Doowon Koh

Michigan State University

East Lansing, MI 48824

Position: Postdoc (August, 2009 - Current)

Office: A344 Wells Hall

Phone: (517) 353-6882

Email:

### Education

#### Ph. D (December, 2008), University of Missouri.

#### Master (Feburary, 2000), Chung-Ang University .

#### Bachelor (Feburary, 1998), Chung-Ang University .

### Curriculum vitae-Click here.

### Teaching

- See my CV above.

### 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

#### Summary of my papers .

#### Research Statement .

### Advisors and mentor

#### My MS thesis advisor is Yong-Kum Cho .

#### Ph.D advisor is Alex Iosevich .

#### My mentor for Postdoc is Ignacio Uriarte-Tuero .

### Coworkers

#### Alex Iosevich .

#### M. Burak Erdogan .

#### Chun-Yen Shen .

#### David Covert .

#### Derrick Hart .

#### Ignacio Uriarte-Tuero .

#### Jeremy M. Chapman .

#### Misha Rudnev .

#### Steven Senger .

### 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.

### Some links

Last update: May 31, 2011.