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RONALD J. STERN
Professor Emeritus 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
Surgery on Nullhomologous
Tori, R.A. Fintushel, and R.J. Stern, 2011 preprint, |
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Pinwheels and nullhomologous surgery on 4-manifolds with b+=1, R.A. Fintushel,
and R.J. Stern, Algebraic & Geometric Topology 11 (2011)
1649–1699 |
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Exotic group actions on simply-connected smooth 4-manifolds, R.A. Fintushel, R.J. Stern, and N. Sunukjian, Journal of Topology 2 (2009), 769-822 |
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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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Surfaces in 4-manifolds ,R.A. Fintushel and R.J. Stern , Mathematical Resarch Letters
4 (1997), 907-914 |
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A fake smooth CP^2 # RP^4 ,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
Cornell 50th Topology Festival (2012)
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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, 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, Assistant
Professor, U. Minnesota
- Ahmet Beyaz, 2006,
Assistant Professor, Middle Eastern Technical University, Ankara, Turkey
- Dan
Nash, 2010, Assistant Professor, University of San Diego
Editorial Positions
Geometry
and Topology, editor
Pacific
Journal of Mathematics, Past President and current Treasurer of the Board
of Governors