Pavel Paták

Research interests

• Computational algebraic topology and topological data analysis
• Combinatorics, especially Ramsey theory
• Algebra (with focus on posets and mathematical logic)

List of publications

1. P. Paták, Jordan-Hölder Theorem with Uniqueness for Semimodular Lattices, Order, 2024
2. P. Paták, M. Tancer, Embeddings of k-Complexes into 2k-Manifolds, Discrete & Computational Geometry, 2024
3. X. Goaoc, J. Matoušek, P. Paták, Z. Safernová, M. Tancer, Simplifying Inclusion–Exclusion Formulas, Combinatorics, Probability and Computing, 2015
4. O. Aichholzer and J. Obmann and P. Paták, D. Perz and J. Tkadlec and B. Vogtenhuber, Disjoint Compatibility via~Graph Classes, Graph-Theoretic Concepts in Computer Science, 2022
5. P.Paták, M. Tancer, Shellability Is Hard Even for Balls, Proceedings of the 55th Annual {ACM} Symposium on Theory of Computing, 2023
6. P. Paták, A Sharper Ramsey Theorem for Constrained Drawings, Journal of Graph Theory, 2025
7. J. Cibulka, J. Matoušek, P. Paták, Three-monotone interpolation, Discrete Comput. Geom., 2015
8. R. Karasev, J. Kynčl, P. Paták, Z. Patáková, M. Tancer, Bounds for Pach's selection theorem and for the minimum solid angle in a simplex, Discrete Comput. Geom., 2015
9. É. Colin de Verdière, V. Kaluža, P. Paták, Z. Patáková, M. Tancer, A direct proof of the strong Hanani-Tutte theorem on the projective plane, Journal of Graph Algorithms and Applications, 2017
10. X. Goaoc, I. Mabillard, P. Paták, Z. Patáková, M. Tancer, U. Wagner, On generalized Heawood inequalities for manifolds: a van Kampen—Flores-type nonembeddability result, Israel Journal of Mathematics, 2017
11. X. Goaoc, P. Paták, Z. Patáková, M. Tancer, U. Wagner, Bounding Helly numbers via Betti numbers, A journey through discrete mathematics, 2017
12. K. A. Adiprasito, P. Brinkmann, A. Padrol, P. Paták, Z. Patáková, R. Sanyal, Colorful simplicial depth, Minkowski sums, and generalized Gale transforms, International Mathematics Research Notices. IMRN, 2019
13. X. Goaoc, P. Paták, Z. Patáková, M. Tancer, U. Wagner, Shellability is NP-complete, Journal of the ACM, 2019
14. X. Goaoc, J. Matoušek, P. Paták, Z. Safernová, M. Tancer, Simplifying inclusion-exclusion formulas, The Seventh European Conference on Combinatorics, Graph Theory and Applications (conference version), 2013
15. X. Goaoc, I. Mabillard, P. Paták, Z. Patáková, M. Tancer, U. Wagner, On generalized Heawood inequalities for manifolds: a van Kampen—Flores-type nonembeddability result, 31st International Symposium on Computational Geometry, SoCG 2015 (conference version)
16. X. Goaoc, P. Paták, Z. Patáková, M. Tancer, U. Wagner, Bounding Helly numbers via Betti numbers, 31st International Symposium on Computational Geometry, SoCG 2015 (conference version)
17. É. Colin de Verdière, V. Kaluža, P. Paták, Z. Patáková, M. Tancer, A direct proof of the strong Hanani-Tutte theorem on the projective plane, Graph drawing and network visualization 2016, (conference version)
18. X. Goaoc, P. Paták, Z. Patáková, M. Tancer, U. Wagner, Shellability is NP-complete, 34th International Symposium on Computational Geometry, SoCG 2018 (conference version, best paper award)

Teaching