Doowon Koh
Department of Mathematics
Michigan State University
East Lansing, MI 48824
Position: Postdoc (August, 2009 - Current)
Office: A344 Wells Hall
Phone: (517) 353-6882
Email: koh@math.msu.edu
Education
Curriculum vitae-Click here.
Teaching
Research interest
- Harmonic Analysis in Finite Fields
- Fourier analysis
- Analytic Number Theory
- Geometric Combinatorics
Publications
8. Sharp extension theorems and Falconer distance problems for algebraic curves in two dimensional vector spaces over finite fields
( joint work with Chun-Yen Shen) , Revista Matematica Iberoamericana, to appear in Volume 28, issue 1 (2012).
pdf .
7. Pinned distance sets, k-simplices, Wolff's exponent in finite fields and sum-product estimates
( joint work with J. Chapman, M. B. Erdogan, D. Hart, and A. Iosevich), Math. Z., currently published online, March 22 (2011).
pdf .
6. Averages over hyperplanes, sum-product theory in vector spaces over finite fields and the Erdos-Falconer distance conjecture
( joint work with D. Hart, A. Iosevich, and M. Rudnev), Trans. Amer. Math. Soc. Volume 363, June (2011), no.6, 3255-3275.
pdf .
5. Extension theorems for paraboloids in the finite field setting
( joint work with Alex Iosevich), Math. Z. 266(2010), no.2, 471-487.
pdf .
4. Extension theorems for spheres in the finite field setting
( joint work with Alex Iosevich), Forum Math. 22 (2010), no. 3, 457–483.
pdf .
3. Generalized incidence theorems, homogeneous forms and sum-product estimates in finite fields
( joint work with D. Covert, D. Hart, A. Iosevich, and M. Rudnev ), European J. Combin. 31 (2010), no. 1, 306--319.
pdf .
2. Extension theorems for the Fourier transform associated with nondegenerate quadratic surfaces in vector spaces over finite fields
( joint work with Alex Iosevich), Illinois J. Math. 52 (2008), no. 2, 611--628.
pdf .
1. The Erdos-Falconer distance problem, exponential sums, and Fourier analytic approach to incidence theorems in vector spaces over finite fields
( joint work with Alex Iosevich), SIAM J. Discrete Math. 23 (2008/09), no. 1, 123--135.
pdf .
Submitted Papers for Publication
1. Extension and averaging operators in vector spaces over finite fields
( joint work with Chun-Yen Shen), (2011).
pdf .
2. The generalized Erdos-Falconer distance problems in vector spaces over finite fields
( joint work with Chun-Yen Shen), (2011).
pdf .
3. Additive energy and the Falconer distance problem in finite fields
( joint work with Chun-Yen Shen),(2010).
pdf .
4. Distance graphs in vector spaces over finite fields, coloring, pseudo-randomness and arithmetic progressions
(joint work with D. Hart, A. Iosevich, S. Senger, and I. Uriarte-Tuero)
pdf .
Papers to be submitted soon
1. Mapping Properties of k-Plane Transforms and Conical Surface Transforms in Finite Fields, Preprint, (2011).
pdf .
papers in preparation
1. L^p-L^q estimates for Euclidean averaging operators, (2011).
2. Note on sharp X-ray and 2-plane transforms in finite fields(joint work with Chun-Yen Shen), (2011).
3. Fourier method and non-degenerate polynomials( joint work with Chun-Yen Shen), (2011).
Unpublished preprints
1. Harmonic analysis related to homogeneous varieties in three dimensional vector spaces over finite fields
(joint work with Chun-Yen Shen), (2010).
3. Extension and averaging operators for finite fields, Preprint (2009).
3. Note on the Minkowski dimension of distance sets in R^2
( joint work with A. Iosevich, I. Uriarte-Tuero, and Y. Wang),(2009).
Summary of my papers and Research statement
Advisors and mentor
My MS thesis advisor is
Yong-Kum Cho
.
Coworkers
Family
- My wife, a daughter, and two sons are my family.
My wife is Insook Min and
Minjeong Koh is my daughter, third-grader at Cornell Elementry School.
My first son is Daniel Hyunbin Koh, three years old, and the last son is David Hyunchan Koh, one year old.
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Last update: May 31, 2011.