Danylo Radchenko

Contact: danradchenko@gmail.com

I'm currently a Hermann-Weyl-Instructor at the Institute for Mathematical Research at ETH Zurich.
Starting from February 2022 I will be a CNRS research fellow working at Laboratoire Paul Painlevé at the University of Lille.

My research interests include modular forms, algebraic number theory, convex and discrete geometry, combinatorics, as well as approximation theory and Fourier analysis.

Publications

  1. (with A. Arman, A. Bondarenko, and A. Prymak) Upper bounds on chromatic number of 𝔼n in low dimensions
    Preprint, 2021. arXiv:2112.13438

  2. (with M. Stoller) Fourier non-uniqueness sets from totally real number fields
    Preprint, 2021. arXiv:2108.11828

  3. (with D. Berghaus, B. Georgiev, and H. Monien) On Dirichlet eigenvalues of regular polygons
    Preprint, 2021. arXiv:2103.01057

  4. (with D. Zagier) Arithmetic properties of the Herglotz function
    Preprint, 2020. arXiv:2012.15805

  5. (with S. Charlton and H. Gangl) Functional equations of polygonal type for multiple polylogarithms in weights 5, 6 and 7
    Preprint, 2020. arXiv:2012.09840

  6. (with A. Bondarenko and K. Seip) Fourier interpolation with zeros of zeta and L-functions
    Preprint, 2020. arXiv:2005.02996

  7. (with S. Charlton and H. Gangl) Explicit formulas for Grassmannian polylogarithms
    Preprint, 2019. arXiv:1909.13869

  8. (with H. Cohn, A. Kumar, S. D. Miller, and M. Viazovska) Universal optimality of the E8 and Leech lattices and interpolation formulas
    Preprint, 2019. arXiv:1902.05438, to appear in Annals of Mathematics

  9. (with D. Grigoriev) On a tropical version of the Jacobian conjecture
    J. Symb. Comput. 109, pp. 399–403 (2022)
    arXiv:1902.07733

  10. (with A. Bondarenko and A. Prymak) Spherical coverings and X-raying convex bodies of constant width
    Canad. Math. Bull., first published: 13 Dec. 2021, pp. 1–7, doi:10.4153/S0008439521001016
    arXiv:2011.06398

  11. (with F. Villegas) Independence polynomials and hypergeometric series
    Bull. Lond. Math. Soc. 53 (2), pp. 1834–1848 (2021)
    arXiv:1908.11231

  12. (with S. Charlton and H. Gangl) On functional equations for Nielsen polylogarithms
    Comm. N. Th. Phys. 15 (2), pp. 363–454 (2021)
    arXiv:1908.04770

  13. (with A. Bakan, H. Hedenmalm, A. Montes-Rodriguez, and M. Viazovska) Fourier uniqueness in even dimensions
    PNAS 118(15), e2023227118 (2021)
    arXiv:2007.03981

  14. Unit distance graphs and algebraic integers
    Discrete Comput. Geom. 66, pp. 269–272 (2021)
    arXiv:1807.03726

  15. (with M. Viazovska) Fourier interpolation on the real line
    Publ. Math. Inst. Hautes Études Sci. 129, pp. 51–81 (2019)
    arXiv:1701.00265

  16. (with F. Villegas) Goursat rigid local systems of rank four
    Res. Math. Sci. 5:38 (2018), in the collection: Modular Forms are Everywhere: Celebration of Don Zagier’s 65th Birthday
    arXiv:1803.08379

  17. (with A. Bondarenko, A. Mellit, A. Prymak, and M. Viazovska) There is no strongly regular graph with parameters (460,153,32,60)
    In: Dick J., Kuo F., Woźniakowski H. (eds) Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan. Springer, Cham (2018)
    arXiv:1509.06286

  18. (with H. Cohn, A. Kumar, S.D. Miller, and M. Viazovska) The sphere packing problem in dimension 24
    Annals of Mathematics 185, pp. 1017–1033 (2017)
    arXiv:1603.06518

  19. (with A. Bondarenko and A. Prymak) Non-existence of (76, 30, 8, 14) strongly regular graph and some structural tools
    Linear Algebra Appl. 527, pp. 53–72 (2017)
    arXiv:1410.6748

  20. Higher cross-ratios and geometric functional equations for polylogarithms
    PhD Thesis, Bonn University, 2016. Link

  21. (with A.V. Bondarenko and M.S. Viazovska) Well-separated spherical designs
    Constructive Approximation, Vol. 41(1), pp. 93–112 (2015)
    arXiv:1303.5991

  22. Local Maxima of the Potential Energy on Spheres
    Ukr. Math. Journal, Vol. 65(10), pp. 1585–1587 (2014)
    arXiv:1103.2552

  23. (with A.V. Bondarenko and M.S. Viazovska) Optimal asymptotic bounds for spherical designs
    Annals of Mathematics 178, pp. 443–452 (2013)
    arXiv:1009.4407

  24. (with I.V. Livinskii) Representations of algebras defined by a multiplicative relation, corresponding to the Dynkin diagrams D4, E6, E7, E8
    Ukr. Math. Journal, Vol. 64(12), pp. 1865–1892 (2013)

  25. (with A.V. Bondarenko) On a family of strongly regular graphs with λ = 1
    Journal of Combinatorial Theory, Series B 103, pp. 521–531 (2013)
    arXiv:1201.0383

  26. (with A.V. Bondarenko and A. Prymak) On concentrators and related approximation constants
    J. Math. Anal. Appl., Vol. 402(1) pp. 234–241 (2013)
    arXiv:1404.2161

  27. Approximation by Maps with Nonnegative Jacobian
    Mat. Zametki 93:2, pp. 263–275 (2013)
    arXiv:1010.5448

  28. (with D. Leviatan and I.A. Shevchuk) Positive results and counterexamples in comonotone approximation
    Constructive Approximation, Vol. 36(2), pp. 243–266 (2012)

  29. (with I. Feschenko, L. Radzivilovsky, and M. Tantsiura) Dissecting a brick into bars
    Geometriae Dedicata, Vol. 145(1), pp. 159–168 (2010)
    arXiv:0809.1883

© 2022 Danylo Radchenko