RNDr. Pavel Paták, Ph.D.

Postdoc
IST Austria and Charles University in Prague
patak AT kam DOT mff.cuni.cz

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) 2019
  2. 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 2019(6), pp. 1894–1919 2019
  3. 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), pp. 939-981 2017
  4. 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), pp. 841-866 2017
  5. X. Goaoc, I. Mabillard, P. Paták, Z. Patáková, M. Tancer, U. Wagner Bounding Helly numbers via Betti numbers “Journey Through Discrete Mathematics. A Tribute to Jiří Matoušek”, Springer, Cham 2017
  6. 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
  7. J. Cibulka, J. Matoušek, P. Paták Three-monotone interpolation Discrete and Computational Geometry, Vol. 54(1): 3-21 2015
  8. X.Goaoc, J. Matoušek, P. Paták, Z. Safernová, M. Tancer Simplifying inclusion exclusion formulas Comb. Probab. Comput. Volume 24(2): 438-456 2015

Peer-reviewed Conferences

  1. X. Goaoc, P. Paták. Z. Patáková, M. Tancer, U. Wagner Shellability is NP-complete 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 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 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 Symposium on Computational Geometry 2015

Preprints

  1. Pavel Paták Jordan-Hölder with uniqueness for semimodular semilattices Preprint arXiv:1908.09912 2019
  2. Pavel Paták Tverberg type theorems for matroids Preprint arXiv:1702.08170 2016

Selected talks

  1. Almost-embeddability into manifolds and Helly-type theorems UNAM Juriquilla), Mexico, 2016
  2. Tight colorful Tverberg for matroids Transversal, Helly and Tverberg type Theorems in Geometry, Combinatorics and Topology III, Oaxaca, Mexico, 2016
  3. Colorful simplicial depth Mini-symposia M04: Applied Algebraic Topology meets Topological Combinatorics of 7ECM, Berlin, 2016
  4. Bounding Helly numbers via Betti numbers SoCG 2015, Eindhoven
  5. Three-monotonne interpolation Sum(m)it 240,Budapest, 2014

About me

Positions

2018–2020 Postdoc
IST Austria, Austria
Supervisor: Uli Wagner
2017–2018 Postdoc
Faculty of Science, Masaryk University, Brno, Czech Republic
Supervisor: Jan Slovák and Martin Čadek
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
2005–2008 Bachelor 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