RNDr. Pavel Paták, Ph.D.

Postdoc
IST Austria & Charles University
patak AT kam.mff.cuni DOT cz

Research interests

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

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

2018–now Postdoc
IST Austria & Charles University in Prague
Supervisor: Uli Wagner
2017–2018 Postdoc
Faculty of Science, Masaryk University, Brno, Czech Republic
Supervisor: Jan Slovák
2015–2017 Postdoc
Einstein Institute of Mathematics, Hebrew University of Jerusalem, Israel
Supervisors: Karim Adiprasito and Gil Kalai

Education

2010–2015 Ph.D. degree in Algebra, Number Theory and Mathematical Logic
Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Thesis:Using Algebra in Geometry
Advisor: Pavel Růžička
2008–2010 Master degree in Mathematical Structures
Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Thesis:Combinatorics of First Order Structures
Advisor: Jan Krajíček
2008–2010Bachelor degree in General Mathematics
Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Thesis:Definability of First Order Structures (in Czech)
Advisor: Jan Krajíček