Preprints

  • with D. P. Hardin and E. B. Saff, Asymptotics of k-nearest neighbor Riesz energies, arXiv:2201.00474
  • with D. Bilyk, R. Matzke, Positive definiteness and the Stolarsky invariance principle, arXiv:2110.04138
  • with A. Anderson, A. Reznikov, and E. White, Polarization and covering on sets of low smoothness, arXiv:2106.11956
  • with D. P. Hardin and E. B. Saff, Asymptotic properties of short-range interaction functionals, arXiv:2010.11937
  • Discreteness of the minimizers of weakly repulsive interaction energies on Riemannian manifolds, arXiv:2003.01597

Publications

  • with D. Bilyk, D. Ferizović, A. Glazyrin, R. Matzke, and J. Park, Potential theory with multivariate kernels, arXiv:2104.03410, Math. Zeitschrift., accepted.
  • with D. Bilyk, A. Glazyrin, R. Matzke, and J. Park, Optimal measures for p-frame energies on spheres, arXiv:1908.00885, Rev. Matemática Iberoam., accepted.
    Auxiliary files: [ipynb] [html].
  • with D. Bilyk, A. Glazyrin, R. Matzke, and J. Park, Energy on spheres and discreteness of minimizing measures, J. Funct. Anal. 280 (2021), no. 11. doi:10.1016/j.jfa.2021.108995 arXiv:1908.10354
  • with A. Reznikov, Riesz energy on self-similar sets, Proc. Am. Math. Soc., accepted. doi:10.1090/proc/14663 arXiv:1810.01557
  • with T. Michaels, N. Flyer, and B. Fornberg, Fast high-dimensional node generation with variable density, Comput. Math. Appl. 76 (2018), no. 7, 1739–1757. doi:10.1016/j.camwa.2018.07.026 arXiv:1710.05011
  • with A. Reznikov and E. B. Saff, A minimum principle for potentials with application to Chebyshev constants, Potential Anal. 47 (2017), no. 2, 235–244. doi:10.1007/s11118-017-9618-x
  • with D. P. Hardin and E. B. Saff, Generating Point Configurations via Hypersingular Riesz Energy with an External Field, SIAM J. Math. Anal. 49 (2017), no. 1, 646–673. doi:10.1137/16m107414x
  • with D. Leviatan and I. A. Shevchuk, Positive results and counterexamples in comonotone approximation II, J. Approx. Theory 179 (2014), 1–23. doi:10.1016/j.jat.2013.11.004

Other

  • Log-energy, β-ensembles, and tessellations: problems old and new (2018), [pdf]