Research

Preprints

• David de Laat, Nando Leijenhorst, and Willem de Muinck Keizer, Optimality and uniqueness of the D₄ root system, preprint, 2024. arXiv:2404.18794

• Henry Cohn, David de Laat, Nando Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024. arXiv:2403.16874

• David de Laat, Fabrício Caluza Machado, and Willem de Muinck Keizer, The Lasserre hierarchy for equiangular lines with a fixed angle, preprint, 2022. arXiv:2211.16471

• Henry Cohn, David de Laat, and Andrew Salmon, Three-point bounds for sphere packing, preprint, 2022. arXiv:2206.15373

Journal papers

• Felipe Gonçalves, David de Laat, and Nando Leijenhorst, Multiplicity of nontrivial zeros of primitive L-functions via higher-level correlations, Math. Comp. 94 (2025), no. 354, 2041–2058. doi:10.1090/mcom/4005 arXiv:2303.01095

• Nando Leijenhorst and David de Laat, Solving clustered low-rank semidefinite programs arising from polynomial optimization, Math. Program. Comput. 16 (2024), no. 3, 503–534. doi:10.1007/s12532-024-00264-w arXiv:2202.12077

• Maria Dostert, David de Laat, and Philippe Moustrou, Exact semidefinite programming bounds for packing problems, SIAM J. Optim. 31 (2021), no. 2, 1433–1458. doi:10.1137/20M1351692 arXiv:2001.00256

• David de Laat, Fabrício Caluza Machado, Fernando de Oliveira Filho, and Frank Vallentin, k-point semidefinite programming bounds for equiangular lines, Math. Program. 194 (2022), no. 1-2, Ser. A, 533–567. doi:doi.org/10.1007/s10107-021-01638-x arXiv:1812.06045

• Andrés Chirre; Valdir José Pereira Júnior, and David de Laat, Primes in arithmetic progressions and semidefinite programming, Math. Comp. 90 (2021), no. 331, 2235–2246. doi:10.1090/mcom/3638 arXiv:2005.02393

• Nima Afkhami-Jeddi, Henry Cohn, Thomas Hartman, David de Laat, Amirhossein Tajdini, High-dimensional sphere packing and the modular bootstrap, J. High Energy Phys. 2020 (2020), no. 12, Paper No. 066, 44 pp. doi:10.1007/jhep12(2020)066 arXiv:2006.02560

• Andrés Chirre, Felipe Gonçalves, and David de Laat, Pair correlation estimates for the zeros of the zeta-function via semidefinite programming Adv. Math. 361 (2020), 106926, 22 pp. doi:10.1016/j.aim.2019.106926 arXiv:1810.08843

• David de Laat, Moment methods in energy minimization: New bounds for Riesz minimal energy problems, Trans. Amer. Math. Soc. 373 (2020), no. 2, 1407–1453. doi:10.1090/tran/7976 arXiv:1610.04905

• Sander, Gribling, David de Laat, and Monique Laurent, Lower bounds on matrix factorization ranks via noncommutative polynomial optimization. Found. Comput. Math. 19 (2019), no. 5, 1013–1070. doi:10.1007/s10208-018-09410-y arXiv:1708.01573

• Sander Gribling, David de Laat, and Monique Laurent, Bounds on entanglement dimensions and quantum graph parameters via noncommutative polynomial optimization, Math. Program. 170 (2018), no. 1, Ser. B, 5–42. doi:10.1007/s10107-018-1287-z arXiv:1708.09696

• Sander Gribling, David de Laat, and Monique Laurent, Matrices with high completely positive semidefinite rank, Linear Algebra Appl. 513 (2017), 122–148. doi:10.1016/j.laa.2016.10.015 arXiv:1605.00988

• David de Laat and Frank Vallentin, A semidefinite programming hierarchy for packing problems in discrete geometry, Math. Program. 151 (2015), no. 2, Ser. B, 529–553. doi:10.1007/s10107-014-0843-4 arXiv:1311.3789

• David de Laat, Fernando de Oliveira Filho, and Frank Vallentin, Upper bounds for packings of spheres of several radii, Forum Math. Sigma 2 (2014), Paper No. e23, 42 pp. doi:10.1017/fms.2014.24 arXiv:1206.2608

• Evan DeCorte, David de Laat, and Frank Vallentin, Fourier analysis on finite groups and the Lovász θ-number of Cayley graphs, Exp. Math. 23 (2014), no. 2, 146–152. doi:10.1080/10586458.2014.882170 arXiv:1307.5703

Expositions

• David de Laat and Frank Vallentin, A Breakthrough in Sphere Packing: The Search for Magic Functions, Nieuw Archief voor Wiskunde 5 (2016), no. 17, 184-192, arXiv:1607.02111

Non-refereed publications

• David de Laat, Three-point bounds for sphere packing, In: Etienne de Klerk, Didier Henrion, Frank Vallentin, Angelika Wiegele, Conic Linear Optimization for Computer-Assisted Proofs. Oberwolfach Rep. 19 (2022), no. 2, pp. 1039–1089, doi:10.4171/OWR/2022/20.

• David de Laat, Exploiting symmetry in conic optimization, In: Etienne de Klerk, Didier Henrion, Frank Vallentin, Angelika Wiegele, Conic Linear Optimization for Computer-Assisted Proofs. Oberwolfach Rep. 19 (2022), no. 2, pp. 1039–1089, doi:10.4171/OWR/2022/20.

• David de Laat, Larry Rolen, Zack Tripp, and Ian Wagner, Pair correlation for Dedekind zeta functions of abelian extensions, preprint, 2019, arXiv:1908.04876.

• David de Laat, High precision computations for energy minimization, In: Didier Henrion, Maria Infusino, Salma Kuhlmann, Victor Vinnikov, Real Algebraic Geometry With a View Toward Moment Problems and Optimization. Oberwolfach Rep. 14 (2017), no. 1, pp. 771–862, doi:10.4171/OWR/2017/14.

• David de Laat, Optimal densities of packings consisting of highly unequal objects, preprint, 2016, arXiv:1603.01094.

• David de Laat, Polydisperse spherical cap packings, In: Christine Bachoc, Peter Grabner, Edward B. Saff, Achill Schürmann, Optimal and Near Optimal Configurations on Lattices and Manifolds. Oberwolfach Rep. 9 (2012), no. 3, pp. 2429–2492, doi:10.4171/OWR/2012/40.

Theses

• David de Laat, Moment methods in extremal geometry, Ph.D. thesis, Delft University of Technology, 2016, doi:10.4233/uuid:fce81f72-8261-484d-b9f4-d3d0c26f0473

• David de Laat, Approximating manifolds by meshes: Asymptotic bounds in higher codimension, Master thesis, University of Groningen, 2011.

• David de Laat, Contractibility and self-intersections of curves on surfaces, Bachelor thesis, University of Groningen, 2009.