# Steven R Bell

## EDUCATION

B.S.    University of Michigan, 1976
Ph.D.   M.I.T., January, 1980

Thesis Advisor: Norberto Kerzman

Thesis Title: Applications of the Bergman projector
in the theory of functions of several complex variables.


## PROFESSIONAL EXPERIENCE

Research Associate & Lecturer, M.I.T.   1980
Visiting Fellow, Princeton University   1980-81
Instructor, Princeton University        1981-82
Asst. Professor, Princeton University   1982-84
Visiting Assoc. Prof., Princeton Univ   1984-85
Assoc. Professor, Purdue University     1984-88
Prof. Assoc., Univ. de Bordeaux         May, 1987
Professor, Purdue University            1988-
Graduate Chair, Purdue Math             1997-2000


## HONORS

Distinguished Achievement in Applied Mathematics Award, Univ of Michigan, 1975
Distinguished Scholar Award, Univeristy of Michigan, 1976
NSF Postdoctoral Fellowship, 1980
Alfred P. Sloan Fellowship, 1984
Invited One Hour Address, American Mathematical Society, 1986
AMS Centennial Research Fellowship, 1988
Stefan Bergman Prize, 1990
Distinguished Alumnus Award, John Glenn High School, Westland, MI, 1991
Distinguished Lecturer on Frontiers of Math, Texas A&M University, 1993
Ruth and Joel Spira Award for Excellence in Undergraduate Teaching, 2005
Charles B. Murphy Outstanding Undergraduate Teaching Award, 2006
Purdue Teaching Academy, Inducted 2007
Purdue Book of Great Teachers, Inscribed 2008
Purdue Provost's Award for Outstanding Graduate Mentor, 2011
Fellow of the American Mathematical Society, 2012
Shoemaker Lectures, Univ. of Toledo, 2015


## RESEARCH INTERESTS

Complex Variables, Partial Differential Equations

## PUBLICATIONS

1. Bell S., Non-vanishing of the Bergman Kernel Function at Boundary Points of Certain Domains in $C^n$, Math. Ann. 244; 69-74, 1979.
2. Bell S. and Ligocka E., A Simplification and Extension of Fefferman's Theorem on Biholomorphic Mappings, Invent. Math. 57; 283 -289, 1980.
3. Bell S., Biholomorphic Mappings and the $\bar\partial$-problem, Ann. of Math, 114; 103-113, 1981.
4. Bell S., Proper Holomorphic Mappings and the Bergman Projection, Duke Math. J. 48; 167-175, 1981.
5. Bell S., Extendability of Proper holomorphic Mappings and Global Analytic Hypoellipticity of the $\bar\partial$-Neumann Problem, Proc. of the National Academy of Science 78(11); 6600-6601, 1981.
6. Bell S. and Boas H.P., Regularity of the Bergman Projection in Weakly Pseudoconvex Domains, Math. Ann. 257; 23-30, 1981.
7. Bell S., Analytic Hypoellipticity of the $\bar\partial$-Neumann Problem and Extendability of Holomorphic Mappings, Acta Math. 147; 107-116, 1981.
8. Bell S., Smooth Bounded Strictly and Weakly Pseudoconvex Domains Cannot be Biholomorphic, Bull. of the A.M.S. 4; 119-120, 1981.
9. Bell S., The Bergman Kernel Function and Proper Holomorphic Mappings, Trans. of the A.M.S. 270; 685-691, 1982.
10. Bell S., A Representation Theorem in Strictly Pseudoconvex Domains, Illinois J. Math 26; 19-26, 1982.
11. Bell S., A Sobolev Inequality for Pluriharmonic Functions, Proc. of the A.M.S. 85; 350- 352, 1982.
12. Bell S., A Duality Theorem for Harmonic Functions, Michigan Math. J. 29; 123-128, 1982.
13. Bell S., Proper holomorphic mappings between circular domains, Comm. Math. Helvitici 57 (1982), 532-538.
14. Bell S. and Catlin D.W., Boundary Regularity of Proper Holomorphic Mappings, Duke Math. J. 49; 385-396, 1982.
15. Bell S. and Bedford E., Proper Self Maps of Weakly Pseudoconvex Domains, Math. Ann 261; 47-49, 1982.
16. Bell S. and Catlin D.W., Proper Holomorphic Mappings Extend Smoothly to the Boundary, Bull. of the A.M.S. 7; 269-272, 1982.
17. Bell S., An Extension of Alexander's Theorem on Proper Self Maps of the Ball in $C^n$, Indiana Math. J. 32; 69-71, 1983.
18. Bell S., Regularity of the Bergman Projection in Certain Non- pseudoconvex Domains, Pacific J. Math. 105; 273-277, 1983.
19. Bell S., Bedford E. and Catlin D., Boundary Behavior of Proper Holomorphic Mappings, Michigan Math. J. 30; 107-111, 1983.
20. Bell S. and Bedford E., Boundary Continuity of Proper Holomorphic Correspondences, Seminaire Dolbeault - Lelong - Skoda, 1982-83, Springer Lecture Notes 1198, Springer Verlag, 1986.
21. Bell S. and Bedford E., Holomorphic Correspondences of Bounded Domains in $C^n$, Proceedings Colloque Analyse Complexe, Toulouse, 1983, Springer Lecture Notes 1094; Springer Verlag, 1984.
22. Bell S., Boundary Behavior of Proper Holomorphic Mappings Between Non- pseudoconvex Domains, Amer. J. Math. 106; 639-643, 1984.
23. Bell S., Local Boundary Behavior of Proper Holomorphic Mappings, Proc. of Symposia in Pure Math. 41; 1-7, Amer. Math. Soc., Providence, 1984.
24. Bell S., Boundary Behavior of Holomorphic Mappings, Several Complex Variables: Proceedings of the 1981 Hangzhou Conference, Birkhauser, 1984.
25. Bell S. and Boas H.P., Regularity of the Bergman Projection and Duality of Holomorphic Function Spaces, Math. Ann. 267; 473-478, 1984.
26. Bell S., Proper Holomorphic Mappings That Must be Rational, Trans. of the A.M.S. 284; 425-429, 1984.
27. Bell S. and Krantz S.G., Smoothness to the Boundary of Conformal Maps, Rocky Mountain Math. J. 17; 23-40, 1987.
28. Bell S., Proper Holomorphic Correspondences Between Circular Domains, Math. Ann. 270; 393-400, 1985.
29. Bell S. and Bedford E., Extension of Proper Holomorphic Mappings Past the Boundary, Manuscripta Math. 50; 1-10, 1985.
30. Bell S. and Bedford E., Boundary Behavior of Proper Holomorphic Correspondences, Math. Ann. 272; 505-518, 1985.
31. Bell S., Differentiability of the Bergman Kernel and Pseudo-local Estimates, Math. Zeitschrift 192; 467-472, 1986.
32. Bell S., Numerical Computation of the Ahlfors Map of a Multiply Connected Planar Domain, J. of Mathematical Analysis and Applications, 120 (1986), 211-217.
33. Bell S., Compactness of Families of Holomorphic Mappings up to the Boundary, Proceedings of a conference held at Penn. State Univ., 1986, Springer Lecture Notes 1268, Springer Verlag, 1987.
34. Bell S., Extendibility of the Bergman Kernel Function, Proceedings of a conference held at Univ. of Maryland, 1986, Springer Lecture Notes 1276, Springer Verlag, 1987.
35. Bell S., A Generalization of Cartan's Theorem to Proper Holomorphic Mappings, J. Math. Pure Appl., 67 (1988), 85-92.
36. Bell S., Baouendi M.S. and Rothschild L.P., CR Mappings of Finite Multiplicity and Extension of Proper Holomorphic Mappings, Bull. A.M.S. 16 (1987), 265-270.
37. Bell S., Weakly Pseudoconvex Domains with Non-Compact Automorphism Groups, Math. Ann., 280 (1988), 403-408.
38. Bell S., Baouendi M.S. and Rothschild L.P., Mappings of Three- Dimensional CR Manifolds and Their Holomorphic Extensions, Duke Math. J., 56 (1988), 503-530.
39. Bell S., Local Regularity of CR Homeomorphisms, Duke Math. J., 57 (1988), 295-300.
40. Bell S., Mapping Problems in Complex Analysis and the $\bar\partial$- problem, Bull. of the AMS 22 (1990), 233-259.
41. Bell S. and Catlin D., Regularity of CR Mappings, Math Zeitschrift 199 (1988), 357-368.
42. Bell S. and Lempert L., A $C^\infty$ Reflection Principle in One and Several Complex Variables, J. Diff. Geometry 32 (1990), 899-915.
43. Bell S. and Narasimhan R., Proper holomorphic mappings of complex spaces, Encyclopedia of Mathematical Sciences, Several Complex Variables VI, Springer Verlag, pp. 1-38, 1991.
44. Bell S. and Narasimhan R., Proper holomorphic mappings of complex spaces, Complex Manifolds, Springer Verlag, pp. 1-38, 1998.
45. Bell S., Solving the Dirichlet problem in the plane by means of the Cauchy integral, Indiana Math. J., 39 (1990), 1355-1371.
46. Bell S., The Szegö projection and the classical objects of potential theory, Duke Math. J., 64 (1991), 1-26.
47. Bell S., CR maps between hypersurfaces in $C^n$, Proc. of Symposia in Pure Math. 52, part 1, pp. 13-22, Amer. Math. Soc., Providence, 1991.
48. Bell S., The Cauchy transform, potential theory, and conformal mapping, CRC Press, Boca Raton, 1992 (149 page book).
49. Bell S., The Cauchy transform, the Szegö projection, the Dirichlet problem, and the Ahlfors map, Contemporary Math., vol. 137, pp. 43-61, 1992.
50. Bell S., Algebraic mappings of circular domains in $C^n$, Proceedings of the special year in several complex variables at the Mittag-Leffler Institute, 1987-88, Princeton University Press, Mathematical Notes, vol. 38, pp. 126-135, 1993.
51. Bell S., Unique continuation theorems for the $\bar\partial$-operator and applications, J. of Geometric Analysis, 3 (1993), 195-224.
52. Bell S., Complexity of the classical kernel functions of potential theory, Indiana University Mathematics Journal 44 (1995), 1337-1369.
53. Bell S., Simplicity of the Szegö, Bergman, and Poisson kernels, Mathematical Research Letters 2 (1995), 267-277.
54. Bell S., Recipes for classical kernel functions associated to a multiply connected domain in the plane, Complex Variables Theory and Applications 29 (1996), 367-378.
55. Bell S., The role of the Ahlfors mapping in the theory of kernel functions in the plane, Reproducing kernels and their applications, Int. Soc. Anal. Appl. Comput. 3 (1999), 33--42. International Society for Analysis, Applications and Computation, 3. Kluwer Academic Publishers, Dordrecht, 1999.
56. Bell S., Evidence for the transcendental nature of the objects of potential theory in the plane, preprint.
57. Bell S., A Riemann surface attached to domains in the plane and complexity in potential theory, Houston J. Math. 26 (2000), 277-297.
58. Bell S., Finitely generated function fields and complexity in potential theory in the plane, Duke Math. J. 98 (1999), 187-207.
59. Bell S., The fundamental role of the Szegö kernel in potential theory and complex analysis, Journal für die reine und angewandte Mathematik 525 (2000), 1-16.
60. Bell S., Ahlfors maps, the double of a domain, and complexity in potential theory and conformal mapping, Journal d'Analyse Mathematique 78 (1999), 329-344.
61. Bell S., Complexity in complex analysis, Advances in Math. 172 (2002), 15-52.
62. Bell S., Möbius transformations, the Carathéodory metric, and the objects of complex analysis and potential theory in multiply connected domains, Michigan Math. J. 51 (2003), 351-362.
63. Bell S., The Bergman kernel and quadrature domains in the plane, Operator Theory: Advances and Applications 156 (2005), 61-78.
64. Bell S., Quadrature domains and kernel function zipping, Arkiv för matematik 43 (2005), 271-287.
65. Bell S., Ebenfelt P., Khavinson D., Shapiro H., On the classical Dirichlet problem with rational data, Journal d'Analyse Mathematique 100 (2006), 157-190.
66. Bell S., Ebenfelt P., Khavinson D., Shapiro H., Algebraicity in the Dirichlet problem in the plane with rational data, Complex Variables and Elliptic Equations 52 (2007), 235-244.
67. Bell S., Bergman coordinates, Studia Math. 176 (2006), 69-83.
68. Bell S., Kaleem F., The structure of the semigroup of proper holomorphic mappings of a planar domain to the unit disc, Computational Methods and Function Theory 8 (2008), 225-242.
69. Bell S., The Green's function and the Ahlfors map, Indiana Univ. Math. J. 57 (2008), 3049-3063.
70. Bell S., Deger E., Tegtmeyer T., A Riemann mapping theorem for two-connected domains in the plane, Computational Methods and Function Theory 9 (2009), No. 1, 323-334.
71. Bell S., Density of Quadrature domains in one and several complex variables, Complex Variables and Elliptic Equations 54 (2009), 165-171.
72. Bell S., Björn Gustafsson, and Zachary Sylvan, Szegö coordinates, quadrature domains, and double quadrature domains, Computational Methods and Function Theory 11 (2011), No. 1, 25-44.
73. Bell S., The Szegö kernel and proper holommorphic mappings to a half plane, Computational Methods and Function Theory 11 (2011), No. 1, 179-191.
74. Bell S., An improved Riemann mapping theorem and complexity in potential theory, Arkiv för matematik 51 (2013), 223-249.
75. Bell, S., Timothy Ferguson, Erik Lundberg, Self-commutators of Toeplitz operators and isoperimetric inequalities, Mathematical Proceedings of the Royal Irish Academy 114 (2014) 1-18.
76. Bell, S., B. Ernst, S. Fancher, C. Keeton, A. Komanduru, E. Lundberg, Spiral Galaxy Lensing: A model with twist, Mathematical Physics, Analysis, and Geometry 17 (2014), 305-322.
77. Bell, S., The Dirichlet and Neumann and Dirichlet-to-Neumann problems in quadrature, double quadrature, and non-quadrature domains, Analysis and Mathematical Physics 5 (2015), 113-135, DOI 10.1007/s13324-014-0089-6.
78. Bell, S., The Cauchy transform, potential theory, and conformal mapping, 2nd Edition, CRC Press,Taylor and Francis, Boca Raton, 2015 (209 page book).
79. Bell, S., The adjoint of a composition operator via its action on the Szegö kernel, Analysis and Mathematical Physics 8(2) (2018), 221-236, DOI 10.1007/s13324-018-0215-y.
80. Bell, S., The Cauchy integral formula, quadrature domains, and Riemann mapping theorems, Computational Methods and Function Theory, in press.

## REU STUDENTS

Seth Streitmatter, Summer 2002
Jason Anema, Summer 2003
Damir Dzhafarov, Summer 2004
Matt Barrett, Amber Meyerratken, Joey Steenbergen, Jamie Weigandt, Summer 2006
Zachary Sylvan, Spring and Summer 2008
Joshua Hunsberger, Alex Krzywda, John Mason, Summer 2009
Roenika Wiggins, Summer 2011
Brett Ernst, Sean Fancher, Abi Komanduru (co-mentored with Erik Lundberg), Summer 2012
Jack VanShaik, Summer 2017
Luis Reyna de la Torre, Summer 2018


## Ph.D. STUDENTS

Wilhelm Klingenberg, Jr., 1987
Peiming Ma, 1991
Moonja Jeong, 1991
Moohyun Lee, 1992
Young-Bok Chung, 1993
Khalid Filali Adib, 1994
Anthony Thomas, 1994
Zhenjun Hu, 1996
Loredana Lanzani, 1997 (Outstanding Alumna Award, 2011)
Thomas Tegtmeyer, 1998
Faisal Kaleem, 2006
Kuan Tan, 2007
Ersin Deger, 2007
George Hassapis, 2008
Alan Legg, 2016


## OTHER ACTIVITIES

• Associate Editor for the "Journal of Geometric Analysis," 1990-2013
• Associate Editor for the "Proceedings of the American Mathematical Society," 1997-2001
• Editor for MacGraw-Hill's "Walter Rudin Book Series of Advanced Mathematics Texts"
• AMS Committee on Publications 2012-2015
• Faculty Advisor for the Purdue University Juggling Club 1986-2014