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

#### 35. Sum-product estimates over arbitrary finite fields, (joint work with Sujin Lee, Thang Pham, and Chun-Yen Shen), Illinois J. Math., accepted for publication. pdf .

#### 34. A new bound on Erdos distinct distances problem in the plane over prime fields, (joint work with Alex Iosevich, Thang Pham, Chun-Yen Shen, Le Anh Vinh), Acta Arithmetica, accepted for publication . pdf .

#### 33.Expanding phenomena over matrix rings, (joint work with Yesim Demiroglu Karabulut, Thang Pham, Chun-Yen Shen, and Le Anh Vinh), Forum Math, to appear. pdf .

#### 32. Conjecture and improved extension theorems for paraboloids in the finite field setting, Math.Z., to appear. pdf .

#### 31. On the quotient set of the distance set, (joint work with Alex Iosevich and Hans Parshall), Moscow Journal of Combinatorics and Number Theory (MJCNT), to appear. pdf .

#### 30. On the determinants and permanents of matrices with restricted entries over prime fields , (joint work with Thang Pham, Chun-Yen Shen, and Le Anh Vinh), Pacific J. Math. to appear. pdf .

#### 29. The generalized k-resultant modulus set problem in finite fields, (joint work with David Covert and Youngjin Pi), J. Fourier Anal. Appl., to appear. pdf .

#### 28. Expansion for the product of matrices in groups, (joint work with Thang Pham, Chun-Yen Shen, and Le Anh Vinh), Forum Math. 31 (2019), no. 1, 35-48. pdf .

#### 27. Restricted averaging operators to cones over finite fields, (joint work with Chun-Yen Shen and Seongjun Yeom), Forum Math. 30 (2018), no. 6, 1345-1361. pdf .

#### 26. Four-variable expanders over the prime fields, (joint work with Hossein Nassajian Mojarrad, Thang Pham, and Claudiu Valculescu, Proc. Amer. Math. Soc. 146 (2018), no. 12, 5025-5034. pdf .

#### 25. L^p-L^r estimates for k-plane transforms in finite fields, (joint work with Dongyoon Kwak), Proc. Amer. Math. Soc., 146 (2018), no. 8, 3381-3391. pdf .

#### 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. Finite field restriction estimates for the paraboloid in high even dimensions, (joint work with Mark Lewko and Alex Iosevich), submitted for publication. pdf .

#### 2. On restriction estimates for spheres in finite fields, (joint work with Alex Iosevich, Sujin Lee, Thang Pham, and Chun-Yen Shen), submitted for publication. pdf .

#### 3. Exponential sum estimates over prime fields, (joint work with Mozhgan Mirzaei, Thang Pham, and Chun-Yen Shen), submitted for publication. pdf .

#### 4. Extension theorems and Distance problems over finite fields, (joint work with Thang Pham, and Le Anh Vinh), submitted for publication. pdf .

#### 5. Extension theorems for Hamming varieties over finite fields, (joint work with Daewoong Cheong and Thang Pham), submitted for publication. pdf .

#### 6. Distribution of determinant of sum of matrices, (joint work with Daewoong Cheong, Thang Pham, Le Anh Vinh), submitted for publication. pdf .

#### 7. A new perspective on the distance problem over prime fields, (joint work with Alex Iosevich and Thang Pham), 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 .

#### Daewoong Cheong .

#### David Covert .

#### Yesim Demiroglu Karabulut .

#### M. Burak Erdogan .

#### Derrick Hart .

#### Alex Iosevich .

#### Hunseok Kang .

#### Dongyoon Kwak .

#### Sujin Lee .

#### Mozhgan Mirzaei .

#### Hossein Nassajian Mojarrad .

#### Hans Parshall .

#### Thang Pham .

#### Youngjin Pi .

#### Misha Rudnev .

#### Steven Senger .

#### Chun-Yen Shen .

#### Igor Shparlinski .

#### Hae-Sang Sun .

#### Ignacio Uriarte-Tuero .

#### Claudiu Valculescu .

#### Le Anh Vinh .

#### Seongjun Yeom .

### Former Graduate Students

#### Youngjin Pi .

#### Seongjun Yeom .

#### Dongyoon Kwak .

### Current Graduate Students

#### Sujin Lee .

#### Miran Cheong .

### Family

- My wife, a daughter, and two sons are my family. My wife is Insook Min and Minjeong Koh is my daughter, 2nd-grader at Ilsin Woman High School. My first son and second son are Daniel Hyunbin Koh and David Hyunchan Koh who are 6th-grader and 4th-grader at Changsin elementary school, respectively.

### Some links

Last update: May 15, 2019.