Ronald Fintushel

University Distinguished Professor of Mathematics, Emeritus

Michigan State University

B.A. 1967, Columbia University
M.A. 1969, University of Illinois
Ph.D. 1975, SUNY Binghamton

Email: ronfint@math.msu.edu

 

 

    
 

Research Interests

My areas of research are 4-dimensional topology and geometry and gauge theory. These fields have been rapidly changing since the 1980's. Part of the intrigue of studying 4-manifolds comes from its close ties with many other fields: geometric analysis, mathematical physics, and knot theory are just a few.

 

My Ph. D. Students

Franz Maier,1987
Weiping Li,1992, SW Bell Professor of Mathematics, Oklahoma State University
Wojciech Wieczorek,1995, Lecturer, Stanford University
Jongil Park,1996, Professor, Seoul National University
Thomas Mark, 2000, Associate Professor, University of Virginia
Scott Baldridge, 2001, Associate Professor, Louisiana State University
Stanislav Jabuka, 2002, Associate Professor, University of Nevada, Reno
Inanc Baykur, 2007, Assistant Professor, University of Massachusetts, Amherst
Adam Knapp, 2008, Ritt Assistant Professor, Columbia University
Nathan Sunukjian, 2010, Postdoctoral Instructor, Stony Brook
Christopher Hays , 2013, Postdoctoral Fellow, University of Pennsylvania
Kyungbae Park , 2014, Research Fellow, Korea Institute for Advanced Study

 

Honors

Invited Hour Speaker, Regional A.M.S. Meeting, Baton Rouge, LA, 1996
Invited Speaker, 1998 International Congress of Mathematicians, Berlin
Michigan State University, Distinguished Faculty Award, 1997
Frame Teaching Award, MSU Dep't of Mathematics, 2000
Fellow of the American Mathematical Society

 
Selected Publications
An exotic free involution on S4, Annals of Math. 113 (1981), 357-365 (with Ronald Stern).
Pseudofree orbifolds, Annals of Math. 122 (1985), 335-364 (with R. Stern).
Donaldson invariants of 4-manifolds with simple type, J. Diff. Geom. 42 (1995), 577-633 (with R. Stern).
The blowup formula for Donaldson invariants, Annals of Math. 143 (1996), 529-546 (with R. Stern).
Rational blowdowns of smooth 4-manifolds, J. Diff. Geom. 46 (1997), 181-235 (with R. Stern).
Knots, links, and 4-manifolds, Inventiones Math. 134 (1998), 363-400 (with R. 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 R. Stern)
Surfaces in 4-manifolds, Math. Res. Letters 4 (1997), 907-914 (with R. Stern).
Symplectic surfaces in a fixed homology class, J. Diff. Geom. 52 (2000), 203-222 (with R. Stern)
Families of simply connected 4-manifolds with the same Seiberg-Witten invariants, Topology 43 (2004), 1449 - 1467 (with R. Stern).
Invariants for Lagrangian tori, Geom. Topol. 8 (2004), 947-968 (with R. Stern).
Tori in symplectic 4-manifolds, Geometry and Topology Monographs, Vol. 7 (2004), Proceedings of the Casson Fest, 311-333 (with R. Stern).
Double node neighborhoods and families of simply connected 4-manifolds with b+=1, J. Amer. Math. Soc. 19 (2006), 171-180 (with R. Stern).
Surgery on nullhomologous tori and simply connected 4-manifolds with b+=1, Journal of Topology 1 (2008), 1-15 (with R. Stern).
Reverse engineering small 4-manifolds, Algebraic & Geometric Topology 7 (2007), 2103 – 2116 (with B.D. Park and R. Stern).
Exotic group actions on simply connected smooth 4-manifolds, Journal of Topology, 2 (2009), 769--778 (with R. Stern and N. Sunukjian).

Pinwheels and nullhomologous surgery on 4-manifolds with b+=1, Algebraic & Geometric Topology 11 (2011), 1649 – 1699 (with R. Stern).

Surgery on nullhomologous tori, Geometry & Topology Monographs 18 (2012), (with R. Stern).
 
Talks
Surgery on nullhomologous tori, L.S.U. Nov. 9, 2006
Reverse-engineering families of 4-manifolds, Beijing University, June 18, 2007
Reverse engineering, Hiroshima University, Feb. 6, 2008
Constructions of 4-manifolds, Stockholm University, May 24, 2008

Exotic Cyclic Group Actions on Smooth 4-Manifolds, BIRS, Mar. 25, 2009

Simply connected 4-manifolds with b+ = 1, Georgia Topology Conf., May 22, 2009

Life in 4-dimensions, First National Forum of Young Topologists, Tulane U, Nov 13,14, 2009

Smooth 4-Manifolds: 2011, Conference in honor of Mike Freedman, June 6, 2011 (Video link).

Surgery on nullhomologous tori, Video of lecture given at the Aarhus Gauge Theory Workshop, Aug. 11, 2011 (This is a video download.)
 
 

 

Ron Stern and me with longtime New Orleans notables Vic and Nat'ly

(Many thanks to Scott Baldridge, Terry Lawson, and Tom Mark for arranging for Bunny Matthews to draw this.)


  

 

 

 

 

 

The old days (1992)

Front row: Tom Parker, Weiping Li, Shuguang Wang, Selman Akbulut.

Back row: Terry Lawson, me, Simon Donaldson, Yongbin Ruan.

  
 

 

 

MSU at the Clay Institute Summer School in Budapest, June 2004

MSU students, faculty, graduates, and postdocs played an active role in the Clay Mathematics Institute Summer School on Floer Homology, Gauge Theory, and Low Dimensional Topology.

 

In this photo:

Front row: Bugra Ozer, Hyunjoo Cho, Jongil Park

Middle row: Oh Hoon Kwon, Adam Knapp, Inanc Baykur, Burak Ozbagci

Back row: Slaven Jabuka, Me, Tom Mark

Also participating in the summer school, but missing from the photo:

Selman Akbulut, Firat Arikan

 

  
     
 

 

 

MSU at the Institute for Advanced Study/ Park City Mathematics Institute PCMI 2006

There were many MSU students, faculty, graduates, and postdocs at the
Park City Mathematics Institute Summer Session on Low Dimensional Topology.

 

In this photo:

Front row: Tom Leness, Shuguang Wang, Me, A future MSU great, Bill Vautaw

Middle row: Jongil Park, Mei-Lin Yau, Inanc Baykur, Ali Elgindi, Adam Knapp, Elly Ionel, Doug Park, Wojciech Wieczorek (and yet another future mathematician)

Back row: Nathan Sunukjian, Stefano Vidussi, Tom Mark, Andrew Cooper, Burak Ozbagci, Dave Futer

Also participating in PCMI, but missing from the photo: Scott Baldridge, Slaven Jabuka, Slava Krushkal

 

  
     
 

 

With Past and Present Students at my Birthday Conference in New Orleans, 2006

 

 

  
     
 

 

Symposium in honor of Terry Lawson, Tulane, 2007

 

From the left: Me, Danny Ruberman, Terry Lawson, Reinhard Schultz, Allan Edmonds, Nikolai Saveliev
Proceedings of the Symposium

 

  
     
 

Deane Montgomery Tribute

  
     
 

 

                   Somehow I can't resist showing these photos (from Oslo).