Home page of Dmitriy Bilyk

Dmitriy Bilyk            


School of Mathematics
University of Minnesota
Vincent Hall, office 328
206 Church St. SE
Minneapolis, MN, 55408 USA

E-mail: dbilyk@math.umn.edu
Dmitriy Bilyk 
  • Curriculum Vitae

  • Publications

  • Talks

    RESEARCH INTERESTS:  Harmonic analysis, functional  analysis,  discrepancy theory.
    The research is supported by the NSF grants DMS 0801036 (2008-2011), DMS 1101519 (2011-2015), DMS 1665007 (2017-2020), and the Simons Foundation Collaboration Grant (2016-2021).

    PUBLICATIONS (published, accepted, submitted):


    • Discreteness of minimizing measures,  JMM 2020, Dencer, CO.
    • Discrete minimizers of energies on the sphere, 10th Discrete Geometry and Algebraic Combinatorics Conference, South Padre Island, TX, Sep 2019.
    • Discrepancy bounds and related questions, Program "Equidistribution: Arithmetic, Computational and Probabilistic Aspects'', IMS, Singapore, May 2019.
    • Distributing points on a sphere, Conference ``Optimal Point Configurations and Potential Theory'', CIEM, Castro Urdiales, Spain, April  2019.
    • Tutorial talk Discrepancy Theory', RICAM, Linz, Austria,  Nov 2018.
    • Point distributions and harmonic analysis, 4-lecture series, TU Graz, Austria, October 2018.
    • Discrepancy and energy optimization on the sphere, 6th International Conference on Uniform Distribution Theory (UDT2018), CIRM, Luminy, France, Sep 2018.
    • Energy minimization on the sphere, ICM 2018 Satellite Conference Harmonic Analysis, Federal University of Rio Grande do Sul, Porto Alegre, Brazil, July 24-29, 2018.
    • Plenary talk Point distributions on the sphere: energy minimization, discrepancy, and more, 34th Southeastern Analysis Meeting (SEAM) conference, Georgia Tech, Atlanta, GA, Mar 2018.
    • Point distributions on the sphere: energy minimization, discrepancy, and more, workshop "Optimal and Random Point Configurations", ICERM, Providence, RI, Feb 2018.
    • On some problems of uniform distribution and energy minimization on the sphere, , workshop "Discrepancy theory and quasi-Monte Carlo methods", ESI, Vienna, Sep 2017.
    • Uniform distribution problems on the sphere, Vilnius Conference in Combinatorics and Number Theory, July 2017.
    • Various uniform distribution problems on the sphere,  workshop "Approximation Theory and Function Spaces", CRM, Barcelona, Spain, June 2017.
    • Discrepancy and energy optimization on the sphere, conference ``Optimal point configurations and orthogonal polynomials 2017", CIEM, Castro Urdiales, Spain, April 2017.
    • Lacunary Fourier series: from Weierstrass to our days, "HalloWeierstrass" (a special Halloween/Weierstrass birthday talk), University of Minnesota, Oct 31, 2016.
    • Stolarsky-type identities, energy optimization, uniform tessellations, and one-bit sensing,  workshop "Optimal and Random Point Configurations: From Statistical Physics to Approximation Theory", Institut Henri Poincare, Paris, France, Jun-Jul 2016.
    • Points on a sphere: Stolarsky-type identities, energy optimization, uniform tessellations, and one-bit sensing,  workshop on Function Spaces and High-dimensional Approximation, CRM, Barcelona, Catalunya, May 2016.
    • Tessellations of the sphere, one-bit sensing, restricted isometries, and discrepancy, AMS sectional meeting, Athens, GA, March 2016.
    • Geometric discrepancy, AIM workshop "Hereditary discrepancy and factorization norms", San Jose, CA, Feb 2016.
    • Uniform distribution: approximating continuous objects by discrete ones, "Introduction to Research" seminar (an introductory talk for graduate students), University of Minnesota, February 2016.
    • Methods of harmonic analysis in discrepancy theory (four 1.5-hr lectures), Winter School on Complexity and Discrepancy, Traunkirchen, Austria, Nov-Dec 2015.
    • Small ball inequality and low discrepancy constructions, "Diophantine approximation and related topics" conference, Aarhus, Denmark, July 2015.
    • Small ball inequality and low discrepancy constructions, Johannes-Kepler Universität, Linz, Austria, June 2015.
    • Sphere tessellations and discrepancy, Information-based Complexity program, Banach Center, Będlewo, Poland, April 2015.
    • Discrepancy theory and analysis, colloquium, Duke University, Durham, NC, February 2015.
    • The L2 discrepancy of Fibonacci (and other) lattices, workshop on "Optimal Point Configurations and Applications", program on "Minimal Energy Point Sets, Lattices, and Designs", Erwin Schrödinger Institute, Vienna, Austria, October 2014.
    • Discrepancy function estimates in various function spaces, Analysis Seminar, Brown University, Providence, RI, November 2014.
    • Tutorial talk Relationship of discrepancy with harmonic analysis, approximation theory and probability, ICERM, Brown University, Providence RI, October 2014.
    • Uniform distribution, lacunary Fourier series, and Riesz products, Hausdorff Institute, Bonn, Germany, May 2014.
    • The L1 dichotomy for the discrepancy function estimates, 11th International Conference on Monte-Carlo and Quasi-Monte Carlo Methods in Scienti c Computing, MCQMC 2014, Leuven, Belgium, April 2014.
    • On some distributions with low L2 discrepancy, International conference "Nonlinear approximations and applications" dedicated to 60th birthday of V. Temlyakov, Steklov Institute, Moscow, Russia, October 2013.
    • Discrepancy theory and harmonic analysis, Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria, October 2013.
    • Small ball inequalities and discrepancy, Oberwolfach workshop "Uniform Distribution Theory and Applications", Oberwolfach, Germany, September 2013.
    • Discrepancy estimates, small ball inequalities, and hyperbolic cross approximations, workshop "Discrepancy, Numerical Integration and Hyperbolic Cross Approximation", Hausdorff Center for Mathematics, University of Bonn, September 2013.
    • Discrepancy theory and harmonic analysis, Palanga Conference in Combinatorics and Number Theory, Palanga, Lithuania September 2013.
    • Plenary lecture Discrepancy theory and analysis, 2nd International Conference "Mathematics in Armenia. Advances and Perspectives", Armenia, August 2013.
    • Simultaneous Diophantine approximation and rotated lattices, Georgia Analysis Symposium, University of Georgia, Athens, GA, March 2013.
    • Discrepancy theory and the small ball inequality, Analysis seminar, Universite Paris-Sud XI, Orsay, France, November 2012.

    Here are some pictures of my native city,

    Kharkov - my home town