Curriculum Vitae
Peter Dragnev
Department of Mathematical Sciences
Indiana-Purdue University
2101 E. Coliseum Blvd.
Fort Wayne, IN 46805
Tel: (260) 481-6382
E-mail: dragnevp@ipfw.edu
Education:
Ph.D. – 1997 (mathematics) Department of
Mathematics, University of South Florida,
MS – 1989, Department of Mathematics, Sofia
University, Sofia, Bulgaria.
BS – 1987, Department of
Mathematics, Sofia State University, Sofia, Bulgaria.
Employment Experience:
08/11 – present: Purdue Speaker of the IPFW
Senate, Fort Wayne, IN.
07/11 – present: Interim Chair, Department of
Mathematical Sciences, IPFW, Fort Wayne, IN.
07/11 – present: Professor, Department of
Mathematical Sciences, IPFW, Fort Wayne, IN.
08/03 – 06/11: Associate Professor, Department
of Mathematical Sciences, IPFW, Fort Wayne, IN.
07/98 – 08/03: Assistant Professor, Department
of Mathematical Sciences, IPFW, Fort Wayne, IN.
08/97 – 06/97: Visiting Assistant Professor,
Department of Mathematical Sciences, IPFW, Fort Wayne, IN.
08/92 – 08/97: Teaching Assistant, Department of
Mathematics, University of South Florida, Tampa.
08/90 – 08/92: Assistant, Department of
Mathematics, Plovdiv University, Bulgaria.
Research Interests:
Real and Complex Analysis; Approximation
Theory; Potential Theory; Orthogonal Polynomials;
Minimal energy problems; Optimal
configurations on the sphere; Logarithmic and Riesz potential; Asymptotics of
orthogonal polynomials; Lebesgue function;
Mathematics Subject Classification Numbers: 26, 31, 33, 41, 43
Academic Activities:
Member of AMS, MAA, and
Sigma Xi Research Society.
IPFW Chapter President of
Sigma Xi Research Society for 2004, 2007.
Mini-Symposium Organizer, 12th International
Conference in Approximation Theory, San Antonio, TX – March, 2007
Research Grants:
PRF Summer Research Award – 2003, PU
"Geometry of
Polynomials and Electrostatics"
PRF Summer Research Award – 2001,
PU
"The Extremal Support in the Presence of External Field"
IPFW Summer Research Grant – 2000, IPFW
"Minimal Discrete
Energy on Closed Surfaces"
IPFW Summer Research Grant – 1999, IPFW
"Constrained energy
problem and electrostatics of semiconductors"
Awards:
Research in Pairs – Oberwolfach Mathematics Institute, Germany, May 2009
Leibniz Fellow Guest Researcher – Oberwolfach Mathematics Institute, Germany, October 2008
IPFW
Research Fellow – Spring 2004
PRF Pippert Science Research Scholar
– 2003
Researcher of the Year Award – 2002, IPFW Sigma Xi Chapter
Travel Grants:
NSF Supplemental Travel Grant – 2001, 2007, NSF
Austrian Science Foundation – 2008, Technical University of Graz, Graz, Austria
PRF International Travel Grant – 2001, 2010, Purdue University
IU Overseas Conference Fund Grant – 1999, 2007, 2009, Indiana University
NATO Advanced Study Institute Local Grant – 2000, NATO ASI Organizing committee
FoCM Organizing Committee Local Grant – 1999, City University of Hong Kong
IPFW International Supplemental Travel Grant – 1999, 2001, 2007, 2009 IPFW
Research papers:
1.
J. S. Brauchart, P. D. Dragnev, E. B. Saff,
and C. E. van de Woestijne, Mysterious sequences of polynomials arising from electrostatics problem
on the sphere, to appear in Acta Math. Hungarica (2011)
2.
D. Benko, S. B. Damelin, and P. D.
Dragnev, On supports of equilibrium measures with
concave signed equilibria, to appear in J.
Comput. Anal. Appl. (2011)
3.
Benko and P. D. Dragnev,
On Ping pong balayage and convexity of equilibrium measures, to appear in
Constr. Approx. (2011)
4.
D. Benko, P. D. Dragnev, and V. Totik, Convexity of harmonic densities, to
appear in Revista Math. Iberoamer.
(2011)
5.
Peter Dragnev and
Erwin Mina-Diaz, On a series representation for Carleman
Orthogonal Polynomials, Proc. AMS,
138 (2010), 4271-4279.
6.
Peter Dragnev and
Erwin Mina-Diaz, Asymptotic Behavior and
Zero Distribution of Carleman Orthogonal Polynomials, J. Approx. Theory, 162 (11), 1982-2003.
7.
J. S. Brauchart, P. D. Dragnev, and E. B. Saff,
Riesz extremal measures on the sphere for
axis-supported external fields – JMAA, 356, no. 2, (2009), 769-792.
8.
J. S. Brauchart, P. D. Dragnev, and E. B. Saff,
Minimal Riesz energy on the sphere for axis-supported external fields.
Oberwolfach Preprint Series, OWP 2009-04 (2009), 1-44.
9.
P. D. Dragnev, J.
S. Brauchart, and E. B. Saff,
On an energy problem with Riesz external
field, Oberwolfach reports, Volume 4, Issue 2 (2007), 1042-1044.
10.
P. D. Dragnev and
E. B. Saff, Riesz spherical potentials with
external fields and minimal energy points separation, Potential Anal. 26
(2007), 139-162.
11.
D. Benko, S. B. Damelin and P. D.
Dragnev, On the support of the equilibrium measure for arcs of the unit
circle and for real intervals, ETNA 25 (2006), 27-40.
12.
P. D. Dragnev, D.
A. Legg, and D. W. Townsend, Polynomial Approximation of the Checkmark
Function, in Advances in Constructive Approximation, M. Neamtu
and E. B. Saff (edts),
(2004), 149-164.
13.
P. D. Dragnev, On
the Separation of Logarithmic Points on the Sphere, in Approximation Theory
X: Abstract and Classical Analysis, Charles Chui, Larry L. Schumaker,
and Joachim Stoeckler, (eds.), (2002), 137-144.
14.
P. D. Dragnev, D.
A. Legg, and D. W. Townsend, Discrete Logarithmic Energy on the Sphere,
Pacific J. Math. 207, no. 2 (2002), 345-358.
15.
S. B. Damelin, P. D. Dragnev, and A. B. J. Kuijlaars The
support of the equilibrium measure for a class of non-convex external fields on
a finite interval, Pacific J. of Math. 199, no. 2 (2001), 303-320.
16.
D. Coroian and P. D. Dragnev, Constrained Leja points and numerical solution of the constrained
energy problem, J. Comp. and Appl. Math. 131, no. 1-2 (2001),
427-444.
17.
P. D. Dragnev and
E. B. Saff, A problem in Potential theory and zero
asymptotics of Krawtchouk
polynomials, J. Approx. Theory 102, (2000), 120-140.
18.
A.B.J. Kuijlaars
and P. D. Dragnev, Equilibrium problems associated with fast decreasing
polynomials, Proceedings of Amer. Math. Soc. 127, no. 4 (1999),
1065-1074.
19.
P. D. Dragnev, D.
A. Legg and D. W. Townsend, Generalized Bernstein-Erdos
Conjecture, Approximation theory IX, Volume 1: Theoretical aspects, Charles
K. Chui and Larry Schumaker (eds.), (1998), 119-126.
20.
P. D. Dragnev and
E. B. Saff, Constrained energy problems with
applications to orthogonal polynomials of a discrete variable, Journal
Anal. Math., 72 (1997), 223-259.
21.
P. D. Dragnev and
E. B. Saff, Open problems in Approximation theory,
Tampa – 96, East Journal of Approx. 2, no. 4 (1996), 499-517.
Invited Presentations:
International Symposium in
Approximation Theory, Nashville, TN –
May, 2011
A fascinating polynomial sequence arising from an
electrostatics problem on the sphere – Orthogonal Polynomials Mini-symposium
New Perspectives in
Univariate and Multivariate Orthogonal Polynomials, BIRS, Banff, Canada – October, 2010
“Ping pong balayage and convexity of equilibrium measures”
Troy
University Colloquium, Troy, AL – November 3,
2010
Electrons,
Buckyballs, and Orifices: Nature's Way of Minimizing
Energy
University of South
Alabama Colloquium, Mobile, AL – October 7,
2010
Electrons,
Buckyballs, and Orifices: Nature's Way of Minimizing
Energy
Math
Circle, Mobile, AL – October 4, 2010
Famous
Sequences of Numbers: The Untold Story of Difference Equations
University of South
Florida, Tampa,
FL – October 1, 2010
Ping pong
balayage and convexity of Riesz and logarithmic equilibrium
measures
University of South
Alabama Mobile, AL –
September 30, 2010
Discrete orthogonal
polynomials on the real line and constrained energy problem
University of South
Alabama Mobile, AL –
September 29, 2010
Orthogonal polynomials on
the real line and external field problem
University of North
Florida Colloquium, Jacksonville, FL –
September 24, 2010
Ping
pong balayage and convexity of equilibrium measures
University of South
Alabama Mobile, AL –
September 23, 2010
On a classical theorem of
potential theory in the complex plane – II
University of South
Alabama Mobile, AL –
September 22, 2010
On a discrete Zolotarev problem with applications to the Alternating
Direction Implicit (ADI) method.
University of South
Alabama Mobile, AL –
September 21, 2010
On a classical theorem of
potential theory in the complex plane – I
University of South
Alabama, Mobile, AL – September 14, 2010
Generalization
of Bernstein-Erdos conjecture and the Lebesgue function
University of South
Alabama Colloquium, Mobile, AL – September
16, 2010
Minimal
energy problems and applications: Ping pong balayage and convexity of equilibrium measures
University of South
Alabama, Mobile, AL – September 14, 2010
Generalization
of Bernstein-Erdos conjecture and the Lebesgue function
University of Mississippi
Colloquium, Oxford,
MS – September 10, 2010
Ping
pong balayage and convexity of equilibrium measures
International Conference –
Constructive Theory of Functions,
Sozopol, Bulgaria – June, 2010
"The
asymptotic behavior of Carleman orthogonal polynomials"
International Conference –
Optimal Configurations on the Sphere and Other Manifolds, Nashville, TN – May, 2010
"Separation
results for optimal Riesz energy points on the sphere and axis-supported
external fields"
13th
International Conference in Approximation Theory, San Antonio, TX – March, 2010
"The
asymptotic behavior of Carleman orthogonal polynomials" – Frontiers in Orthogonal Polynomials Mini-symposium
Computational Methods and
Function Theory 2009, Ankara, Turkey –
June, 2009
" Axis-supported External Fields on the Sphere"
Western Kentucky University Math Symposium, Bowling Green, KY – October,
2008
“School Districts on Mars, Fuel Depots on Jupiter,
Inimical Dictators on Neptune?!
Or How to Arrange Points on the Sphere”
Technical University
Colloquium, Graz, Austria – October,
2008
”Iterative balayage
algorithm - applications to Riesz and logarithmic potentials”
University of South
Alabama Math Circle, Mobile, AL –
October, 2008
“School Districts on Mars, Fuel Depots on Jupiter,
Inimical Dictators on Neptune?!
Or How to Arrange Points on the Sphere”
University of Mississippi
Colloquium, Oxford, MS – October,
2008
“Electrons, Buckyballs, and Orifices: Nature’s Way of Minimizing
Energy”
Western Kentucky
University Colloquium, Bowling Green,
KY – January, 2008
“Balayage Iteration and Minimal Energy Problems”
Modern Approaches in Asymptotics of Polynomials, BIRS, Banff, Canada – November, 2007
“Iterative Balayage Techniques with Applications to Riesz and
Logarithmic Potentials”
Geometric
Measure Theoretic Approaches to Potentials on Fractals and Manifolds, Oberwolfach Mathematics Institute, Germany – April,
2007 "Minimal Energy Problems with Riesz External Fields and
Applications"
12th
International Conference in Approximation Theory, San Antonio, TX – March, 2007
"On an Energy Problem
with Riesz External Field"
Sofia University
Colloquium, Sofia, Bulgaria – June,
2006
“Riesz energy points
distribution”
Western Kentucky
University Colloquium, Bowling Green,
KY – April, 2006
“Minimal Energy Points on
the Sphere”
Special Session, 2005 AMS
Sectional Meeting, Bowling Green, KY
– March, 2005
“Separation of minimal
s-energy points on the sphere”
Constructive Functions
Tech-04, International Conference in Georgia Tech, Atlanta, GA – November, 2004
“Riesz spherical
potentials with external fields and minimal energy points
separation”
Special Session AMS
National meeting, Phoenix, AZ –
January, 2004
“On a class of classical
polynomials, uniformly approximating the checkmark function”
Vanderbilt University
Seminar, Nashville, TN – October,
2003
"On a discrete Zolotarev problem with applications to the Alternating
Direction Implicit (ADI) method"
Troy University Colloquium, Troy, AL – September, 2003
“Minimal Arrangements on
the Sphere”
Advances in Constructive
Approximation 2003, Nashville, TN –
May, 2003
"Polynomial
Approximation of the Checkmark Function”
Sigma Xi Brown Bag talk, IPFW – December, 2002
"The
Science of Spherical Arrangements - Fulerenes,
Electrons, and Soccer Ball Designs
Constructive Function
Theory 2002, Varna, Bulgaria – June,
2002
"Optimal Point Configurations on the Sphere”
AMS regional meeting --
Special Session, Chattanooga, TN –
October, 2001
"Logarithmic Points on the Sphere"
Computational Methods and Function Theory 2001, Portugal – June,
2001
"Minimal Discrete Energy on the Sphere"
Texas A&M Colloquium – March, 2001
"The support of the equilibrium measure"
University of Houston Colloquium- Downtown – March, 2001
"Soccer ball design and energy problems"
Indiana-Purdue University – April, 2000, Pi Math Club
"Chemistry, Physics, and Mathematics behind the Soccer Ball Design – Or
How to Distribute Dictators on a Planet"
Plovdiv University Colloquium, Plovdiv, Bulgaria – March, 2000
"Minimal problems and their applications to orthogonal
polynomials"
FoCM International Workshop on Minimal
Energy Problems, Hong Kong – November, 1999
"Constrained energy problem and applications"
University of Akron Colloquium– September, 1998
"Constrained energy problem and discrete orthogonal polynomials"
Katolieke Universiteit
Leuven Colloquium, Belgium – July, 1998
"Constrained Leja points and numerical
solution of the constrained energy problem"
Ohio State University Seminar – November, 1997
"Constrained energy problem and zero asymptotics
of discrete orthogonal polynomials"
Contributed Presentations:
11th
International Conference in Approximation Theory, Gatlinburg, TN – May, 2004
"On a discrete Zolotarev problem and its applications to the Alternating
Direction Implicit (ADI) method"
Sigma Xi National Meeting, Galveston, TX – November, 2002
"Spherical Arrangements with Minimal Energy”
10th
International Conference in Approximation Theory, St. Louis, MO – March, 2001
"Discrete Logarithmic Energy on the Sphere"
NATO ASI and International Conference on Special Functions 2000, Tempe,
AZ – June, 2000
"The support of the equilibrium measure for a class of external fields
on a finite interval"
AMS regional meeting – Contributed Papers Session, Buffalo, NY – April,
1999
"Constrained Leja Points and
Applications"
9th International Conference in Approximation Theory,
Nashville, TN – January, 1998
"Generalized Bernstein-Erdos conjecture"