Danylo Radchenko

Contact: danradchenko@gmail.com

I am a CNRS researcher 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 S. Charlton, A. Matveiakin, and D. Rudenko) The Hopf algebra of multiple polylogarithms
    Preprint, 2024. arXiv:2411.15071

  2. (with J. P. G. Ramos) Perturbed lattice crosses and Heisenberg uniqueness pairs
    Preprint, 2024. arXiv:2410.04557

  3. (with A. Arman, A. Bondarenko, and A. Prymak) On a Gallai-type problem and illumination of spiky balls and cap bodies
    Preprint, 2024. arXiv:2408.01341

  4. (with A. Bondarenko, J. Ortega-Cerdà, and K. Seip) Hörmander and Bernhardsson's extremal function I
    Preprint, 2024. arXiv:2407.00970

  5. (with A. Arman, A. Bondarenko, and A. Prymak) Small volume bodies of constant width with tetrahedral symmetries
    Preprint, 2024. arXiv:2406.18428
    Illustration: 3D

  6. (with A. Arman, A. Bondarenko, F. Nazarov, and A. Prymak) Small volume bodies of constant width
    Preprint, 2024. arXiv:2405.18501
    Illustrations: 2D, 3D

  7. (with J. P. G. Ramos) Sharp Gaussian decay for the one-dimensional harmonic oscillator
    Preprint, 2023. arXiv:2305.18546

  8. (with D. Berghaus and H. Monien) A database of modular forms on noncongruence subgroups
    Preprint, 2023. arXiv:2301.02135

  9. (with K. Klinger-Logan and S.D. Miller) The D6R4 interaction as a Poincaré series, and a related shifted convolution sum
    Preprint, 2022. arXiv:2210.00047

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

  11. (with K. Fedosova and K. Klinger-Logan) Convolution identities for divisor sums and modular forms
    PNAS 121(44), e2322320121 (2024)
    arXiv:2312.00722

  12. (with A. Arman, A. Bondarenko, and A. Prymak) Upper bounds on chromatic number of 𝔼n in low dimensions
    The Electronic Journal of Combinatorics, Volume 31, Issue 2 (2024)
    arXiv:2112.13438

  13. (with D. Berghaus, B. Georgiev, and H. Monien) On Dirichlet eigenvalues of regular polygons
    Journal of Mathematical Analysis and Applications, Volume 538, Issue 2, 128460 (2024)
    arXiv:2103.01057

  14. (with D. Berghaus, R.S. Jones, and H. Monien) Computation of Laplacian eigenvalues of two-dimensional shapes with dihedral symmetry
    Advances in Computational Mathematics Volume 50, article number 38 (2024)
    arXiv:2210.13229

  15. (with K. J. Böröczky and J. P. G. Ramos) A quantitative stability result for the sphere packing problem in dimensions 8 and 24
    Journal für die reine und angewandte Mathematik, vol. 2024, no. 808, pp. 241-270 (2024)
    arXiv:2303.07908

  16. (with S. Charlton, H. Gangl, and D. Rudenko) On the Goncharov Depth Conjecture and polylogarithms of depth two
    Selecta Mathematica New Series 30, article number 27 (2024)
    arXiv:2210.11938

  17. (with D. Berghaus and H. Monien) On the computation of modular forms on noncongruence subgroups
    Mathematics of Computation 93, pp. 1399-1425 (2024)
    arXiv:2207.13365

  18. (with A. Bondarenko and K. Seip) Fourier interpolation with zeros of zeta and L-functions
    Constructive Approximation, Volume 57, pp. 405-461 (2023)
    arXiv:2005.02996

  19. (with S. Charlton and H. Gangl) Functional equations of polygonal type for multiple polylogarithms in weights 5, 6 and 7
    Pure and Applied Mathematics Quarterly 19(1), pp. 85-93 (2023), https://doi.org/10.4310/PAMQ.2023.v19.n1.a5
    arXiv:2012.09840

  20. (with D. Zagier) Arithmetic properties of the Herglotz function
    Journal für die reine und angewandte Mathematik, vol. 2023 no. 797, pp. 229-253 (2023), https://doi.org/10.1515/crelle-2023-0009
    arXiv:2012.15805

  21. (with H. Cohn, A. Kumar, S.D. Miller, and M. Viazovska) Universal optimality of the E8 and Leech lattices and interpolation formulas
    Annals of Mathematics 196(3), pp. 983-1082 (2022)
    arXiv:1902.05438

  22. (with M. Stoller) Fourier non-uniqueness sets from totally real number fields
    Comment. Math. Helv. 97 no. 3, pp. 513-553 (2022)
    arXiv:2108.11828

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

  24. (with A. Bondarenko and A. Prymak) Spherical coverings and X-raying convex bodies of constant width
    Canad. Math. Bull. 65(4), pp. 860-866 (2022), https://doi.org/10.4153/S0008439521001016
    arXiv:2011.06398

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

  26. (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

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

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

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

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

  31. (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

  32. (with H. Cohn, A. Kumar, S.D. Miller, and M. Viazovska) The sphere packing problem in dimension 24
    Annals of Mathematics 185(3), pp. 1017-1033 (2017)
    arXiv:1603.06518

  33. (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

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

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

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

  37. (with A.V. Bondarenko and M.S. Viazovska) Optimal asymptotic bounds for spherical designs
    Annals of Mathematics 178(2), pp. 443-452 (2013)
    arXiv:1009.4407

  38. (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)

  39. (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

  40. (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

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

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

  43. (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

© 2024 Danylo Radchenko