Doowon Koh

Chungbuk National University

Cheongju city, Chungbuk-Do 361-763, Korea

Position: Associate Professor (October, 2015 - Current)

Office: S40µ¿ 422

Phone: (043) 261-2244

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

#### 24. The k-resultant modulus set problem on algebraic varieties over finite fields, (joint work with David Covert and Youngjin Pi), Finite Fields Appl. 48 (2017), 68-86. pdf .

#### 23. Restricted averaging problems to algebraic varieties in finite fields (joint work with Seongjun Yeom), Taiwanese J. Math, 21 (2017), no.1, 211-229. pdf .

#### 22. Averaging operators over homogeneous varieties over finite fields , (joint work with Chun-Yen Shen and Igor Shparlinski), The Journal of Geometric Analysis, 26 (2016), no.2, 1415-1441. pdf .

#### 21. On the sums of any k points in finite fields, (joint work with David Covert and Youngjin Pi), SIAM J. Discrete Math, 30 (2016), no.1, 367-382. pdf .

#### 20. Sharp L^p- L^r estimates of restricted averaging operators over curves on planes in finite fields,Journal of the Chungcheong Mathematical Society, Volume 28(2015), no. 2, 251-259. pdf .

#### 19. Distance sets determined by two sets in vector spaces over finite fields, ( joint work with Hae-Sang Sun), Proc. Amer. Math. Soc. 143 (2015), no. 4, 1679-1692. pdf .

#### 18. Averaging operators over nondegenerate quadratic surfaces in finite fields, Forum Math., 27 (2015), 1227-1247. pdf .

#### 17. Weak version of restriction estimates for spheres and paraboloids in finite fields, (joint work with Hunseok Kang), J. Math. Anal. Appl., 419 (2014) 783-795. pdf .

#### 16. Restriction operators acting on radial functions on vector spaces over finite fields, Canad. Math. Bull. 57 (2014), no. 4, 834-844. pdf .

#### 15. Size of dot product sets determined by pairs of subsets of vector spaces over finite, (joint work with Yongjin Pi), Journal of the Chungcheong Mathematical Society, Volume 26(2013), no. 4, 853-867. pdf .

#### 14. Additive energy and the Falconer distance problem in finite fields ( joint work with Chun-Yen Shen), Integers, 13 (2013), A28 1-10. pdf .

#### 13. Distance graphs in vector spaces over finite fields(joint work with Derrick Hart, Alex Iosevich, Steve Senger and Ignacio Uriarte-Tuero), the Springer volume in honor of Kostya Oskolkov's 65th birthday, Recent Advances in Harmonic Analysis and Applications, Springer Proceedings in Mathematics and Statistics Volume 25, 2013, pp 139-160. pdf .

#### 12. Sharp endpoint estimates for the X-ray transform and the Radon transform in finite fields, Proc. Amer. Math. Soc. 141 (2013), no. 8, 2799-2808. pdf .

#### 11. Extension and averaging operators for finite fields ( joint work with Chun-Yen Shen), Proc. Edinb. Math. Soc. (2) 56 (2013), no. 2, 599–614. pdf .

#### 10. Harmonic analysis related to homogeneous varieties in three dimensional vector spaces over finite fields ( joint work with Chun-Yen Shen) ,Canad. J. Math. 64(2012), 1036-1057 Published:2011-12-23 (Printed: Oct 2012). pdf .

#### 9. The generalized Erdos-Falconer distance problems in vector spaces over finite fields ( joint work with Chun-Yen Shen) , Journal of Number Theory 132(2012),no.11, 2455-2473 (Printed: November 2012). pdf .

#### 8. 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., Volume 271, June (2012), no.1, 63-93. pdf .

#### 7. 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, Volume 28(2012), no.1, 157-178. 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 .

### Preprints and Submitted Papers for Publication

#### 1. Conjecture and improved extension theorems for paraboloids in the finite field setting, submitted for publication. pdf .

#### 2. L^p-L^r estimates for k-plane transforms in finite fields, (joint work with Dongyoon Kwak), submitted for publication. pdf .

#### 3. The generalized k-resultant modulus set problem in finite fields, (joint work with David Covert and Youngjin Pi), submitted for publication. pdf .

#### 4. Restricted averaging operators to cones over finite fields, (joint work with Chun-Yen Shen and Seongjun Yeom), submitted for publication. pdf .

#### 5. Four-variable expanders over the prime fields, (joint work with Hossein Nassajian Mojarrad, Thang Pham, and Claudiu Valculescu, submitted for publication. pdf .

### 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

#### Jeremy M. Chapman .

#### David Covert .

#### M. Burak Erdogan .

#### Derrick Hart .

#### Alex Iosevich .

#### Hunseok Kang .

#### Dongyoon Kwak .

#### Hossein Nassajian Mojarrad .

#### Thang Pham .

#### Youngjin Pi .

#### Misha Rudnev .

#### Steven Senger .

#### Chun-Yen Shen .

#### Igor Shparlinski .

#### Hae-Sang Sun .

#### Ignacio Uriarte-Tuero .

#### Claudiu Valculescu .

#### Seongjun Yeom .

### Students

#### Youngjin Pi .

#### Seongjun Yeom .

#### Dongyoon Kwak .

#### Sujin Lee .

### Family

- My wife, a daughter, and two sons are my family. My wife is Insook Min and Minjeong Koh is my daughter, 3rd-grader at Cheongju Woman Middle School. My first son and second son are Daniel Hyunbin Koh and David Hyunchan Koh who are 4th-grader and 2nd-grader at Changsin elementary school, respectively.

### Some links

Last update: August 14th, 2017.