RNDr. Pavel Paták, Ph.D.

Pavel Paták
PositionPostdoc (Kalai's group)
AddressEinstein Institute of Mathematics
Edmond J. Safra Campus, The Hebrew University of Jerusalem, 9190401 Israel
Contactppatak AT seznam DOT cz

Research interests

Publications

  1. 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
  2. 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
  3. X. Goaoc, P. Paták, Z. Patáková, M. Tancer, U. Wagner, Bounding Helly Numbers via Betti Numbers, Proceedings of SoCG 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, Proceedings of SoCG 2015
  5. J. Cibulka, J. Matoušek, P. Paták, Three-monotone Interpolation, Discrete & Computational Geometry, Vol. 54, Issue 1, 2015, pp 3-21
  6. 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)

Preprints

  1. 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
  2. X. Goaoc, P. Paták, Z. Patáková, M. Tancer, U. Wagner, Bounding Helly numbers via Betti numbers
  3. K. Adiprasito, P. Brinkmann, A. Padrol, P. Paták, Z. Patáková, R. Sanyal, Colorful simplicial depth, Minkowski sums, and generalized Gale transforms
  4. 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

Selected talks

  1. Almost-embeddability into manifolds and Helly-type theorems, UNAM Juriquilla, Mexico, 2016
  2. Tight colorful Tverberg for matroids, at Transversal, Helly and Tverberg type Theorems in Geometry, Combinatorics and Topology III, Oaxaca, Mexico, 2016
  3. Colorful simplicial depth, at 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

My thesis

The papers "Generalized Heawood Inequalities for Manifolds: A van Kampen-Flores-type Nonembeddability Result" and "Bounding Helly Numbers via Betti numbers" are based on a systematic study of non-emebddability results from homological point of view. In my thesis, we have improved the bounds and develop the technique further, so that it can deal with multiple intersections. Now some bounds for questions like "Given k, r and a manifold M, how large can a simplex be, so that for every continuous map of it into M there are r points with the same image?" can be effectively proven.

Education

2015Ph.D. in Algebra, Number Theory and Mathematical Logic
Faculty of Mathematics and Physics, Charles University in Prague
Thesis: Using algebra in geometry
2010Master degree in Mathematical Structures
Faculty of Mathematics and Physics, Charles University in Prague
Thesis: Combinatorics of mathematical structures
Advisor: Jan Krajíček
2008Bachelor degree in General Mathematics
Faculty of Mathematics and Physics, Charles University in Prague
Thesis: Definovatelnost v matematických strukturách (in Czech)
Advisor: Jan Krajíček

Teaching

During my studies at Charles University, I have led several seminars and recitations. Full list can be found at my old pages.

Miscellaneous

List of open problems I find interesting