My primary interest:
Discrete Computational Geometry
Additive Combinatorics
Geometric Measure Theory
My Co-Authors (50):
Dao Nguyen Van Anh, Tanbir Ahmed, Arie Bialostocki, Pablo Bhowmick, Philipp Birklbauer, Paige Bright, Daewoong Cheong, Francois Clement, Ye ̧sim Demiro ̆glu Karabulut, Jeong Han Kim, Pertti Mattila, Brendan Murphy, Mojgan Mirzaei, Ben Lund, Sujin Lee, Le Quang Ham, Le Quang Hung, Do Duy Hieu, Pham Duc Hiep, Alex Iosevich, Doowon Koh, Ali Mohammadi, Hossein N. Mojarrad, Janos Pach, Eyvi Palsson, Quy Pham, Giorgis Petridis, Jonathan Pakianathan, Nguyen Duy Phuong, Misha Rudnev, Steven Senger, Nguyen Minh Sang, Andrew Suk, Sophie Stevens, Chun-Yen Shen, Dung The Tran, Michael Tait, Craig Timmons, Gabor Tardos, Nguyen Trung-Tuan, Nguyen Duc-Thang, Vu Thi Huong Thu, Nguyen Pham Minh Tri, Le Anh Vinh, Claudiu Valculescu, Robert Won, Audie Warren, Boqing Xue, Semin Yoo, Frank de Zeeuw.
Preprints:
Packing sets in Euclidean space by affine transformations, 2024, submitted.
On the distance problem over finite p-adic rings, 2024, submitted.
On the solvability of systems of equations revisited, 2024, submitted.
New–type Quasirandom Groups and Applications, 2023, submitted.
On a radial projection conjecture in F_q^d, 2023, submitted.
VC-dimension and pseudo-random graphs, 2023, submitted.
Intersection patterns and incidence theorems, 2023, submitted.
A discretized point-hyperplane incidence bound in R^d, 2023, submitted.
Orthogonal projections in the plane over prime order fields, 2023, submitted.
Radial projection theorems in finite spaces, 2022, submitted.
Discretized sum-product type problems: Energy variants and Applications, 2022, submitted.
Published papers
2024
Falconer type functions in three variables, Journal of Functional Analysis, 286(4) (2024), 110246.
Pinned simplices and connections to product of sets on paraboloids, accepted in Indiana University Mathematics Journal.
Geometric structures in pseudo-random graphs, accepted in Canadian Journal of Mathematics.
Multi-linear forms, graphs, and L^p-improving measures in F_q^d, accepted in Canadian Journal of Mathematics.
Triangles with one fixed side-length, a Furstenberg type problem, and incidences in finite vector spaces, accepted in Forum Mathematicum.
Product of sets on varieties in finite fields, Journal of Fourier Analysis and Applications, 30(2) (2024), 1-15.
Parallelograms and the VC-dimension of the distance sets, Discrete Applied Mathematics, 349 (2024), 195-200.
An improved point-line incidence bound over arbitrary finite fields via the VC-dimension theory, European Journal of Combinatorics, 118 (2024), 103928.
Group action and L^2 norm estimates of geometric problems, Journal of Mathematical Analysis and Applications, 531(1) (2024), 127748.
A spherical extension theorem and applications in positive characteristic, to appear in Finite Fields and Their Applications.
2023
A Point-Conic Incidence Bound and Applications, European Journal of Combinatorics, 107 (2023), 103596.
An energy decomposition theorem for matrices and related questions, Canadian Mathematical Bulletin, 66(4) (2023), 1280-1295.
Threshold functions for incidence properties in finite vector spaces, Finite Fields and Their Applications, 87 (2023), 102149.
Distribution of pinned distance trees in the plane F2p, Discrete Mathematics, 346(12) (2023), 113613.
Structural theorems on the distance sets over finite fields, Forum Mathematicum, 35(4) (2023), 925-938.
Configurations of rectangles in a set in 𝔽_q^2 , Finite Fields and Their Applications, 86(2023), 102147.
2022
On the pinned distances problem in positive characteristic, Journal of the London Mathematical Society, 105(1) (2022), 469-499.
On the cone restriction conjecture in four dimensions and applications in incidence geometry, International Mathematics Research Notices, 2022(21), 17079-17111.
On the Mattila-Sjolin distance theorem for product sets, Mathematika, 68(4) (2022), 1258-1267.
Distribution of distances in five dimensions and related problems , SIAM Journal on Discrete Mathematics, 36(3) (2022), 2271-2281.
A point-sphere incidence bound in odd dimensions and applications , Comptes Rendus. Mathématique, 360.G6 (2022), 687-698.
2021
On restriction estimates for spheres in finite fields, Canadian Journal of Mathematics, 73(3) (2021), 769-786.
Extension theorems for Hamming varieties over finite fields, Proceedings of the American Mathematical Society, 150(1) (2021), 161-170.
Extension theorems and Distance problems over finite fields, Journal of Functional Analysis, 281(8) (2021), 109137.
Moderate Expanders Over Rings, Journal of Number Theory , 218(2021), 223-233.
An asymmetric bound for sum of distance sets, Proceedings of the Steklov Institute of Mathematics, 314 (2021), 279–289. (dedicated to 130th anniversary of Academician Ivan Matveevich Vinogradov)
Mattila--Sjolin type functions: A finite field model, Vietnam Journal of Mathematics, 2021, 1-14.
2020
A sharp exponent on sum of distance sets over finite fields, Mathematische Zeitschrift, 297 (2020), 1-17.
Distribution of determinant of sum of matrices, Revista Matematica Iberoamericana, 37(4) (2020), 1365–1398.
On a theorem of Hegyvari and Hennecart, Pacific Journal of Mathematics, 305(2) (2020), 407--421.
Exponential sum estimates over prime fields, International Journal of Number Theory, 16(02)(2020), 291-308.
Distribution of distances in vector spaces over prime fields, Pacific Journal Mathematics, 309 (2020), 437-451.
A new perspective on the distance problem over prime fields, European Journal of Combinatorics, 86 (2020), 103080.
Structures of distance sets over prime fields, Proceedings of the American Mathematical Society, 148(2020), 3209--3215.
A new lower bound on the Erdos distinct distances problem over prime fields, Acta Arithmetica, 193 (2020), 165-174.
2019
Three-variable expanding polynomials and higher-dimensional distinct distances, Combinatorica, 39(2) (2019), 411-426.
Power sum polynomials as weak and relaxed EGZ polynomials, INTEGER, 19, A49, (2019).
A Sum-product theorem in matrix rings over finite fields, C. R. Acad. Sci. Paris, Ser. I. 357(10) (2019), 766-770.
Expanding phenomena over matrix rings, Forum Mathematicum, 31(4) (2019), 951-970.
Expansion for the product of matrices in groups, Forum Mathematicum, 31(1) (2019), 35-48.
On the determinants and permanents of matrices with restricted entries over prime fields, Pacific Journal of Mathematics, 300(2)(2019): 405-417.
Incidences between planes over finite fields, Proceedings of the American Mathematical Society, 147(5) (2019), 2185-2196.
Distance sets for small sets over arbitrary finite fields, Illinois Journal of Mathematics, 63(3) (2019), 469-484.
2018
A structure theorem for product sets in extra special groups, Journal of Number Theory, 184 (2018), 461-472.
Conditional expanding bounds for two-variable functions over arbitrary fields, Journal of Number Theory, 186 (2018), 137-146.
Four-variable expanders over the prime fields, Proceedings of the American Mathematical Society, 146(12) (2018), 5025-5034.
Distances from points to planes, Acta Arithmetica, 186 (2018): 219-224.
Distinct distances between points and lines in F_q^2, Forum Mathematicum, 30(4) (2018), 799-808.
Distinct spreads in vector spaces over finite fields, Discrete Applied Mathematics, 239 (2018), 154-158.
2017
Some combinatorial number theory problems in finite spaces, Illinois Journal of Mathematics, 61(2) (2017), 243-257.
A Szemeredi-Trotter type theorem, sum-product estimates in finite quasifields, and related results, Journal of Combinatorial Theory, Series A, 147 (2017), 55-74.
Schwartz-Zippel bounds for two-dimensional products, Discrete Analysis, 20 (2017), 20pp.
Conditional expanding bounds for two-variable functions over finite valuation rings, European Journal of Combinatorics, 60 (2017): 114-123.
Distinct distances on regular varieties over finite fields, Journal of Number Theory, 173(2017), 602-613.
An improvement on the number of simplices in F_q^d , Discrete Applied Mathematics, 221 (2017), 95-105.
Right angles in finite spaces, preprint, (2017).
Paths in pseudorandom graphs and applications, Ars Combinatoria, 153 (2017), 195-207.
Incidences between points and generalized spheres over finite fields and related problems, Forum Mathematicum, 29(2) (2017), 449-456.
2016
An additive problem in finite cyclic rings with powers of elements of large multiplicative order, Applicable Analysis and Discrete Mathematics, 10(2) (2016), 325-331.
2015
Erdos-Renyi graph, Szemeredi-Trotter type theorem, and sum-product estimates over finite rings, Forum Mathematicum, 27(1) (2015), 331-342.
2012
Orthogonal systems in vector spaces over finite rings, Electronic Journal of Combinatorics, (2012), P48.
Ph. D. Thesis: Erdos Distinct Distances Problem and Extensions over Finite Spaces, EPFL, Lausanne, 2017.
Referee Service:
Annales Fennici Mathematici, Discrete and Computational Geometry (DCG), Discrete Mathematics, European Journal of Combinatorics (EJC), SIAM Journal on Discrete Mathematics (SIDMA), Journal of Combinatorial Theory Series A (JCTA), Discrete Applied Mathematics (DAM), Symposium on Computational Geometry (SoCG), Forum Mathematicum (FORUM), Journal of Fourier Analysis and Applications (JFAA), New York Journal of Mathematics, Finite Fields and Their Applications (FFA), Journal of Number Theory, Proceedings of the American Mathematical Society (PAMS), Vietnam Journal of Mathematics, Math Reviews, ZbMATH