my photo

Zuzana Patáková

Hi! I am an assistant professor at Department of Algebra, Charles University. Previously I was a postdoc fellow at IST Austria in the Wagner group. Before that I was a postdoc at the Einstein Institute of Mathematics of the Hebrew University of Jerusalem. My advisor there was Karim Adiprasito.

I did all my university studies in Prague at Charles University under the guidance of Jirka Matoušek.

Contact:    zuzka AT kam.mff.cuni.cz     or    patakova AT karlin.mff.cuni.cz
Address:    KA MFF UK, Sokolovská 83, 18675 Praha 8

Výuka (Teaching)

2024/25: Počítačová algebra, Algebraické kolokvium
2023/24: Reprezentace grup 1, Úvod do výpočetní topologie, Počítačová algebra, Algebraické kolokvium
2022/23: Úvod do výpočetní topologie, Konvexní optimalizace, Algebra 1 pro informatiky a Algebraické kolokvium
2021/22: Úvod do výpočetní topologie, Algebra 2 pro informatiky, Konvexní optimalizace, Algebra 1 pro informatiky a Algebraické kolokvium
2020/21: Úvod do výpočetní topologie a Algebra 2 pro informatiky, Konvexní optimalizace, cvičení z Algebry 1 a Algoritmů na polynomech

Research interests

Preprints

  1. A. Holmsen, Z. Patáková:
    The fractional Helly number for separable convexity spaces.

  2. K. Adiprasito, Z. Patáková:
    A higher-dimensional version of Fáry's theorem.

  3. Z. Patáková, M. Sharir:
    Covering points by hyperplanes and related problems. Appeared at SoCG 2022.

  4. X. Goaoc, A. Holmsen, Z. Patáková:
    Intersection patterns in spaces with a forbidden homological minor. Preliminary version (with different title) appeared at SoCG 2021.

Publications

  1. Z. Patáková:
    Bounding Radon numbers via Betti numbers. International Mathematics Research Notices, 2024(11): 9482-9500, 2024. Also in Proceedings of SoCG 2020.

  2. Z. Patáková, M. Tancer, U. Wagner:
    Barycentric cuts through a convex body. Discrete Comput. Geom.68, 1133–1154, 2022. Also in Proceedings of SoCG 2020, arXiv

  3. G. Kalai, Z. Patáková:
    Intersection patterns of planar sets. Discrete Comput. Geom. 64(2): 304–323, 2020.

  4. X. Goaoc, P. Paták, Z. Patáková, M. Tancer, U. Wagner:
    Shellability is NP-complete. Journal of the ACM, 66(3), 2019, art. no. 21. Also in Proceedings of SoCG 2018, best paper award.

  5. K. Adiprasito, P. Brinkmann, A. Padrol, P. Paták, Z. Patáková, R. Sanyal: CM 66 (2019), no. 3, Art. 21
    Colorful simplicial depth, Minkowski sums, and generalized Gale transforms. International Mathematics Research Notices, 2019(6):1894-1919, 2019. arXiv

  6. X. Goaoc, P. Paták, Z. Patáková, M. Tancer, U. Wagner:
    Bounding Helly numbers via Betti numbers. Chapter in A Journey Through Discrete Mathematics, A Tribute to Jiří Matoušek, 407-447. 2017 (online). Also in Proceedings of SoCG 2015, arXiv

  7. 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. Israel Journal of Mathematics 222(2):841-866, 2017. Also in In Proceedings of SoCG 2015, arXiv

  8. E. Colin de Verdiere, 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, 21(5):939-981, 2017. Proceedings of the 24th International Symposium on Graph Drawing (GD 2016), arXiv

  9. J. Kynčl, Z. Patáková:
    On the nonexistence of k-reptile simplices in R3 and R4. The Electronic Journal of Combinatorics 24(3): P3.1, 2017, arXiv

  10. 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, arXiv

  11. J. Matoušek, Z. Patáková:
    Multilevel polynomial partitions and simplified range searching. Discrete and Computational Geometry, 54(1):22-41, 2015, arXiv

  12. X. Goaoc, J. Matoušek, P. Paták, Z. Safernová, M. Tancer:
    Simplifying inclusion-exclusion formulas. Combinatorics, Probability and Computing. 24(2):438-456. 2015, arXiv

  13. M. Eliáš, J. Matoušek, E. Roldán Pensado, Z. Safernová:
    Lower bounds on geometric Ramsey functions. SIAM J. Discrete Math., 28(4):1960-1970, 2014. Also in Proceedings of SoCG 2014, arXiv

  14. H. Kaplan, J. Matoušek, Z. Safernová, M. Sharir:
    Unit Distances in Three Dimensions. Combinatorics, Probability and Computing. 21(4): 597-610. 2012, arXiv

  15. J. Matoušek, Z. Safernová:
    On the nonexistence of k-reptile tetrahedra. Discrete and Computational Geometry. 46(3): 599-609. 2011, arXiv