Dmitriy Bilyk

Home page of Dmitriy Bilyk

Dmitriy Bilyk

Assistant Professor

Department of Mathematics
University of South Carolina
LeConte College, office 300D
1523 Greene Street
Columbia, SC 29208, USA

E-mail: bilyk@math.sc.edu

L² discrepancy of lattices and properties of continued fractions, in preparation. (with V.Temlyakov and R.Yu)
On some sets with minimal L² discrepancy, in preparation.
Directional discrepancy of rotated lattices, in preparation. (with X. Ma, J.Pipher, and C.Spencer)
Combinatorial Discrepancy with Respect to Higher Dimensional Boxes, in preparation.
Fibonacci Sets and Symmetrization in Discrepancy Theory, to appear in Journal of Complexity. (with V.Temlyakov and R.Yu)
Directional Discrepancy in Two Dimensions, to appear in The Bulletin of London Math. Soc. (with X. Ma, J.Pipher, and C.Spencer)
Roth’s orthogonal function method in discrepancy theory, Uniform Distribution Theory 6 (2011), no. 1, 143–184.
A three-dimensional signed Small Ball Inequality, “Dependence in Probability, Analysis and Number Theory”, Walter Philipp memorial volume, 73–87, Kendrick Press, Heber City, UT, 2010. (with M.Lacey, I.Parissis, and A.Vagharshakyan)
Cyclic Shifts of the Van der Corput set, Proc. Amer. Math. Soc., 137 (2009), 2591-2600.
Exponential Squared Integrability of the Discrepancy Function in Two Dimensions, Mathematika, 55 (2009), no. 1-2, 1-27. (with M.Lacey, I.Parissis, and A.Vagharshakyan)
Composition of Haar Paraproducts: The Random Case, Analysis Math, 35:1 (2009). (with M.Lacey, X.Li, and B.Wick)
On the Small Ball Inequality in Three Dimensions, Duke Math. J. 143 (2008), no. 1, 81-115. (with M.Lacey)

On the Small Ball Inequality in All Dimensions, J. Funct. Anal. 254 (2008), no. 9, 2470-2502. (with M.Lacey and A.Vagharshakyan)

On the Signed Small Ball Inequality, Online Journal of Analytic Combinatorics, 3 (2008). (with M.Lacey and A.Vagharshakyan)

The interplay between distributional estimates and boundedness in harmonic analysis, The Bulletin of London Math. Soc., 37 (2005) 427-434.
(with L. Grafakos)

The distributional estimates for the bilinear Hilbert transform, Journal of Geometric Analysis 16 (2006) 563-583. (with L. Grafakos)

A new way of looking at distributional estimates; applications for the bilinear Hilbert transform, Proceedings of the 7th International Conference on
Harmonic Analysis and Partial Differential Equations [El Escorial, 2004], Collectanea Mathematica (2006), 141-169. (with L. Grafakos)

Narrow operators on vector-valued sup-normed spaces, Illinois J. Math., 45 (2002) 120-143. (with V. Kadets, R. Shvidkoy, G. Sirotkin, D. Werner)

Narrow operators the Daugavet property for ultraproducts, Positivity, 9 (2005) 45-62. (with V. Kadets, R. Shvidkoy, D. Werner)

On Some Sets with Minimal L2 Discrepancy: 9th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, Warsaw, Poland, August 2010.
Directional Discrepancy: Harmonic Analysis: A Retrospective Workshop, Fields Institute, Toronto, June 2010.
Discrepancy and the Small Ball Inequality: invited one hour talk at the Workshop on Discrepancy Theory and Related Areas, Varenna, Italy, June 2007.
The Discrepancy Theory: classical and new results: a talk for graduate students at the Research Horizons seminar, Georgia Tech, April 2007.
The Discrepancy Function and the Small Ball Inequality in Higher Dimensions: 2007 Fall AMS Western Section Meeting, Albuquerque, NM, October 2007.
Distributional Estimates for Multilinear Operators : Harmonic and Geometric Analysis with Applications to PDE, Sevilla, Spain, August 2006.