Miscellanea

• Old teaching materials: calculus and measure theory, as taught at FSU. Includes some demo Maxima and Jupyter notebooks.
• I was a co-organizer of the Point Distributions Webinar; the archives are available following that link.
• Log-energy, β-ensembles, and tessellations: problems old and new (2018), [pdf]
  

Preprints

• with D. Bilyk, D. Ferizović, A. Glazyrin, R. Matzke, and J. Park, Optimizers of three-point energies and nearly orthogonal sets
  arXiv:2303.12283
  
• 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 J. Batle and O. Ciftja, Correspondence between electrostatics and contact mechanics with further results in equilibrium charge distributions
  Ann. Phys., accepted (2023)
• with D. Bilyk, D. Ferizović, A. Glazyrin, R. Matzke, and J. Park, Optimal measures for multivariate geometric potentials
  Indiana Univ. Math. J., accepted (2023), arXiv:2303.14258
  
• with D. P. Hardin and E. B. Saff, Asymptotics of k-nearest neighbor Riesz energies
  Constr. Approx. (2023), doi:10.1007/s00365-023-09641-5, arXiv:2201.00474
  
• with A. Anderson, A. Reznikov, and E. White, Polarization and covering on sets of low smoothness
  Adv. Math. (2022) doi:10.1016/j.aim.2022.108720, arXiv:2106.11956
  
• with D. Bilyk, R. Matzke, Positive definiteness and the Stolarsky invariance principle
  J. Math. Anal. Appl. (2022) doi:10.1016/j.jmaa.2022.126220, arXiv:2110.04138
  
• with D. Bilyk, D. Ferizović, A. Glazyrin, R. Matzke, and J. Park, Potential theory with multivariate kernels
  Math. Zeitschrift (2022). doi:10.1007/s00209-022-03000-z, arXiv:2104.03410.
  
• with D. Bilyk, A. Glazyrin, R. Matzke, and J. Park, Optimal measures for p-frame energies on spheres
  Rev. Mat. Iberoam. 38 (2022), no. 4, 1129–1160. doi:10.4171/RMI/1329, arXiv:1908.00885
  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, arXiv:1607.07283
  
• 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, arXiv:1605.03840
  
• 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