Position | Postdoc (Kalai's group) |

Address | Einstein Institute of Mathematics |

Edmond J. Safra Campus, The Hebrew University of Jerusalem, 9190401 Israel | |

Contact | ppatak AT seznam DOT cz |

- Interaction of algebraic topology, combinatorics and discrete geometry
- Model theory

- 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, 54(3):610-636, 2015 - X. Goaoc, J. Matoušek, P. Paták, Z. Safernová, M. Tancer,
*Simplifying Inclusion-Exclusion Formulas*,Combinatorics, Probability and Computing, Vol. 24, Issue 02, 2015, pp 438-456 - X. Goaoc, P. Paták, Z. Patáková, M. Tancer, U. Wagner,
*Bounding Helly Numbers via Betti Numbers*, Proceedings of SoCG 2015 - 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*, Proceedings of SoCG 2015 - J. Cibulka, J. Matoušek, P. Paták,
*Three-monotone Interpolation*, Discrete & Computational Geometry, Vol. 54, Issue 1, 2015, pp 3-21 - 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*, Extended Abstract in Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016)

- 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* - X. Goaoc, P. Paták, Z. Patáková, M. Tancer, U. Wagner,
*Bounding Helly numbers via Betti numbers* - K. Adiprasito, P. Brinkmann, A. Padrol, P. Paták, Z. Patáková, R. Sanyal,
*Colorful simplicial depth, Minkowski sums, and generalized Gale transforms* - 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*

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

2015 | Ph.D. in Algebra, Number Theory and Mathematical Logic Faculty of Mathematics and Physics, Charles University in Prague Thesis: Using algebra in geometry |

2010 | Master degree in Mathematical Structures Faculty of Mathematics and Physics, Charles University in Prague Thesis: Combinatorics of mathematical structuresAdvisor: Jan Krajíček |

2008 | Bachelor degree in General Mathematics Faculty of Mathematics and Physics, Charles University in Prague Thesis: Definovatelnost v matematických strukturách (in Czech)Advisor: Jan Krajíček |