preprints
[S3] K. Leipold, F. Vallentin, Computing the EHZ capacity is NP-hard, 9 pages
[S2] C. Riener, J. Rolfes, F. Vallentin, A semidefinite programming hierarchy for covering problems in discrete geometry, 14 pages
[S1] A. Heimendahl, M. Lücke, F. Vallentin, M.C. Zimmermann, A semidefinite program for least distortion embeddings of flat tori into Hilbert spaces, 23 pages
papers in journals
[J42] D. Castro-Silva, F.M. de Oliveira Filho, L. Slot, F. Vallentin – A recursive theta body for hypergraphs, 23 pages, Combinatorica 43 (2023), 909-938.
[J41] A. Heimendahl, A. Marafioti, A. Thiemeyer, F. Vallentin, M.C. Zimmermann, Critical even unimodular lattices in the Gaussian core model, IMRN (2023), 5352-5396
[J40] D. de Laat, F.C.Machado, F.M. de Oliveira Filho, F. Vallentin, k-point semidefinite programming bounds for equiangular lines, Math. Program. 194 (2022), 533-567.
[J39] D. Castro-Silva, F.M. de Oliveira Filho, L. Slot, F. Vallentin – A recursive Lovász theta number for simplex-avoiding sets, Proc. AMS 150 (2022), 3307-3322.
[J38] E. DeCorte, F.M. de Oliveira Filho, F. Vallentin, Complete positivity and distance avoiding sets, Math. Program. 191 (2022), 487-558.
[J37] S.T. McCormick, B. Peis, R. Scheidweiler, F. Vallentin, A polynomial time algorithm for solving the closest vector problem in zonotopal lattices, SIAM J. Discrete Math. 35 (2021), 2345–2356.
[J36] M. Dutour Sikirić, D. Madore, P. Moustrou, F. Vallentin, Coloring the Voronoi tessellation of lattices, J. Lond. Math. Soc. (2) 104 (2021) 1135-1171.
[J35] M. Dutour Sikirić, A. Schürmann, F. Vallentin, A simplex algorithm for rational CP-factorization, Math. Program. 187 (2021), 25-45.
[J34] A. Heimendahl, F. Montealegre-Mora, F. Vallentin, D. Gross – Stabilizer extent is not multiplicative, Quantum 5, 400 (2021), 15 pages.
[J33] M. Dostert, F. Vallentin, New dense superball packings in three dimensions, Adv. Geom. 20 (2020), 473-482.
[J32] F.M. de Oliveira Filho, F. Vallentin, On the integrality gap of the maximum-cut semidefinite programming relaxation in fixed dimension, Discrete Analysis, 2020:10, 17 pages
[J31] F.M. de Oliveira Filho, F. Vallentin, A counterexample to a conjecture of Larman and Rogers on sets avoiding distance 1, Mathematika 65 (2019), 785-787.
[J30] J.H. Rolfes, F. Vallentin, Covering compact metric spaces greedily, Acta Mathematica Hungarica 155 (2018), 130-140.
[J29] M. Dostert, C. Guzman, F.M. de Oliveira Filho, F. Vallentin, New upper bounds for the density of translative packings of three-dimensional convex bodies with tetrahedral symmetry, Discrete Comput. Geom. 58 (2017), 449-481.
[J28] M. Dutour Sikirić, A. Schürmann, F. Vallentin, Rational factorizations of completely positive matrices, Linear Algebra and Appl. 523 (2017) 46-51.
[J27] C. Dobre, M.E. Dür, L. Frerick, F. Vallentin, A copositive formulation of the stability number of infinite graphs, Math. Program., Ser. A 160 (2016), 65-83.
[J26] E. de Klerk, F. Vallentin, On the Turing model complexity of interior point methods for semidefinite programming, SIAM J. Optim. 26 (2016), 1944-1961.
[J25] D. de Laat, F. Vallentin, A semidefinite programming hierarchy for packing problems in discrete geometry, Math. Program., Ser. B 151 (2015), 529-553.
[J24] C. Bachoc, P.E.B. DeCorte, F.M. de Oliveira Filho, F. Vallentin, Spectral bounds for the independence ratio and the chromatic number of an operator, Israel J. Math. 202 (2014), 227-254.
[J23] D. de Laat, F.M. de Oliveira Filho, F. Vallentin, Upper bounds for packings of spheres of several radii, Forum Math. Sigma 2 (2014), e23 (42 pages).
[J22] P.E.B. DeCorte, D. de Laat, F. Vallentin, Fourier analysis on finite groups and the Lovász theta-number of Cayley graphs, Experiment. Math. 23 (2014), 146-152.
[J21] J. Briet, F.M. de Oliveira Filho, F. Vallentin, Grothendieck inequalities for semidefinite programs with rank constraint, Theory of Computing 10 (2014), 77-105.
[J20] F.M. de Oliveira Filho, F. Vallentin, A quantitative version of Steinhaus’ theorem for compact, connected, rank-one symmetric spaces, Geometriae Dedicata 167 (2013), 295-307.
[J19] C. Bachoc, A. Passuello, F. Vallentin, Bounds for projective codes from semidefinite programming, Advances in Mathematics of Communications 7 (2013), 127-145.
[J18] M. Dutour Sikirić, A. Schürmann, F. Vallentin, Inhomogeneous extreme forms, Annales de l’Institut Fourier 62 (2012), 2227-2255.
[J17] M. Dutour Sikirić, A. Schürmann, F. Vallentin, The contact polytope of the Leech lattice, Discr. Comp. Geom. 44 (2010), 904-911.
[J16] F.M. de Oliveira Filho, F. Vallentin, Fourier analysis, linear programming, and densities of distance avoiding sets in R^n, J. Eur. Math. Soc. 12 (2010), 1417-1428.
[J15] H.D. Mittelmann. F. Vallentin, High accuracy semidefinite programming bounds for kissing numbers, Experiment. Math. 19 (2010), 174-178.
[J14] C. Bachoc, G. Nebe, F.M. de Oliveira Filho, F. Vallentin, Lower bounds for measurable chromatic numbers, Geom. Funct. Anal. 19 (2009), 645-661.
[J13] M. Dutour Sikirić, A. Schürmann, F. Vallentin, Complexity and algorithms for computing Voronoi cells of lattice, Math. Comput. 78 (2009), 1713-1731.
[J12] C. Bachoc, F. Vallentin, Semidefinite programming, multivariate orthogonal polynomials, and codes in spherical caps, European J. Combin. 30 (2009), 625-637. (special issue dedicated to the 60th birthday of Eiichi Bannai)
[J11] N. Gvozdenović, M. Laurent, F. Vallentin, Block-diagonal semidefinite programming hierarchies for 0/1 programming, Oper. Res. Lett. 37 (2009), 27-31.
[J10] C. Bachoc, F. Vallentin, Optimality and uniqueness of the (4,10,1/6) spherical code, J. Comb. Theory Ser. A 116 (2009), 195-204.
[J9] F. Vallentin, Symmetry in semidefinite programs, Linear Algebra and Appl. 430 (2009), 360-369.
[J8] M.A. Hernandez Cifre, A. Schürmann, F. Vallentin, The isodiametric problem with lattice-point constraints, Monatsh. Math. 155 (2008), 125-134.
[J7] C. Bachoc, F. Vallentin, New upper bounds for kissing numbers from semidefinite programming, J. Amer. Math. Soc. 21 (2008), 909-924.
[J6] M. Dutour Sikirić, A. Schürmann, F. Vallentin, A generalization of Voronoi’s reduction theory and its applications, Duke Math. J. 142 (2008), 127-164.
[J5] F. Vallentin, Optimal embeddings of distance transitive graphs into Euclidean spaces, J. Comb. Theory Ser. B 98 (2008), 95-104.
[J4] M. Dutour Sikirić, A. Schürmann, F. Vallentin, Classification of eight dimensional perfect forms, Electron. Res. Announc. Amer. Math. Soc. 13 (2007), 21-32.
[J3] F. Santos, A. Schürmann, F. Vallentin, Lattice Delone simplices with super-exponential volume, Europ. J. Comb. 28 (2007), 801-806.
[J2] A. Schürmann, F. Vallentin, Computational approaches to lattice packing and covering problems, Discr. Comp. Geom. 35 (2006), 73-116.
[J1] A. Schürmann, F. Vallentin, Local covering optimality of lattices: Leech lattice versus root lattice E_8, Int. Math. Res. Notices 32 (2005), 1937-1955.
papers in refereed proceedings
[PR5] P. Moustrou, F. Vallentin, Least distortion Euclidean embeddings of flat tori. Proceedings of the International Symposium on Symbolic & Algebraic Computation (ISSAC 2023, July 24–27, 2023, Tromsø, Norway), 13–23, ACM, 2023.
[PR4] J. Briet, F.M. de Oliveira Filho, F. Vallentin, The positive semidefinite Grothendieck problem with rank constraint, pages 31-42 in Proceedings of the 37th International Colloquium on Automata, Languages and Programming, ICALP 2010 (S. Abramsky et al. eds.), Part I, LNCS 6198, 2010.
[PR3] J. Briet, F.M. de Oliveira Filho, F. Vallentin, The Grothendieck problem with rank constraint, in Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2010), Budapest, Hungary, 5-9 July 2010, 3 pages.
[PR2] C. Bachoc, F. Vallentin, Semidefinite programming bounds for spherical codes (extended abstract), pages 1801-1805 in Proceedings of „2007 IEEE International Symposium on Information Theory“, June 2007, Nice, France.
[PR1] M. Dutour, F. Vallentin, Some six-dimensional rigid forms, pages 102-108 in Voronoi’s Impact on Modern Science, Book 3 (H. Syta, A. Yurachivsky, P. Engel eds.; Institute of Math., Kyiv 2005 = Vol.55 of Proc. Inst. Math. Nat. Acad. Sci.).
book chapters
[BC3] F. Vallentin, Semidefinite programming bounds for error-correcting codes, pages 267-281 in Concise Encyclopedia of Coding Theory (W.C. Huffman, J.-L. Kim, P. Solé (ed.)), CRC Press, 2021
[BC2] F.M. de Oliveira Filho, F. Vallentin, Computing upper bounds for packing densities of congruent copies of a convex body, pages 155-188 in New Trends in Intuitive Geometry (G. Ambrus, I. Barany, K.J. Böroczky, G. Fejes Toth, J. Pach (ed.)), Springer, 2018.
[BC1] C. Bachoc, D.C. Gijswijt, A. Schrijver, F. Vallentin, Invariant semidefinite programs, pages 219-269 in Handbook on Semidefinite, Conic and Polynomial Optimization (M.F. Anjos, J.B. Lasserre (ed.)), Springer, 2012.
papers in other proceedings
[PN15] F. Vallentin, LP and SDP bounds for packing and energy minimization, In: „Real Algebraic Geometry with a View Toward Hyperbolic Programming and Free Probability“. Abstracts from the workshop held March 1-7, 2020. Organized by D. Henrion, S. Kuhlmann, R. Speicher, V. Vinnikov, Oberwolfach Rep. (2020).
[PN14] F. Vallentin, Sums-of-squares for extremal discrete geometry on the unit sphere, In: „Mixed-integer Nonlinear Optimization: A Hatchery for Modern Mathematics“. Abstracts from the workshop held June 2-8, 2019. Organized by L. Liberti, S.Sager, A. Wiegele, Oberwolfach Rep. (2019).
[PN13] F. Vallentin, New upper bounds for the density of translative packings of three-dimensional convex bodies, In: „Discrete Geometry“. Abstracts from the workshop held April 9-15, 2017. Organized by I. Barany, X. Goaoc, G. Rote, Oberwolfach Rep. (2017).
[PN12] F. Vallentin, MINLP from a discrete geometry point of view, In: „Mixed-integer Nonlinear Optimization: A Hatchery for Modern Mathematics“. Abstracts from the workshop held October 18-24, 2015. Organized by L. Liberti, S.Sager, A. Wiegele, Oberwolfach Rep. (2015).
[PN11] F. Vallentin, Invariant SOS, In: „Real Algebraic Geometry With A View Toward Systems Control and Free Positivity“. Abstracts from the workshop held April 6-12, 2014. Organized by D. Henrion, S. Kuhlmann, V. Vinnikov, Oberwolfach Rep. 11 (2014), 1037-1038.
[PN10] F. Vallentin, Linear and semidefinite programming bounds, In: „Optimal and near optimal configurations on lattices and manifolds“. Abstracts from the workshop held August 19-25, 2012. Organized by C. Bachoc, P. Grabner, E.B. Saff, A. Schürmann, Oberwolfach Rep. 9 (2012), 2477-2480.
[PN9] F. Vallentin, Triangulations and subdivisions in the geometry of numbers, In: “Triangulations”. Abstracts from the workshop held April 29-May 5, 2012. Organized by W.H. Jaco, F.H. Lutz, F. Santos, J.H. Sullivan, Oberwolfach Rep. 9 (2012), 1417-1419.
[PN8] F. Vallentin, Applications of semidefinite programming and harmonic analysis, In: “Combinatorial Optimization”. Abstracts from the workshop held November 13-19, 2011. Organized by M. Goemans, M. Laurent, J. Vygen, Oberwolfach Rep. 8 (2011), 3063-3066.
[PN7] F. Vallentin, Upper bounds for densest packings with congruent copies of convex bodies, In: “Discrete Geometry”. Abstracts from the workshop held September 4-10, 2011. Organized by J. Matousek, G. Rote, I. Barany, Oberwolfach Rep. 8 (2011), 2527-2530.
[PN6] F. Vallentin, Infinite-dimensional semidefinite programs, In: “Exploiting symmetry in optimization”. Abstracts from the workshop held August 22-28, 2010. Organized by V. Kaibel, L. Liberti, A. Schürmann, R. Sotirov. Oberwolfach Rep. 7 (2010), 2273-2274.
[PN5] F. Vallentin, Fourier analysis, linear programming, and densities of distance avoiding sets in R^n, In: “Discrete Geometry”. Abstracts from the workshop held September 21-27, 2008. Organized by M. Henk, J. Matousek, E. Welzl. Oberwolfach Rep. 5 (2008), 2484-2487.
[PN4] C. Bachoc, F. Vallentin, Optimality and uniqueness of the (4,10,1/6) spherical code (extended abstract), pages 133-136 in Proceedings „DMHF 2007: COE Conference on the Development of Dynamic Mathematics with High Functionality“, October 2007, Fukuoka, Japan.
[PN3] C. Bachoc, F. Vallentin, More semidefinite programming bounds (extended abstract), pages 129-132 in Proceedings „DMHF 2007: COE Conference on the Development of Dynamic Mathematics with High Functionality“, October 2007, Fukuoka, Japan.
[PN2] F. Vallentin, Sphere Coverings in dimensions 1-24, In: “Gitter und Anwendungen”. Abstracts from the workshop held January 2-8, 2005. Organized by C. Bachoc, E. Bayer-Fluckiger, G. Nebe. Oberwolfach Rep. 2 (2005) 1, 48-51.
[PN1] A. Schürmann, F. Vallentin, Methods in the local theory of packing and covering lattices, pages 122-136 in Proceedings of „COE Workshop on Sphere Packings“, November 2004, Fukuoka, Japan.
expositions
[POP7] [pdf] D. de Laat, F. Vallentin, A Breakthrough in Sphere Packing: The Search for Magic Functions, Nieuw Archief voor Wiskunde (17) 2016, 184-192.
[POP6] F. Vallentin, Optimization in discrete geometry, Optima 100, Mathematical Optimization Society Newsletter, May, 2016
[POP5] F.M. de Oliveira Filho, F. Vallentin, Mathematical optimization for packing problems, SIAG/OPT Views and News, Volume 23 Number 2, December 2015, 5-14
[POP4] F. Vallentin, The continuing story of the kissing number problem, Quadraad, TU Delft, 2011.
[POP3] F. Vallentin, Semidefinite programming and Fourier analysis, het proefschrift, TU Delft, 2010.
[POP2] A. Schürmann, F. Vallentin, Computational paths to discovery with optimization, MaCHazine, studievereniging Christaan Huygens, TU Delft, 2009
[POP1] F. Vallentin, Nieuwe bovengrens voor kusgetal, pages 84-85 in Wetenschap in Nederland: Op onderzoek, Redactie M. Senten (Boom, Amsterdam/Den Haag 2007).
technical reports & lecture notes
[T3] F. Vallentin, Lecture notes: Semidefinite programing and harmonic analysis, 31 pages.
[T2] F. Vallentin, A note on space-tiling zonotopes, arXiv:math/0402053v1 [math.MG], 7 pages.
[T1] B. Hemkemeier, F. Vallentin, On the decomposition of lattices, Electronic Colloquium on Computational Complexity, 1998. (Revision „Incremental Algorithms For Lattice Problems“)
reviews
[R2] A. Schürmann, F. Vallentin, Neue Bücher aus Oberwolfach, Mitteilungen der DMV 20(3) 2012.
[R1] F. Rendl, F. Vallentin, Neue Bücher aus Oberwolfach, Mitteilungen der DMV 18(2): 72, 2010.
thesis
[D3] F. Vallentin, Sphere coverings, lattices, and tilings (in low dimensions), Ph.D. thesis, Technical University Munich, Germany, 2003, 128 pages, written under the supervision of J. Richter-Gebert
[D2] F. Vallentin, Über die Paralleloeder-Vermutung von Voronoi, Diploma thesis, University of Dormtund, 2000, 73 pages, written under the supervision of R. Scharlau
[D1] F. Vallentin, Zur Komplexität des „Shortest Vector Problem“ und seine Anwendungen in der Kryptographie, Diploma thesis, University of Dortmund, 1999, 89 pages, written under the supervision of I. Wegener