RNDr. Pavel Paták, Ph.D.

• Výuka
• Research interests
• Past teaching
• Publications
• Experience

Výuka

Cvičení Lineární algebra (Čt 14:00)

Cvičení Diskrétní matematika (Pá 12:20)

Research interests

• Generalizations of convexity
• Ramsey theory
• Topological and algebraical combinatorics

Past teaching

• 2019/2020 Advanced graph theory, IST Austria
  Treewidth, Choosability, Graphs on Surfaces, Nowhere dense graph classes
• 2018/2019 Using topology, Masaryk University
  Following the book Using Borsuk-Ulam by J. Matoušek

Publications

Papers in peer-reviewed journals

1. X. Goaoc, P. Paták, Z. Patáková, M. Tancer, U. Wagner Shellability is NP-complete Journal of the ACM, Vol. 66(3): Art. 21, 18 2019
2. X. Goaoc, I. Mabillard, P. Paták, Z. Patáková, M. Tancer, U. Wagner Bounding Helly numbers via Betti numbers In “Journey Through Discrete Mathematics. A Tribute to Jiří Matoušek”, Eds. M. Loebl, J. Nešetřil, R. Thomas; Springer, Cham, pp. 407-447 2017
3. X. Goaoc, I. Mabillard, P. Paták, Z. Patáková, M. Tancer, U. Wagner Generalized Heawood Inequalities for Manifolds: a Van Kampen–Flores-type Nonembeddability Result Israel Journal of Mathematics Vol. 222(2): 841-866 2017
4. K. Adiprasito, P. Brinkmann, A. Padrol, P. Paták, Z. Patáková, R. Sanyal Colorful simplicial depth, Minkowski sums, and generalized Gale transforms International Mathematics Research Notices Vol. 6: 1894-1919 2017
5. 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 Vol. 21(5): 939-981 2017
6. J. Cibulka, J. Matoušek, P. Paták Three-monotone interpolation Discrete and Computational Geometry, Vol. 54(1): 3-21 2015
7. X.Goaoc, J. Matoušek, P. Paták, Z. Safernová, M. Tancer Simplifying inclusion exclusion formulas Comb. Probab. Comput. Volume 24(2): 438-456 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 and Computational Geometry, Vol. 54(3): 610-636 2015

Peer-reviewed Conferences

1. X. Goaoc, P. Paták, Z. Patáková, M. Tancer, and U. Wagner Shellability is NP-complete Extended abstract in Proceedings of the 34th International Symposium on Computational Geometry 2018 Best paper award
2. 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 Presented at 24th International Symposium of Graph Drawing and Network Visualization 2017
3. X. Goaoc, P. Paták. Z. Patáková, M. Tancer, U. Wagner Bounding Helly number via Betti numbers Extended abstract in Proceedings of Symposium on Computational Geometry 2015
4. 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 Extended abstract in Proceedings of Symposium on Computational Geometry 2015
5. X. Goaoc, J. Matoušek, P. Paták, Z. Safernová, and M. Tancer Simplifying inclusion-exclusion formulas The Seventh European Conference on Combinatorics, Graph Theory and Applications 2013

Preprints

1. Pavel Paták Properties of closure operators in the plane Preprint arXiv:1909.08489 2020
2. O. Aichholzer, J. Obmann, P. Paták, D. Perz, and J. Tkadlec Disjoint tree-compatible plane perfect matchings Accepted for EuroCG 2020 2020
3. Pavel Paták Jordan-Hölder with uniqueness for semimodular semilattices Preprint arXiv:1908.09912 2019
4. Pavel Patákand M. Tancer Embeddings of k-complexes into 2k-manifolds Preprint arXiv:1904.02404 2019
5. Pavel Paták Tverberg type theorems for matroids Preprint arXiv:1702.08170 2017

Experience

Education