43 citations · 135 across the 14 of their papers we have counts for
14 papers
Optimality and uniqueness of the root system
David de Laat, Nando M. Leijenhorst, Willem H. H. de Muinck Keizer
We prove that the root system (the set of vertices of the regular -cell) is the unique optimal kissing configuration in , and is an optimal spherical code. F…
Optimality of spherical codes via exact semidefinite programming bounds
Henry Cohn, David de Laat, Nando Leijenhorst
We show that the spectral embeddings of all known triangle-free strongly regular graphs are optimal spherical codes (the new cases are points in dimensions, points i…
Multiplicity of nontrivial zeros of primitive L-functions via higher-level correlations
Felipe Gonçalves, David de Laat, Nando Leijenhorst
We give universal bounds on the fraction of nontrivial zeros having given multiplicity for L-functions attached to a cuspidal automorphic representation of $\mathrm{GL}_m/\mathbb{Q…
The Lasserre hierarchy for equiangular lines with a fixed angle
David de Laat, Fabrício Caluza Machado, Willem de Muinck Keizer
We compute the second and third levels of the Lasserre hierarchy for the spherical finite distance problem. A connection is used between invariants in representations of the orthog…
Three-point bounds for sphere packing
Henry Cohn, David de Laat, Andrew Salmon
We define three-point bounds for sphere packing that refine the linear programming bound, and we compute these bounds numerically using semidefinite programming by choosing a trunc…
Solving clustered low-rank semidefinite programs arising from polynomial optimization
Nando Leijenhorst, David de Laat
We study a primal-dual interior point method specialized to clustered low-rank semidefinite programs requiring high precision numerics, which arise from certain multivariate polyno…
-point semidefinite programming bounds for equiangular lines
David de Laat, Fabrício Caluza Machado, Fernando Mário de Oliveira Filho +1
We give a hierarchy of -point bounds extending the Delsarte-Goethals-Seidel linear programming -point bound and the Bachoc-Vallentin semidefinite programming -point bound…
Lower bounds on matrix factorization ranks via noncommutative polynomial optimization
Sander Gribling, David de Laat, Monique Laurent
We use techniques from (tracial noncommutative) polynomial optimization to formulate hierarchies of semidefinite programming lower bounds on matrix factorization ranks. In particul…
Moment methods in energy minimization: New bounds for Riesz minimal energy problems
David de Laat
We use moment techniques to construct a converging hierarchy of optimization problems to lower bound the ground state energy of interacting particle systems. We approximate (from b…
A Breakthrough in Sphere Packing: The Search for Magic Functions
David de Laat, Frank Vallentin
This paper is an exposition, written for the Nieuw Archief voor Wiskunde, about the two recent breakthrough results in the theory of sphere packings. It includes an interview with…
Matrices with high completely positive semidefinite rank
Sander Gribling, David de Laat, Monique Laurent
A real symmetric matrix is completely positive semidefinite if it admits a Gram representation by (Hermitian) positive semidefinite matrices of any size . The smallest such…
A semidefinite programming hierarchy for packing problems in discrete geometry
David de Laat, Frank Vallentin
Packing problems in discrete geometry can be modeled as finding independent sets in infinite graphs where one is interested in independent sets which are as large as possible. For…
Fourier analysis on finite groups and the Lovász theta-number of Cayley graphs
Evan DeCorte, David de Laat, Frank Vallentin
We apply Fourier analysis on finite groups to obtain simplified formulations for the Lovász theta-number of a Cayley graph. We put these formulations to use by checking a few cases…
Upper bounds for packings of spheres of several radii
David de Laat, Fernando Mario de Oliveira Filho, Frank Vallentin
We give theorems that can be used to upper bound the densities of packings of different spherical caps in the unit sphere and of translates of different convex bodies in Euclidean…