Since May 2023 I work as an Assistant Professor of Operations Research at Tilburg University, Tilburg School of Economics and Management, Department of Econometrics and Operations Research.
I obtained my PhD in mathematics under supervision Lex Schrijver at the University of Amsterdam (September 2019). After my PhD, I have worked as an operations research engineer at ORTEC - Optimize Your World in Zoetermeer (October 2019 - August 2020). After that, I worked as a postdoctoral researcher with Monique Laurent at Centrum Wiskunde en Informatica (CWI) in the research group Networks and Optimization (September 2020 - April 2023).
My PhD-thesis, New methods in coding theory: Error-correcting codes and the Shannon capacity, can be found here and on arXiv:2005.02945 (see this link for general information about the thesis). I also hold a master's degree in Dutch Law (obtained at the University of Amsterdam, 2017).
My research is in the intersection of discrete mathematics and optimization. I am interested in convex relaxations of hard optimization problems and in using algebraic techniques to reduce complexity in combinatorial, polynomial and semidefinite optimization. I am broadly interested in discrete mathematics, including coding theory.
Contact information:
Email: s.c.polak *at* tilburguniversity *dot* edu
Koopmans Building, room K 408
Warandelaan 2
5037 AB Tilburg
Netherlands
Preprints:
- P. Buys, S. Polak, J. Zuiddam, A group-theoretic approach to Shannon capacity of graphs and a limit theorem from lattice packings, 2025, arXiv:2506.14654
- D. Gijswijt, S. Polak, Semidefinite lower bounds for covering codes, 2025, arXiv:2504.01932
Published:
- M. Laurent, S.C. Polak, L.F. Vargas, Semidefinite approximations for bicliques and biindependent pairs, Mathematics of Operations Research, 50 (2025), 537-572, Informs PubsOnLine, arXiv:2302.08886
- D. Brosch, S.C. Polak, New lower bounds on crossing numbers of Km,n from semidefinite programming, Mathematical Programming, Series A, 207 (2024), 693-715, Springer, arXiv:2206.02755
- S.J. Gribling, S.C. Polak, Mutually unbiased bases: polynomial optimization and symmetry, Quantum, 8, 1318, 2024, Quantum, arXiv:2111.05698
- S.C. Polak, Symmetry reduction to optimize a graph-based polynomial from queueing theory, SIAM Journal on Applied Algebra and Geometry, 6 (2022), 243-266, SIAM, arXiv:2104.08264
- S. Della Fiore, A. Gnutti, S.C. Polak, The maximum cardinality of trifferent codes of lengths 5 and 6, Examples and Counterexamples, 2 (2022), 100051, ScienceDirect, arXiv:2201.06846
- S.C. Polak, A. Schrijver, New lower bound on the Shannon capacity of C7 from circular graphs, Information Processing Letters, 143 (2019), 37-40, ScienceDirect, arXiv:1808.07438
- S.C. Polak, Semidefinite programming bounds for Lee codes, Discrete Mathematics, 342 (2019), 2579-2589, ScienceDirect, arXiv:1810.05066. Link to computer programs used for this paper.
- A.E. Brouwer, S.C. Polak, Uniqueness of codes using semidefinite programming, Designs, Codes and Cryptography, 87 (2019), 1881-1895, PDF, arXiv:1709.021951. Link to computer programs used for this paper: Google Drive, GitHub
- B.M. Litjens, S.C. Polak, V. Sivaraman, Sum-perfect graphs, Discrete Applied Mathematics, 259 (2019), 232-239, ScienceDirect, arXiv:1710.07546
- S.C. Polak, Semidefinite programming bounds for constant weight codes, IEEE Transactions on Information Theory, 65 (2019), 28-38, IEEE Xplore, PDF, arXiv:1703.05171
- S.C. Polak, New nonbinary code bounds based on divisibility arguments, Designs, Codes and Cryptography, 86 (2018), 861-874, PDF, arXiv:1606.05144
- B.M. Litjens, S.C. Polak, A. Schrijver, Semidefinite bounds for nonbinary codes based on quadruples, Designs, Codes and Cryptography, 84 (2017), 87-100, PDF, arXiv:1602.02531
Conference proceedings:
- S. Gribling, S.C. Polak, L. Slot, A note on the computational complexity of the Moment-SOS hierarchy for polynomial optimization, in International Symposium Symbolic and Algebraic Computation (ISSAC 2023), 280-288, Proceedings
- R. Brokkelkamp, S.C. Polak, G. Schäfer, Y. Velaj, Approximate pricing in networks: how to boost the betweenness and revenue of a node, in 30th International Symposium on Algorithms and Computation (ISAAC 2019), 13:1-13:15, Proceedings
- B.M. Litjens, S.C. Polak, B.L. Sevenster, L. Vena, On the chromatic number of a subgraph of the Kneser graph, Electronic Notes in Discrete Mathematics, 68 (2018), 227-232, Proceedings (new extended version on arXiv: arXiv:1803.04342 (2018))
Some recent and future talks:
-EURO, Copenhagen, 30 June-3 July 2024, Semidefinite approximations for bicliques and biindependent pairs (joint work with Monique Laurent and Luis Felipe Vargas)
-Workshop on Real-world Applications of Geometry and Algebra, Eindhoven, June 13-14 2024, New bounds for crossing numbers of complete bipartite graphs (joint work with Daniel Brosch).
-EUROpt, Budapest. 23-25 August 2023, New bounds for crossing numbers of complete bipartite graphs (joint work with Daniel Brosch).
-SIAM Conference on Applied Algebra and Geometry, Eindhoven, July 10-14 2023, On the computational complexity of the moment-SOS Hierarchy (joint work with Sander Gribling and Lucas Slot)
-Workshop Combinatorics in Digital Communication, Eindhoven, 19-21 April 2023, Uniqueness of codes using semidefinite programming (talk partly based on joint work with Andries Brouwer)
-KdVI Discrete Mathematics Seminar, UvA Amsterdam, 1 February 2023, Semidefinite approximations for bicliques and biindependent pairs (joint work with Monique Laurent and Luis Felipe Vargas)
-TU/e Lunch seminar in Combinatorial Optimization, TU Eindhoven, 14 October 2022, Semidefinite approximations for bicliques and biindependent pairs (joint work with Monique Laurent and Luis Felipe Vargas)
-International Conference on Continuous Optimization (ICCOPT), Lehigh University, Pennsylvania. 25-28 July 2022, Semidefinite approximations for bicliques and biindependent pairs (joint work with Monique Laurent and Luis Felipe Vargas)
-POEMA Final workshop, Paris. 5-9 September 2022, New bounds for crossing numbers of complete bipartite graphs (joint work with Daniel Brosch). Youtube recording
-Nordic Combinatorial Conference (NORCOM), Tromsø. 7-9 June 2022, New bounds for crossing numbers from permutation modules and semidefinite programming (joint work with Daniel Brosch)
-International Symposium on Combinatorial Optimization (ISCO), Online. 18-20 May 2022, Semidefinite approximations for bicliques and biindependent pairs (joint work with Monique Laurent and Luis Felipe Vargas)
-Dutch Day of Combinatorics, Eindhoven, 12 May 2022, New bounds for crossing numbers from permutation modules and semidefinite programming (joint work with Daniel Brosch)
-N&O Seminar, CWI, 2 February 2022, Mutually unbiased bases: polynomial optimization and symmetry (joint work with Sander Gribling)
-BrainPop seminar Toulouse, Online, 24 January 2022, Mutually unbiased bases: polynomial optimization and symmetry (joint work with Sander Gribling)
-SIAM conference on Applied Algebra and Geometry, Online, August 16-20, 2021, Symmetry reduction to optimize a graph-based polynomial from queueing theory
-SIAM conference on Optimization, Online, July 20-23, 2021, Symmetry reduction to optimize a graph-based polynomial from queueing theory
-Tilburg TiSEM seminars on Operations Research, Online, May 27, 2021, Symmetry reduction to optimize a graph-based polynomial from queueing theory
-DIAMANT symposium, Online, April 7, 2021, Symmetry reduction to optimize a graph-based polynomial from queueing theory
-University of Amsterdam, Discrete Mathematics Seminar at KdvI, Online, April 1, 2021, Symmetry reduction to optimize a graph-based polynomial from queueing theory
-Landelijk Netwerk Mathematische Besliskunde, Conference on the Mathematics of Operations Research, Lunteren, January 16-18, 2018, Uniqueness of codes using semidefinite programming (joint work with Andries Brouwer)
-Workshop on analytic combinatorics, Zámeček, 27-31 March 2017, New upper bounds for nonbinary codes based on a divisibility argument
-Workshop on Algebraic Graph Theory, Pilsen, 3-7 October 2016, Semidefinite bounds for nonbinary codes based on quadruples (joint work with Bart Litjens and Lex Schrijver)
-6th SDP day at CWI, Amsterdam, 30 June 2016, Semidefinite bounds for nonbinary codes based on quadruples (joint work with Bart Litjens and Lex Schrijver)
Teaching (Lectures):
- 2024/2025: Linear Algebra, Operations Research Methods (Tilburg University, Bachelor Econometrics and Operations Research), Essential Mathematics for Data Science (Tilburg University, Minor Data Science), Networks and Semidefinite Programming (LNMB PhD course, with Monique Laurent)
- 2023/2024: Linear Algebra (Tilburg University, Bachelor Econometrics and Operations Research), Essential Mathematics for Data Science (Tilburg University, Minor Data Science)
- 2022/2023: Networks and Semidefinite Programming (LNMB PhD course, with Monique Laurent)
Teaching (Tutorials at the University of Amsterdam):
- 2017/2018: Linear algebra; Functional analysis
- 2016/2017: Algebra 2 (ring and field theory); Galois theory
- 2015/2016: Analysis on the real line; Introductory graph theory
Running:
In addition to my academic work, I am passionate about running: World Athletics profile
Thesis:
- New methods in coding theory: Error-correcting codes and the Shannon capacity, PhD-thesis under supervision of Lex Schrijver, 2019
- Algorithms for the network analysis of bilateral tax treaties, Master thesis at the CWI/CPB/UvA under supervision of Guido Schaefer, 2014
- Kwadratische Vormen, Bachelor thesis at the UvA (in Dutch) under supervision of Gerard van der Geer, 2012