Most of my publications are available on arXiv, and I try hard to keep the arXiv version fo each one up-to-date. Check out my arXiv page. I am also on Google scholar.

Preprints and other recent works

  1. with A.J.F. Bekker, On the convergence of the $k$-point bound for topological packing graphs, arXiv:2306.02725, 2023, 10pp. [arXiv]

  2. with A.J.F Bekker, O. Kuryatnikova, and J.C. Vera, Optimization hierarchies for distance-avoiding sets in compact spaces, arXiv:2304.05429, 2023, 34pp. [arXiv | data repo]

  3. with D. Castro-Silva, L. Slot, and F. Vallentin, A recursive theta body for hypergraphs, to appear in Combinatorica, arXiv:2206.03929, 2022, 23pp. [arXiv]

Journals and proceedings

  1. with D. Castro-Silva, L. Slot, and F. Vallentin, A recursive Lovász theta number for simplex-avoiding sets, to appear in Proceedings of the AMS 150 (2022) 3307-3322. [arXiv]

  2. with M. Dostert and A. Kolpakov, Semidefinite programming bounds for the average kissing number, Israel Journal of Mathematics 247 (2022) 635-659. [arXiv]

  3. with E. DeCorte and F. Vallentin, Complete positivity and distance-avoiding sets, Mathematical Programming A 191 (2022) 487-558. [arXiv]

  4. with D. de Laat, F.C. Machado, and F. Vallentin, $k$-point semidefinite programming bounds for equiangular lines, Mathematical Programming A 194 (2022) 533-567. [arXiv]

  5. with F. Vallentin, On the integrality gap of the maximum-cut semidefinite programming relaxation in fixed dimension, Discrete Analysis 10 (2020), arXiv:1808.02346, 17pp. [arXiv]

  6. with F. Vallentin, A counterexample to a conjecture of Larman and Rogers on sets avoiding distance 1, Mathematika 65 (2019) 785-785. [arXiv]

  7. with F. Vallentin, Computing upper bounds for the packing density of congruent copies of a convex body, in: New Trends in Intuitive Geometry (G. Ambrus, I. Bárány, K.J. Böröczky, G. Fejes Tóth, and J. Pach, eds.), Bolyai Society Mathematical Studies 27, Springer-Verlag, Berlin, 2019. [arXiv]

  8. with F.C. Machado, Improving the semidefinite programming bound for the kissing number by exploiting polynomial symmetry, Experimental Mathematics 27 (2018) 362-369. [arXiv]

  9. with M. Dostert, C. Guzmán, and F. Vallentin, New upper bounds for the density of translative packings of three-dimensional convex bodies with tetrahedral symmetry, Discrete & Computational Geometry 58 (2017) 449-481. [arXiv]

  10. with M.K. de Carli Silva and C.M. Sato, Flag algebras: A first glance, Nieuw Archief voor Wiskunde 5/17 (2016) 193-199. [arXiv]

  11. with T. Keleti, M. Matolcsi, and I.Z. Ruzsa, Better bounds for planar sets avoiding unit distances, Discrete & Computational Geometry 55 (2016) 642-661. [arXiv]

  12. with F. Vallentin, Mathematical optimization for packing problems, SIAG/OPT Views and News 23(2) (2015) 5-14. [arXiv]

  13. with D. de Laat and F. Vallentin, Upper bounds for packings of spheres of several radii, Forum of Mathematics, Sigma 2 (2014) e23, 31pp. [arXiv]

  14. with J. Briët and F. Vallentin, Grothendieck inequalities for semidefinite programs with rank constraint, Theory of Computing 10 (2014) 77-105. [arXiv]

  15. with C. Bachoc, P.E.B. DeCorte, and F. Vallentin, Spectral bounds for the independence ratio and the chromatic number of an operator, Israel Journal of Mathematics 202 (2014) 227-254. [arXiv]

  16. with F. Vallentin, A quantitative version of Steinhaus’ theorem for compact, connected, rank-one symmetric spaces, Geometriae Dedicata 167 (2013) 295-307. [arXiv]

  17. with J. Briët and F. Vallentin, The positive semidefinite Grothendieck problem with rank constraint, in: Proceedings of the 37th International Colloquium on Automata, Languages, and Programming, ICALP 2010 (S. Abramsky et al. eds.), Lecture Notes in Computer Science 6198, 2010, pp. 31-42. [arXiv]

  18. with F. Vallentin, Fourier analysis, linear programming, and densities of distance avoiding sets in $\mathbb{R}^n$, Journal of the European Mathematical Society 12 (2010) 1417-1428. [arXiv]

  19. with C. Bachoc, G. Nebe, and F. Vallentin, Lower bounds for measurable chromatic numbers, Geometric and Functional Analysis 19 (2009) 645-661. [arXiv]

  20. with C.E. Ferreira, New Reduction Techniques for the Group Steiner Tree Problem, SIAM Journal on Optimization 17 (2007) 1176-1188.

  21. with C.E. Ferreira, Some Formulations for the Group Steiner tree Problem, Discrete Applied Mathematics 154 (2006) 1877-1884.

Book chapters

  1. with E. de Klerk and D.V. Pasechnik, Relaxations of Combinatorial Problems Via Association Schemes, in: Handbook on Semidefinite, Conic, and Polynomial Optimization (M.F. Anjos and J.B. Lasserre, eds.), Springer, 2010.

Theses

  1. New Bounds for Geometric Packing and Coloring via Harmonic Analysis and Optimization, Doctoral Thesis, University of Amsterdam, viii + 114pp, 2009. [pdf]

  2. O problema de Steiner com grupos, Master’s Thesis, University of São Paulo, Institute of Mathematics and Statistics, 79pp, 2005. (in Portuguese; English title: The group Steiner tree problem).