Shira Zerbib

Postdoc T. H. Hildebrandt Assistant Professor,
Department of Mathematics,
University of Michigan, Ann Arbor

Office: East Hall 3060


During fall 2017 I was also a Postdoctoral Fellow at the Geometric and Topological Combinatorics Program at MSRI, and a Visiting Scholar at UC Berkeley. I received my PhD at the Technion - Israel Institute of Technology in 2014.

My research lies in combinatorics, discrete geometry, and combinatorial topology. In particular I am interested in matching theory of graphs and hypergraphs, extremal graph theory, piercing numbers of hypergraphs arising from geometrical structures, epsilon-nets, distinct distances and other Erdos-type problems, fair division problems, and applications of discrete geometry to social sciences; I enjoy exploring for new tools to apply in all the above, with emphasis on topological tools.

Publications and Preprints

  • Frederic Meunier and Shira Zerbib, Envy-free division without assuming the players prefer non-empty pieces. Submitted.
  • Shiliang Gao and Shira Zerbib, The (2,2) and (4,3) properties in families of fat sets in the plane. Submitted.
  •     (This paper was written as part of an REU project I mentored during summer 2017. Shiliang won the George Piranian Excellence in Mathematical Writing Award for it.)
  • Kathryn Nyman, Francis E. Su and Shira Zerbib, Fair division with multiple pieces. Submitted.
  • Francis E. Su and Shira Zerbib, Piercing Numbers in Approval Voting. Submitted.
  • Shira Zerbib, An improved bound in Vizing's conjecture. Submitted.
  • Shira Zerbib, The (p,q) property in families of d-intervals and d-trees. Submitted.
  • Ron Aharoni and Shira Zerbib, A generalization of Tuza's conjecture. Submitted.
  • Florian Frick and Shira Zerbib, Colorful coverings of polytopes and piercing numbers of colorful d-intervals. Combinatorica, to appear.
  • Maria Chudnovsky, Sophie Spirkl and Shira Zerbib, Piercing axis-parallel boxes. Electronic J. of Combinatorics, Volume 25, Issue 1 (2018).
  • Ron Aharoni, Ron Holzman and Shira Zerbib, Edge-covers in d-interval hypergraphs. Discrete & Computational Geometry, 58(3) (2017), 650-662.
  • Ron Aharoni, Tomas Kaiser and Shira Zerbib, Fractional covers and matchings in families of weighted d-intervals. Combinatorica 37(4) (2016) 555-572.
  • Gabriel Nivasch, Janos Pach, Rom Pinchasi and Shira Zerbib, The number of distinct distances from a vertex of a convex polygon. J. Comput. Geom. 4(1) (2013), 1-12.
  • Shira Zerbib, On the zone complexity of a vertex. SIAM J. Discrete Math. 25(2) (2011), 719-730.

  • Shira Zerbib, Problems in Combinatorial Geometry. Ph.D. thesis, Technion, Israel, 2014.
  • Shira Zerbib, On the Projective Analogue of the Brauer-Witt Theorem. M.Sc. thesis, Technion, Israel, 2007.

  • My papers on arXiv

    Work in Progress

  • On Vizing’s conjecture.
  • Clique-coloring of the unit disk graph (with B. Slomka and Y. Yuditsky).
  • Almost all graphs satisfy Tuza’s conjecture (with P. Bennett and A. Dudek).
  • Helly’s theorem with no dimensions (with H. Huang and B. Slomka).
  • Piercing discrete line segments (with D. Oliveros and C. ONeill).

  • Teaching

    Winter 2018:  Math 567 - Introduction to Coding Theory (University of Michigan).
    Winter 2017:  Math 567 - Introduction to Coding Theory (University of Michigan).
    Fall 2016:    Math 465 - Introduction to Combinatorics (University of Michigan).
    Winter 2016:  Math 567 - Introduction to Coding Theory (University of Michigan).
    Fall 2015:    Math 115 - Calculus I (University of Michigan).
    2009-2014:     Teaching Assistant - Linear Algebra, Abstract Algebra, Field Theory, Calculus II (Technion).

    My sculptures