RNDr. Pavel Paták, Ph.D.

Postdoc
Department of Mathematics and Statistics
Masaryk University, Brno
patak AT math DOT muni.cz

Publications

Papers in peer-reviewed journals

  1. X.Goaoc, J. Matoušek, P. Paták, Z. Safernová, M. Tancer Simplifying inclusion exclusion formulas Comb. Probab. Comput. Volume 24(2): 438-456 2015
  2. J. Cibulka, J. Matoušek, P. Paták Three-monotone interpolation Discrete and Computational Geometry, Vol. 54(1): 3-21 2015
  3. 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
  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, rnx184, https://doi.org/10.1093/imrn/rnx184 2017
  5. X. Goaoc, I. Mabillard, P. Paták, Z. Patáková, M. Tancer, U. Wagner Bounding Helly numbers via Betti numbers to appear in “Journey Through Discrete Mathematics. A Tribute to Jiří Matoušek” 2017
  6. X. Goaoc, I. Mabillard, P. Paták. Z. Patáková, M. Tancer, U. Wagner Generalized Heawood Inequalities for Manifolds: a Van Kampen–Flores-type Nonembeddability Result to appear in Israel Journal of Mathematics 2017
  7. 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 to appear in Journal of Graph Algorithms and Applications 2017

Peer-reviewed Conferences

  1. 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
  2. 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
  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 Presented at 24th International Symposium of Graph Drawing and Network Visualization 2017

Preprints

  1. 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

2017–now 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
shortly in 2016 Postdoc
Institue of Science and Technology Austria, Klosterneuburg, Austria
Supervisor: Uli Wagner

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
2008–2010 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