th
Birthday Conference, Hiroshima University February 2006
á
4-dimensional
Worlds, UC Irvine February 25, 2005
á DMV Jahrestagung,
September 2004
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Videos of Conference Talks
á 4-Manifolds:
BIG and Small (MSRI 2008)
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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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My Ph.D.
Students
- Jim Hoste, 1982, Professor,
Pitzer College
- Gordana Matic, 1986,
Professor, University of Georgia
- Kurt
Burnette, 1986, Gregorian University, Pontifical Oriental Institute in
Rome, Italy
- Tran Thuong, 1986,
Professor, Southern Missouri State University
- David Austin, 1989,
Professor, Grand Valley State University
- Kenneth Ferguson,
1991, Director of Research and Development, First Quadrant, Pasadena, CA
- Burak Ozbagci, 1999,
Associate Professor, Koc University, Instanbul, Turkey
- Ki-Heon
Yun, 2000, Assistant Professor, Seoul National University
- Yusuf Gurtas, 2003, Assistant
Professor, St. Louis University
- Anar Akhmedov,
2006, Post Doc, Columbia, Asst. Prof. U. Minn
- Ahmet Beyaz,
2006, Assistant Professor, Middle Eastern Technical University, Ankara,
Turkey
Editorial Positions
Geometry and
Topology, editor
New York Journal
of Mathematics, editor
Pacific Journal of Mathematics,
President and Chair of the Board of Governors
Mathematical Sciences
Publishers, Board of Directors