Fernando Mário de Oliveira Filho


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

Preprints and other recent works

  • arXiv:2206.03929 with D. Castro-Silva, L. Slot, and F. Vallentin, A recursive theta body for hypergraphs, arXiv:2206.03929, 2022, 23pp.

  • arXiv:2106.09360 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, arXiv:2106.09360, 2021, 13pp.

Journals and proceedings

  • arXiv:2003.11832 with M. Dostert and A. Kolpakov, Semidefinite programming bounds for the average kissing number, Israel Journal of Mathematics 247 (2022) 635-659.

  • arXiv:1812.06045 with D. de Laat, F.C. Machado, and F. Vallentin, \(k\)-point semidefinite programming bounds for equiangular lines, Mathematical Programming A (2021), 35pp.

  • arXiv:1808.02346 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:1804.09099 with E. DeCorte and F. Vallentin, Complete positivity and distance-avoiding sets, Mathematical Programming A (2020) 58pp., arXiv:1804:09099.

  • arXiv:1808.07299 with F. Vallentin, A counterexample to a conjecture of Larman and Rogers on sets avoiding distance 1, Mathematika 65 (2019) 785-785.

  • arXiv:1308.4893 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:1609.05167 with F.C. Machado, Improving the semidefinite programming bound for the kissing number by exploiting polynomial symmetry, Experimental Mathematics 27 (2018) 362-369.

  • arXiv:1510.02331 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:1607.04741 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:1501.00168 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:1403.1166 with F. Vallentin, Mathematical optimization for packing problems, SIAG/OPT Views and News 23(2) (2015) 5-14.

  • arXiv:1206.2608 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:1011.1754 with J. Briët and F. Vallentin, Grothendieck inequalities for semidefinite programs with rank constraint, Theory of Computing 10 (2014) 77-105.

  • arXiv:1301.1054 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:1005.0471 with F. Vallentin, A quantitative version of Steinhaus' theorem for compact, connected, rank-one symmetric spaces, Geometriae Dedicata 167 (2013) 295-307.

  • arXiv:0910.5765 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:0808.1822 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:0801.1059 with C. Bachoc, G. Nebe, and F. Vallentin, Lower bounds for measurable chromatic numbers, Geometric and Functional Analysis 19 (2009) 645-661.

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

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

Book chapters

  • 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.



I wrote my PhD thesis at the Center for Mathematics and Computer Science (CWI) in Amsterdam under the supervision of Lex Schrijver and Frank Vallentin:

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

I still have many printed copies, let me know if you would like to have one.


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