Research Interests:
Additive Combinatorics, Harmonic Analysis and Geometric Measure Theory
Publications:
33: Falconer type functions in three variables, (with D. Koh and T. Pham), Journal of Functional Analysis, 2024.
32: Pinned simplices and connections to product of sets on paraboloids, (with A. Iosevich M. Pham, and T. Pham), Indiana Univ Math Journal 2024.
31: Intersection between pencils of tubes, discretized sum-product, and radial projections, (with B. Liu), Asian Journal of Mathematics, 2024.
30: On the Mattila-Sjolin distance theorem for product sets, (with D. Koh, and T. Pham), Mathematika 2023.
29: A two weight local Tb theorem for the Hilbert transform (227 pages), (with E. Sawyer and I. UTuero), Revista Matemática Iberoamericana, 2021.
28: Energy counterexamples in two weight Calderon-Zygmund theory, (with E. Sawyer and I. Uriarte-Tuer), International Mathematics Research Notices, 2021.
27: On Restriction Estimates for the Zero Radius Sphere over Finite Fields, (with A. Iosevich, T. Pham, D. Koh), Canadian Journal of Mathematics, 2021
26: A sharp exponent on sum of distance sets over finite fields (with T. Pham and D. Koh), Math. Z. 2020
25: Two weight T1 theorem for fractional Riesz transforms when one measure is supported on a curve, to appear in Journal d'Analyse Mathmatique 2020 (60 pages)
24: Exponential sum estimates over prime field, (with T. Pham and D. Koh), International Journal of Number Theory, 2020
23: On the determinants and permanents of matrices with restricted entries over prime fields, (with D. Koh, T. Pham and L. Vinh), Pacific Journal of Math 2020
22: Fourier methods and non degenerate polynomials, Finite Fields and their Applications 2019
21: Distance sets over arbitrary fields (with T. Pham, S. Lee and D. Koh), Illinois Journal of Math 2019
20: On the size of the set AA + A, (with O. Newton, I. Ruzsa and I. Shkredov), to appear in Journal of the London Mathematical Society, 2019
19: Restricted averaging operators to cones over finite fields (with D. Koh and S. Yeom), to appear in Forum Mathematicum, 2018 (20 pages)
18: A good lambda lemma, two weight T1 theorems without weak boundedness, and a two weight accretive global Tb theorem (with E. Sawyer and I. Uriarte), Harmonic Analysis, Partial Differential Equations and Applications in Honor of Richard Wheeden 2018 (41 pages).
17: A two weight fractional singular integral theorem with side conditions, energy and k-energy dispersed (with E. Sawyer and I. Uriarte-Tuero), Harmonic Analysis, Partial Differential Equations, Banach Spaces and Operator Theory (Volume 2), Celebrating Cora Sadosky's life 2017 (71 pages).
16: Averaging operators over homogeneous varieties over finite fields (with D. Koh and I. Shparlinski), Journal of Geometric Analysis, 2016 (27 pages)
15: A two weight theorem for alpha fractional singular integrals with an energy side condition (with E. Sawyer and I. Uriarte-Tuero), Rev. Mate. Iberoam, 2016 (102 pages).
14: A note on the failure of energy reversal for classical fractional singular integrals (with E. Sawyer and I. Uriarte-Tuero), Int. Math. Res. Not., Issue 19, 9888-9920, 2015 (33 pages)
13: Two weight inequality for the Hilbert transform: a real variable characterization (with M. Lacey, E. Sawyer and I. Uriarte-Tuero). Duke Math, 2014.
12: Fourier analysis and expanding phenomena in finite fields (with D. Hart and L. Li). Proc. Amer. Math. Soc. 141 (2013), 461-473.
11: The generalized Erdos-Falconer distance problems in vector spaces over finite fields (with D. Koh). Journal of Number Theory, Vol 132, 2455-2473, 2012.
10: Harmonic analysis related to homogeneous varieties in three dimensional vector spaces over finite fields (with D. Koh). Canadian J. Math, Vol 64, 1036-1057, 2012.
9: Extension and averaging operators in vector spaces over finite fields (with D. Koh). Proc. Edinb. Math. Soc. no. 2, 599-614, 2013.
8: Sharp extension theorems and Falconer distance problems for algebraic curves in two dimensional vector spaces over finite fields (with D. Koh). Revista Matematica Iberoamericana, Vol 28, 159-180, 2012.
7: Algebraic methods in sum product phenomena, Israel J. Math. Vol 88, no. 1, 2012.
6: On the size of the set A(A+1) (with M. Garaev). Math. Z. 263 (2010), no. 94.
5: On the sum product estimates and two variables expanders. Publicacions Matematiques, 54 (2010) no. 1.
4: Quantitative sum product estimates on different sets. Electron. J. Combin. 15 (2008), no. 1.
3: An extension of Bourgain and Garaev's sum product estimate. Acta Arith. 135 (2008), no. 4, 351-356.
2: A slight improvement to Garaev's sum product estimate (with Nets Katz). Proc. Amer. Math. Soc. 136 (2008) 2499-2504.
1: Garaev's inequality in finite fields not of prime order (with Nets Katz). J. Analytic Combinatorics 2008.
About Matrices Norm and one complex variable
1: Matrices whose norm are determined by their actions on decreasing sequences (with C-P Chen and H-W Huang). Canadian J. Math, Vol 3, 520-531, 2008.
2: A slight improvement to Korenblum's constant, J. Math. Anal. Appl, No.1, 2008.
Selected Invited Talks:
1: Clay-Fields conference on additive combinatorics, number theory and Harmonic analysis, Fields Institute, Toronto April 2008.
2: Harmonic analysis, Fields Institute, May 2010.
3: Harmonic analysis and additive combinatorics, CMS meeting, Vancouver, Dec 2010.
4: The Kakeya problem, restriction problem and sum-product theory, IPAM UCLA, May 2014.
5: Unlikely Intersections, CIRM (Centre International De Rencontres Mathematiques), Luminy Marseille, France, Feb 2014.
6: Emerging applications of finite fields: applications of algebra and number theory, RICAM (Johann Radon institute for computational and applied mathematics), Lina, Austria, Dec 2013.
7: New Directions in combinatorics, Univ of Singapore, May 2016.
8: Harmonic analysis and PDE, Macquarie Univ, Australia July 2017.
9: Operator algebras and Harmonic analysis, TSIMF, Dec 2017.
10: AIMS conference in Taipei, Harmonic analysis, July 2018.
11: Harmonic Analysis workshop, Osaka Univ, Aug 2018
12: 45 minutes talk, ICCM, NTU Taipei, Dec 2018
13: International workshop on Additive Combinatorics, VIAS Jan 2019
14: Harmonic Analysis workshop, Madison Wisconsin May 2019
15: 45 minutes talk, ICCM, Beijing China June 2019
16: 7th Asia Harmonic Analysis and its Applications, Seoul Korea Aug 2019
17: EACDFM 2020, University of Tokyo Jan 2020
18: Harmonic analysis workshop at Seoul national university, Feb 2020
19: Moscow conference on combinatorics and applications, Moscow Institute of Physics and Technology May 2020
20: 8th Asia Harmonic Analysis and its Applications, Nagoya University, Japan Aug 2021 (online conference)
21: Invited Speaker at Annual Meeting of Australian Mathematical Society, Newcastle, Australia December 2021
22: 7th Kyoto Top Global University Mathematics Workshop for Young Researchers, Feb 2022
23: Harmonic Analysis and PDEs, Summer Meeting of Canadian Mathematical Society, Newfoundland-Labrador Canada, June 2022
24: Invited Speaker, International Congress of Chinese Mathematicians, ICCM 2022
25: 2nd Harmonic Analysis Workshop, Seoul National University, Oct 2022
26: 3rd Harmonic Analysis Workshop, Seoul National University, Oct 2023
27: Workshop on Combinatorics and Geometric Measure Theory, VIASM, Hanoi, July 2023
28: Invited Speaker at Annual Meeting of Australian Mathematical Society, University of Queensland, Dec 2023
29: Harmonic Analytic Connections, Matrix, Australia, May 2024
30: IBS-DIMAG Workshop on Combinatorics and Geometric Measure Theory, Korea, July 2024
31: Taiwan-Hong Kong Joint Conference, NSYSU, Kaohsiung, May 2025
32: Workshop on Harmonic Analysis, SUSC, Shenzhen, June 2025
33: Asia-Pacific International Conference, Sydney, Feb 2026
Researchers
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