Igor E. Pritsker

Work address:
Department of Mathematics
Oklahoma State University
401 Mathematical Sciences
Stillwater, OK 74078-1058
 Phone: (405) 744-8220
E-mail: igor@math.okstate.edu 		Home address:
 940 Lake Vista Rd
Edmond, OK 73034


Web address:
http://www.math.okstate.edu/~igor/

Education

05/95 Ph.D. in Mathematics at the University of South Florida, Tampa, Florida. Advisor: E. B. Saff.
08/92-05/95 Graduate study at the University of South Florida, Tampa, Florida
11/90-08/92 Graduate study and research at the Institute for Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk, Ukraine
09/83-06/90 B.A., M.S. in Mathematics. Donetsk State University, Donetsk, Ukraine. Diploma with Honors.

Professional Experience

05/19-present Vaughn Foundation Professor in Number Theory
07/07-present Professor at Oklahoma State University
07/03-06/07 Associate Professor at OSU
06/99-06/03 Assistant Professor at OSU
06/97-06/99 Visiting Assistant Professor at Case Western Reserve University
08/95-05/97 Visiting Assistant Professor at Kent State University
08/92-04/95 Graduate Teaching Assistant at the University of South Florida
11/90-08/92 Research at the Department of Function Theory, Institute for Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk, Ukraine.

Grants and Honors

05/19-present Vaughn Foundation Professor in Number Theory
05/22-10/22 NSF conference grant DMS-2152935: "Equidistribution and arithmetic dynamics'' (jointly with P. Fili)
01/21-12/23 AIM SQuaRE grant "Random Polynomials"
10/20-09/23 NSA conference grant H98230-21-1-0008: "Equidistribution and arithmetic dynamics'' (jointly with P. Fili)
05/15-09/16 NSA grant H98230-15-1-0229: "Polynomials with Random and Integer Coefficients"
07/11-06/14 AT&T Professor
01/12-01/14 NSA grant H98230-12-1-0227: "Distribution of Algebraic Numbers"
12/08-12/10 NSA grant H98230-09-01-038: "Algebraic Numbers and Equilibrium Measures"
05/06-08/08 Humboldt Research Fellowship (Alexander von Humboldt Foundation, Germany)
03/06-03/08 NSA grant H98230-06-1-0055: "Weighted Potentials in Analytic Number Theory"
02/05 Big 12 Faculty Fellowship (Big 12 Universities Conference)
06/04 NSF conference grant DMS-0411729: "Constructive Functions Tech-04: An International Conference" (jointly with D. Lubinsky, J. S. Geronimo, and X. Li)
01/03-01/05 NSA grant MDA904-03-1-0081: "Polynomials with Integer Coefficients"
07/99-07/03 NSF grant DMS-9996410: "Polynomials in Analysis and Analytic Number Theory"
05/00 Ralph E. Powe Award (Oak Ridge Associated Universities)
06/98-08/00 NSF supplemental grant DMS-9842408: "Potential theory and quasiconformal mappings in zero distribution and weighted approximation" (jointly with V. V. Andrievskii and R. S. Varga)
08/97-07/01 NSF grant DMS-9707359: "Weighted approximation in the complex plane and iterative methods, via potential theory and function theory" (jointly with R. S. Varga)
06/90 Diploma with Honors at DSU
04/90 First Diploma at XXVIII Research Student Conference of the USSR
04/89 First Diploma at XXVII Research Student Conference of the USSR

Research Interests

Analytic Number Theory, Approximation Theory, Complex Analysis, Numerical Analysis, Potential Theory and Probability Theory.

Selected Talks

08/23 2023 Southeastern Probability Conference II, Charlottesville, VA.
06/23 Random nodal domains and related topics, Rennes, France.
07/22 Quantum Chaos and Nodal Sets of Random Waves, London, UK.
01/22 Computational Methods and Function Theory, Valparaiso, Chile.
09/21 Geometry of Random Nodal Domains, Rennes, France.
08/19 AIM workshop on Zeros of Random Polynomials, American Institute of Mathematics, San Jose, CA.
10/18 Sixth International Conference on Uniform Distribution Theory, CIRM, Marseille, France.
07/16 Seventh Jaen Conference on Approximation Theory, Computer Aided Geometric Design, Numerical Methods and Applications, Ubeda, Spain.
05/16 Minisymposium on Random Polynomials at the Fifteenth International Conference in Approximation Theory, San Antonio, TX.
10/15 BIRS workshop The Geometry, Algebra and Analysis of Algebraic Numbers, Banff International Research Station, Canada.
06/15 BIRS-CMO workshop Applied Functional Analysis, Oaxaca, Mexico.
05/15 International Conference on Orthogonal Polynomials and q-Series, Orlando, FL.
05/14 Constructive Functions 2014 (Nashville, TN).
07/13 28th Journees Arithmetiques (Grenoble, France).
06/13 Computational Methods and Function Theory 2013 (Shantou, China).
08/11 Paul Turan Memorial Conference (Budapest, Hungary).
10/10 New Perspectives in Univariate and Multivariate Orthogonal Polynomials (BIRS, Banff, Canada).
05/10 Optimal Configurations on the Sphere and Other Manifolds (Nashville, TN).
06/09 Computational Methods and Function Theory 2009 (Ankara, Turkey).
11/07 Modern Approaches in Asymptotics of Polynomials (BIRS, Banff, Canada).
04/06 Number Theory and Polynomials (Bristol, UK).
11/04 Constructive Functions Tech-04 (Atlanta, Georgia).
02/04 Funktionentheorie (Oberwolfach, Germany).
06/03 Summer Program on Mahler's Measure of Polynomials (Vancouver, Canada).
03/03 Elementary and Analytic Number Theory (Oberwolfach, Germany).
06/01 Computational Methods and Function Theory 2001 (Aveiro, Portugal).
03/01 Tenth International Conference on Approximation Theory (St. Louis, Missouri).
05/00 Millennial Conference on Number Theory (Urbana, Illinois).
06/99 International Conference on Rational Approximation (ICRA '99, Antwerp, Belgium).
01/98 Ninth International Conference on Approximation Theory (Nashville, Tennessee).
10/97 Computational Methods and Function Theory (CMFT '97, Nicosia, Cyprus).
03/95 Constructive Methods in Complex Analysis (Oberwolfach, Germany).
05/91 USA-USSR conference "Methods of complex analysis in approximation theory and mathematical physics" (Leningrad, USSR).

Conferences Organized

01/21-12/23 AIM SQuaRE "Random Polynomials"
06/22 Equidistribution and Arithmetic Dynamics, Oklahoma State University, Stillwater, OK
04/21 Workshop on Random Functions (virtual)
08/19 AIM workshop on Zeros of Random Polynomials, American Institute of Mathematics, San Jose, CA.
05/16 Minisymposium on Random Polynomials at the Fifteenth International Conference in Approximation Theory, San Antonio, TX
10/15 BIRS workshop on The Geometry, Algebra and Analysis of Algebraic Numbers, Banff International Research Station, Canada
05/14 Special Session Polynomials in Analysis and Number Theory at the International Conference Constructive Functions 2014, Nashville, TN
11/04 Constructive Functions Tech-04, Atlanta, GA.

Editorial Work

04/21-present Computational Methods and Function Theory, Springer.
11/16-08/18 Rocky Mountain Journal of Mathematics, RMMC.

Preprints

80. R. Looney and I. Pritsker, Schinzel-type bounds for the Mahler measure on lemniscates.
79. Y. Do, D. S. Lubinsky, H. H. Nguyen, O. Nguyen and I. E. Pritsker, Real roots of random orthogonal polynomials with exponential weights.

Accepted Papers

78. Y. Do, H. H. Nguyen, O. Nguyen and I. E. Pritsker, Central Limit Theorem for the number of real roots of random orthogonal polynomials, Ann. Inst. Henri Poincare Probab. Stat., to appear.

Published Papers

77. A. Dubickas and I. Pritsker, Lower bounds for Mahler-type measures of polynomials, Proc. Amer. Math. Soc. 151 (2023), 3673-3680.
76. I. E. Pritsker, Mahler measure of polynomial iterates, Canad. Math. Bull. 66 (2023), 881-885.
75. D. S. Lubinsky and I. E. Pritsker, Variance of real zeros of random orthogonal polynomials for varying and exponential weights, Electronic J. Probability 27 (2022), 1-32.
74. I. E. Pritsker, House of algebraic integers symmetric about the unit circle. J. Number Theory 236 (2022), 388-403.
73. D. S. Lubinsky and I. E. Pritsker, Variance of real zeros of random orthogonal polynomials, J. Math. Anal. Appl. 498 (2021), 124954.
72. I. E. Pritsker, Heights of polynomials over lemniscates, Acta Arith. 198 (2021), 219-231.
71. A. Dubickas and I. Pritsker, Weighted Fekete points on the real line and the unit circle, Comput. Methods Funct. Theory 20 (2020), 403-429.
70. A. Dubickas and I. Pritsker, Extremal problems for polynomials with real roots, J. Approx. Theory 253 (2020), 105376.
69. I. Pritsker and K. Ramachandran, Random Bernstein-Markov factors, J. Math. Anal. Appl. 473 (2019), 468-478.
68. I. Pritsker and K. Ramachandran, Natural boundary and zero distribution of random polynomials in smooth domains, Comput. Methods Funct. Theory 19 (2019), 401-410.
67. I. E. Pritsker, Zeros of lacunary random polynomials, Dolomites Research Notes on Approximation 11 (2018), 73-78.
66. I. E. Pritsker, Distribution of zeros for random Laurent rational functions, Comput. Methods Funct. Theory 18 (2018), 143-157.
65. I. E. Pritsker, Zero distribution of random polynomials, J. d'Analyse Math. 134 (2018), 719-745.
64. D. S. Lubinsky, I. E. Pritsker and X. Xie, Expected number of real zeros for random orthogonal polynomials, Math. Proc. Camb. Phil. Soc. 164 (2018), 47-66.
63. I. E. Pritsker, Expected zeros of random orthogonal polynomials on the real line, Jaen J. Approx. 9 (2017), 1-24.
62. P. Fili, C. Petsche and I. Pritsker, Energy integrals and small points for the Arakelov height, Arch. Math. 109 (2017), 441-454.
61. I. Pritsker and K. Ramachandran, Equidistribution of zeros of random polynomials, J. Approx. Theory 215 (2017), 106-117.
60. P. Fili and I. Pritsker, Height bounds for algebraic numbers satisfying splitting conditions, J. Number Theory 175 (2017), 250-264.
59. I. E. Pritsker, Inequalities for integral norms of polynomials via multipliers,in "Progress in Approximation Theory and Applicable Complex Analysis," N. K. Govil et al. (eds.), Springer, 2017, pp. 83-104.
58. D. S. Lubinsky, I. E. Pritsker and X. Xie, Expected number of real zeros for random linear combinations of orthogonal polynomials, Proc. Amer. Math. Soc., 144 (2016), 1631-1642.
57. I. E. Pritsker, Asymptotic zero distribution of random polynomials spanned by general bases, Contemp. Math. 661 (2016), 121-140.
56. I. E. Pritsker and X. Xie, Expected number of real zeros for random Freud orthogonal polynomials, J. Math. Anal. Appl. 429 (2015), 1258-1270.
55. I. E. Pritsker, Asymptotic distribution and symmetric means of algebraic numbers, Acta Arith. 168 (2015), 121-138.
54. I. E. Pritsker and A. M. Yeager, Zeros of polynomials with random coefficients, J. Approx. Theory 189 (2015), 88-100.
53. I. E. Pritsker and A. Sola, Expected discrepancy for zeros of random polynomials, Proc. Amer. Math. Soc. 142 (2014), 4251-4263.
52. I. E. Pritsker, E. B. Saff and W. Wise, Reverse triangle inequalities for Riesz potentials and connections with polarization, J. Math. Anal. Appl. 410 (2014), 868-881.
51. I. E. Pritsker, Polynomials with integer coefficients and their zeros, J. Math. Sci. (N.Y.) 183 (2012), 810-822.
50. I. E. Pritsker, Distribution of point charges with small discrete energy, Proc. Amer. Math. Soc. 139 (2011), 3461-3473.
49. I. E. Pritsker, Inequalities for sums of Green potentials and Blaschke products, Bull. London Math. Soc. 43 (2011), 561-575.
48. I. E. Pritsker, Distribution of algebraic numbers, J. Reine Angew. Math. 657 (2011), 57-80.
47. I. E. Pritsker, Equidistribution of points via energy, Ark. Mat. 49 (2011), 149-173.
46. A. Baernstein II, R. S. Laugesen, and I. E. Pritsker, Moment inequalities for equilibrium measures in the plane, Pure Appl. Math. Q. 7 (2011), 51-86.
45. I. E. Pritsker and E. B. Saff, Reverse triangle inequalities for potentials, J. Approx. Theory 159 (2009), 109-127.
44. I. E. Pritsker, Means of algebraic numbers in the unit disk, C. R. Acad. Sci. Paris, Ser. I 347 (2009), 119-122.
43. P. B. Borwein and I. E. Pritsker, The multivariate integer Chebyshev problem, Constr. Approx. 30 (2009), 299-310.
42. I. E. Pritsker and S. Ruscheweyh, Inequalities for products of polynomials II, Aequationes Math. 77 (2009), 119-132.
41. I. E. Pritsker and S. Ruscheweyh, Inequalities for products of polynomials I, Math. Scand. 104 (2009), 147-160.
40. I. E. Pritsker, An areal analog of Mahler's measure, Illinois J. Math. 52 (2009), 347-363.
39. I. E. Pritsker, How to find a measure from its potential, Comput. Methods Funct. Theory 8 (2008), 597-614.
38. I. E. Pritsker, Polynomial inequalities, Mahler's measure, and multipliers, in "Number theory and polynomials" (Conference proceedings, University of Bristol, 3-7 April 2006, editors James McKee and Chris Smyth), LMS Lecture Notes, vol. 352, Cambridge, 2008, 255-276.
37. I. E. Pritsker, Distribution of primes and a weighted energy problem, Electr. Trans. Numer. Anal. 25 (2006), 259-277.
36. I. E. Pritsker, Weighted energy problem on the unit circle, Constr. Approx. 23 (2006), 103-120.
35. I. E. Pritsker, Small polynomials with integer coefficients, J. d'Analyse Math. 96 (2005), 151-190.
34. I. E. Pritsker, The Gelfond-Schnirelman method in prime number theory, Canad. J. Math. 57 (2005), 1080-1101.
33. I. E. Pritsker, Convergence of Julia polynomials, J. d'Analyse Math. 94 (2004), 343-361.
32. I. E. Pritsker, Approximation of conformal mapping via the Szego kernel method, Comput. Methods Funct. Theory 3 (2003), 79-94.
31. R. S. Laugesen and I. E. Pritsker, Potential theory of the farthest-point distance function, Canad. Math. Bull. 46 (2003), 373-387.
30. P. B. Borwein, C. G. Pinner and I. E. Pritsker, Monic integer Chebyshev problem, Math. Comp. 72 (2003), 1901-1916.
29. I. E. Pritsker, Derivatives of Faber polynomials and Markov inequalities, J. Approx. Theory 118 (2002), 163-174.
28. I. E. Pritsker, Norms of products and factors of polynomials, in "Number Theory for the Millennium III," M. A. Bennett, B. C. Berndt, N. Boston, H. Diamond, A. J. Hildebrand and W. Philipp (eds.), pp. 173-189, A K Peters, Ltd., Natick, 2002.
27. I. E. Pritsker, Products of polynomials in uniform norms, Trans. Amer. Math. Soc. 353 (2001), 3971-3993.
26. V. V. Andrievskii, I. E. Pritsker and R. S. Varga, Simultaneous approximation and interpolation of functions on continua in the complex plane, J. Math. Pures Appl. 80 (2001), 373-388.
25. I. E. Pritsker, An inequality for the norm of a polynomial factor, Proc. Amer. Math. Soc. 129 (2001), 2283-2291.
24. V. V. Andrievskii, I. E. Pritsker and R. S. Varga, On zeros of polynomials orthogonal over a convex domain, Constr. Approx. 17 (2001), 209-225.
23. V. V. Andrievskii and I. E. Pritsker, Convergence of Bieberbach polynomials in domains with interior cusps, J. d'Analyse Math. 82 (2000), 315-332.
22. I. E. Pritsker, Chebyshev polynomials with integer coefficients, in "Analytic and Geometric Inequalities and Applications", Th. M. Rassias and H. M. Srivastava (eds.), pp. 335-348, Kluwer Acad. Publ., Dordrecht, 1999.
21. I. E. Pritsker, On the local asymptotics of Faber polynomials, Proc. Amer. Math. Soc. 127 (1999), 2953-2960.
20. I. E. Pritsker and R. S. Varga, Rational approximation with varying weights in the complex plane, in "Computational methods and function theory" (CMFT '97, Nicosia, Cyprus), N. Papamichael, St. Ruscheweyh and E. B. Saff (eds.), pp. 437-448, World Scientific Publishing Co., Singapore, 1999.
19. A. Kroo and I. E. Pritsker, A sharp version of Mahler's inequality for products of polynomials, Bull. London Math. Soc. 31 (1999), 269-278.
18. I. E. Pritsker and R. S. Varga, Weighted rational approximation in the complex plane, J. Math. Pures Appl. 78 (1999), 177-202.
17. I. E. Pritsker, Weighted approximation on compact sets, in "Approximation Theory IX", C. K. Chui and L. L. Schumaker (eds.), vol. I, pp. 271-278, Vanderbilt University Press, Nashville, 1998.
16. I. E. Pritsker, Polynomial approximation with varying weights on compact sets of the complex plane, Proc. Amer. Math. Soc. 126 (1998), 3283-3292.
15. I. E. Pritsker and R. S. Varga, Weighted polynomial approximation in the complex plane, Constr. Approx. 14 (1998), 475-492.
14. I. E. Pritsker and R. S. Varga, Zero distribution, the Szego curve, and weighted approximation in the complex plane, in "Modeling and Computation for Application in Science and Engineering" (May 1996, Northwestern University, Evanston), pp. 167-188, Oxford Univ. Press, Oxford, 1998.
13. I. E. Pritsker, Comparing norms of polynomials in one and several variables, J. Math. Anal. Appl. 216 (1997), 685-695.
12. I. E. Pritsker and R. S. Varga, The Szego curve, zero distribution and weighted approximation, Trans. Amer. Math. Soc. 349 (1997), 4085-4105.
11. N. Papamichael, I. E. Pritsker, E. B. Saff and N. S. Stylianopoulos, Approximation of conformal mappings of annular regions, Numer. Math. 76 (1997), 489-513.
10. N. Papamichael, I. E. Pritsker and E. B. Saff, Asymptotic zero distribution of Laurent-type rational functions, J. Approx. Theory 89 (1997), 58-88.
9. I. E. Pritsker and R. S. Varga, Weighted polynomial approximation in the complex plane, Electr. Res. Announ. Amer. Math. Soc. 3 (1997), 38-44.
8. R. S. Varga and I. E. Pritsker, On a counterexample in the theory of polynomials having concentration at low degrees, Analysis 16 (1996), 365-378.
7. I. E. Pritsker, Ray sequences of Laurent-type rational functions, Electr. Trans. Numer. Anal. 4 (1996), 106-124.
6. I. E. Pritsker and R. S. Varga, Boundary singularities of Faber and Fourier series, Analysis 16 (1996), 283-295.
5. V. I. Belyi and I. E. Pritsker, On the curved wedge condition and the continuity moduli of conformal mappings, Ukrainian Math. J. 45 (1994), 837-844.
4. I. E. Pritsker, Continuity of harmonically conjugate functions in Jordan domains, Ukrainian Math. J. 44 (1993), 1288-1291.
3. I. E. Pritsker, On the convergence of Bieberbach polynomials in domains with interior zero angles, (In "Methods of approximation theory in complex analysis and mathematical physics", Leningrad, 1991. A. A. Gonchar and E. B. Saff, eds.), Lecture Notes in Math. 1550 (1992), 169-172.
2. I. E. Pritsker, On the comparison of the polynomial norms and approximation by Fourier sums in Jordan domains, Dokl. Akad. Nauk Ukr., 1991, #9, 30-34.(Russian)
1. I. E. Pritsker, Order comparison of norms of polynomials in regions of the complex plane, Ukrainian Math. J. 43 (1992), 1190-1193.

Graduate Students

Ph.D. Wilhelmina Wise, Oleksandr Tovstolis, Xiaoju (Sophia) Xie, Mykhailo Bilogliadov, Aaron Yeager, Ali Pirhadi and Ryan Looney.
M.S. Abdurashid Abdurahman, Ya Jin, Danae Engelkes, Semyon Galperin, Ildus Ahmadullin, Zahra Minagar and Ryan Looney.

Postdoctoral Associates

Anatolii Grinshpan, Alan Sola, Paul Fili and Koushik Ramachandran.

References

A. B. J. Kuijlaars, Department of Mathematics, KU Leuven, B-3001 Leuven, Belgium.
D. S. Lubinsky, School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA.
E. B. Saff, Center for Constructive Approximation, Vanderbilt University, Nashville, TN 37240, USA.
C. J. Smyth, School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, Scotland, U.K.
J. D. Vaaler, Department of Mathematics, University of Texas at Austin, Austin, TX 78712, USA.