Doowon Koh

Chungbuk National University

Cheongju city, Chungbuk-Do 28644, Korea

Position: Professor (October, 2020 - Current)

Office: S40 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

#### 46. Extension theorems and Distance problems over finite fields, (joint work with Thang Pham, and Le Anh Vinh), J. Funct. Anal. accepted for publication. pdf .

#### 45. Mattila-Sjolin type functions: A finite field model, (joint work with Daewoong Cheong, Thang Pham and Chun-Yen Shen), Vietnam Journal of Mathematics, accepted for publication. pdf .

#### 44. An asymmetric bound for sum of distance sets, (joint work with Daewoong Cheong and Thang Pham), Memorial volume of Proceedings of the Steklov Institute of Mathematics, accepted for publication. pdf .

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

#### 42. Distribution of the determinants of sums of matrices, (joint work with Daewoong Cheong, Thang Pham, Le Anh Vinh), Revista Matematica Iberoamericana, accepted for publication. pdf .

#### 42. A sharp exponent on sum of distance sets over finite fields, (joint work with Thang Pham, Chun-Yen Shen, and Le Anh Vinh), Math. Z. 297 (2021), no. 3-4, 1749 765. pdf .

#### 40. Moderate Expanders Over Rings, (joint work with Dao Nguyen Van Anh, Le Quang Ham, Mozhgan Mirzaei, and Thang Pham), J. Number Theory 218 (2021), 223 33 pdf .

#### 39. On a theorem of Hegyvari and Hennecart, (joint work with Dao Nguyen Van Anh, Le Quang Ham, Thang Pham, and Le Anh Vinh ), Pacific J. Math. 305 (2020), no. 2, 407-421. pdf .

#### 38. Exponential sum estimates over prime fields, (joint work with Mozhgan Mirzaei, Thang Pham, and Chun-Yen Shen), Int. J. Number Theory 16 (2020), no. 2, 291-308. pdf .

#### 37. Finite field restriction estimates for the paraboloid in high even dimensions, (joint work with Mark Lewko and Alex Iosevich), J. Funct. Anal, 278 (2020), no. 11, 108450. pdf .

#### 36. 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 Arith. 193 (2020), no. 2, 165-174. pdf .

#### 35. New bounds for distance-type problems over prime fields, (joint work with Alex iosevich and Thang Pham), European J. Combin. 86 (2020), 103080, PP. 1-11. pdf .

#### 34. Conjecture and improved extension theorems for paraboloids in the finite field setting, Math.Z. 294, (2020) 1-2, 51-69. pdf .

#### 33. Distance sets over arbitrary finite fields, (joint work with Sujin Lee, Thang Pham, and Chun-Yen Shen), Illinois J. Math., 63 (2019), no. 3, 469-484. pdf .

#### 32. 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. 300 (2019), no. 2, 405-417. pdf .

#### 31.Expanding phenomena over matrix rings, (joint work with Yesim Demiroglu Karabulut, Thang Pham, Chun-Yen Shen, and Le Anh Vnh), Forum Math. 31 (2019), no. 4, 951-970. pdf .

#### 30. On the quotient set of the distance set, (joint work with Alex Iosevich and Hans Parshall), Mosc. J. Comb. Number Theory 8 (2019), no. 2, 103-115. pdf .

#### 29. The generalized k-resultant modulus set problem in finite fields, (joint work with David Covert and Youngjin Pi), J. Fourier Anal. Appl. 25 (2019), no. 3, 1026-1052. 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. Extension theorems for Hamming varieties over finite fields, (joint work with Daewoong Cheong, and Thang Pham), submitted for publication. pdf .

#### 2. On the cone restriction conjecture in four dimensions and applications in incidence geometry, (joint work with Sujin Lee and Thang Pham), submitted for publication. pdf .

#### 3. Contacting spheres in positive characteristic and applications, (joint work with Thang Pham), submitted for publication. pdf .

#### 4. A spherical extension theorem and applications in positive characteristic, (joint work with Thang Pham), submitted for publication. pdf .

#### 5. On the Mattila-Sjolin distance theorem for product sets, (joint work with Thang Pham and Chun-Yen Shen), submitted for publication. pdf .

#### 6. Energy of sets on a paraboloid in finite fields, (joint work with Sujin Lee, Thang Pham and Chun-Yen Shen), submitted for publication. pdf .

#### 7. Averages and maximal averages over Product j-varieties in finite fields (joint work with Sujin Lee), 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

#### Dao Nguyen Van Anh .

#### Daewoong Cheong .

#### David Covert .

#### Yesim Demiroglu Karabulut .

#### M. Burak Erdogan .

#### Le Quang Ham .

#### 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 for Ph.D

#### Youngjin Pi .

#### Seongjun Yeom .

### Former Graduate Students for MS

#### Dongyoon Kwak .

#### Miran Jeong .

### Current Graduate Students

#### Sujin Lee .

### Family

- My wife, a daughter, and two sons are my family. My wife is Insook Min, Minjeong Koh is my daughter, My first son is Daniel Hyunbin Koh, and My last son is David Hyunchan Koh.

### Some links

Last update: May 10, 2021.