Research:

My main research interests are Potential Theory and Energy Optimization, as well as their connections and applications to Approximation Theory, Differential Equations, Frame Theory, and various other areas. I also have interest in Analysis (particularly Harmonic Analysis and Discrepancy Theory), Geometry (in particular Discrete and Convex Geometries), and Combinatorics (in particular Additive Combinatorics and Graph Theory).

Published/Accepted Papers:

• Minimizers for an Aggregation Model with Attractive-repulsive Interaction (with Rupert L. Frank). Accepted to the Archive for Rational Mechanics and Analysis. (ArXiv)
• Optimal Measures for Multivariate Geometric Potentials (with Dmitriy Bilyk, Damir Ferizović, Alexey Glazyrin, Josiah Park, and Oleksandr Vlasiuk). Accepted to the Indiana University Mathematics Journal. (ArXiv)
• Optimizers of Three-point Energies and Nearly Orthogonal Sets (with Dmitriy Bilyk, Damir Ferizović, Alexey Glazyrin, Josiah Park, and Oleksandr Vlasiuk). Proceedings of the American Mathematical Society, 152, 4015-4033 (2024). (ArXiv)
• Riesz Energy, L² Discrepancy, and Optimal Transport of Determinantal Point Processes on the Sphere and the Flat Torus (with Bence Borda and Peter Grabner). Mathematika, 70(2), e12245 (2024). (ArXiv)
• Experimental Survey of Discrete Minimizers of the p-frame Energy (with Dmitriy Bilyk, Alexey Glazyrin, Josiah Park, and Oleksandr Vlasiuk). 2023 57th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, USA, 522-529 (2023).
• Riesz and Green Energy on Projective Spaces (with Austin Anderson, Maria Dostert, Peter J. Grabner, and Tetiana A. Stepaniuk). Transactions of the American Mathematical Society, Series B, 10, 1039-1076 (2023). (ArXiv)
• Positive Definiteness and the Stolarsky Invariance Principle (with Dmitriy Bilyk and Oleksandr Vlasiuk). Journal of Mathematical Analysis and Applications, 513(2), 126220 (2022). (ArXiv)
• Potential Theory with Multivariate Kernels (with Dmitriy Bilyk, Damir Ferizović, Alexey Glazyrin, Josiah Park, and Oleksandr Vlasiuk). Math Zeitschrift, 301, 2907-2935 (2022). (ArXiv)
• Optimal Measures for p-frame Energies on Spheres (with Dmitriy Bilyk, Alexey Glazyrin, Josiah Park, and Oleksandr Vlasiuk). Revista Matemática Iberoamericana, 38(4), 1129-1160 (2022). (ArXiv)
• Energy on Spheres and Discreteness of Minimizing Measures (with Dmitriy Bilyk, Alexey Glazyrin, Josiah Park, Oleksandr Vlasiuk). Journal of Functional Analysis, 280(11), 108995 (2021). (ArXiv)
• On Subgraphs with Prescribed Eccentricities (with Peter Dankelmann, Matthew DeVilbiss, David Erwin, and Kelly Guest). Discussiones Mathematicae Graph Theory, 43(3), 685–702 (2023).
• On the Fejes Tóth Problem about the Sum of Angles Between Lines (with Dmitriy Bilyk). Proceedings of the AMS, 147(1), 2019, 51-59 (2019). (ArXiv)
• The Maximum Size of (k,l)-Sum-Free Sets in Finite Cyclic Groups (with Béla Bajnok). Bulletin of the Australian Mathematical Society, 99(2), 184-194 (2019). (ArXiv)
• The Edge Grundy Number of the Regular Turan Graphs (with Matthew DeVilbiss and Peter Johnson). Bulletin of the Institute of Combinatorics and its Applications, 84, 45-52 (2018).
• Rainbow Connectivitiy in some Cayley Graphs (with Sheng Bau, Peter Johnson, Edna Jones, and Khumbo Kumwenda). The Australasian Journal of Combinatorics, 71(3), 381-393 (2018).
• Stolarsky Principle and Energy Optimization on the Sphere (with Dmitriy Bilyk and Feng Dai). Constructive Approximation, 48(1), 31-60 (2018). (ArXiv)
• Connected Minimum Secure Dominating Sets in Grids (with Johnathan Barnett, Adam Blumenthal, Peter Johnson, Cadavious Jones, and Egbert Mujuni). AKCE International Journal of Graphs and Combinatorics, 14(3), 216-223 (2017).
• The Edge Grundy Number of Some Graphs (with Loren Anderson, Matthew DeVilbiss, Sarah Holliday, Peter Johnson, Anna Kite, and Jessica McDonald). International Journal of Mathematics and Computer Science, 12(1), 13-26 (2017).
• On the Minimum Size of Signed Sumsets in Elementary Abelian Groups (with Béla Bajnok). The Journal of Number Theory, 159, 384-401 (2016). (ArXiv)
• The Minimum Size of Signed Sumsets (with Béla Bajnok). The Electronic Journal of Combinatorics, 22(2), (P2.50) 1-17 (2015). (ArXiv)
• Note on the Secure-Domination Number of a Graph (with Matthew DeVilbiss, Bradley Fain, and Peter Johnson). Bulletin of the Institute of Combinatorics and its Applications, 74, 113-119 (2015).
• Appendix to “Maximizing Expected Powers of the Angle between Pairs of Points in Projective Space” by Tongseok Lim and Robert McCann (with Dmitriy Bilyk, Alexey Glazyrin, Josiah Park, and Oleksandr Vlasiuk). Probability Theory and Related Fields, 184, 1197-1214 (2022). (ArXiv)