Eran Nevo


Institute of Mathematics, Hebrew University,
Givat Ram, Jerusalem 91904, Israel.
E-mail: nevo[at]math.huji.ac.il
TL: +972-2-6586871



Teaching 2024/5:

  • Discrete Mathematics (Fall 2024/5) [website]
  • Polytopes (Spring 2025) [website]

Research

    Interests

    • Combinatorics - with connections to commutative algebra, topology, geometry and convexity.

    Projects (students are welcome to join!)

    • Face numbers and flag-face numbers of simplicial complexes (for example: manifold triangulations) and polytopes (for example: cubical polytopes).
      Tools include for example: the Stanley-Reisner ring, toric varieties, framework rigidity.
      Computational complexity aspects of face numbers are also studied.
    • Betti tables of monomial ideals (for example: edge ideals) and related invariants (for example: regularity).
      Topological tools are also available here via Hochster's formula.
    • Embeddability of simplicial complexes in manifolds.
      Tools include for example: the van-Kampen obstruction and higher minor notions.

    Papers published or accepted

    • Lenses in arrangements of pseudocircles and their applications, (with P. Agarwal, J. Pach, R. Pinchasi, M. Sharir and S. Smorodinsky),
      J. ACM, 51 (2004), 139-186. [pdf] (Also in Proc. 18th ACM Symp. on Computational Geometry (2002), 123-132.)
    • Algebraic shifting and basic constructions on simplicial complexes,
      J. Algeb. Combin., 22 (2005), 411-433. [pdf]
    • A Generalized Macaulay theorem and generalized face rings,
      J. Combin. Theory Ser. A, 113 (2006), 1321-1331. [pdf]
    • Rigidity and the lower bound theorem for doubly Cohen-Macaulay complexes,
      Discrete Comput. Geom., 39 (2008), 411-418. [pdf]
    • Higher minors and Van Kampen's obstruction,
      Math. Scandi., 101 (2007), 161-176. [pdf]
    • Embeddability and stresses of graphs,
      Combinatorica, 27 (2007), 465-472. Old (full) version: [pdf]. Journal version (with the section on algebraic shifting omitted): [pdf]
    • On the independence complex of square grids, with: M. Bousquet-Melou and S. Linusson,
      J. Algebraic Combin. 27 (2008), 423-450. [pdf]
    • On the embeddability of skeleta of spheres, with: U. Wagner,
      Isr. J. Math.174 (2009), 381-402. [pdf]
    • The Lefschetz property for barycentric subdivisions of shellable complexes, with: M. Kubitzke,
      Trans. Amer. Math. Soc. 361 (2009), 6151-6163. [pdf].
    • Lefschetz properties and basic constructions on simplicial spheres, with: E. Babson,
      J. Algebraic Combin. 31 (2010), 111-129.[pdf]
    • Remarks on missing faces and lower bounds on face numbers,
      Elec. J. Combi. 16(2)(the Bjφrner Festschrift volume) (2009), R8.[pdf]
    • A characterization of simplicial polytopes with g_2 = 1, with: E. Novinsky,
      J. Combin. Theory Ser. A 118 (2011), 387-395.[pdf]
    • On $\gamma$-vectors satisfying the Kruskal-Katona inequalities, with T. K. Petersen,
      Discrete Comput. Geom.45 (2010), 503-521.[pdf]
    • Regularity of edge ideals of C_4-free graphs via the topology of the lcm-lattice,
      J. Combin. Theory Ser. A 118 (2011), 491-501[pdf].
    • The $\gamma$-vector of a barycentric subdivision, with: T. K. Petersen and B. E. Tenner,
      J. Combin. Theory Ser. A 118 (2011), 1364-1380.[pdf]
    • On commensurizer growth, with: N. Avni and S. Lim,
      Isr. J. Math., 188 (2012), 259–279.[pdf].
    • On the cd-index and gamma-vector of S*-shellable CW-spheres, with: S. Murai,
      Math. Z. 271 (2012), 1309-1319.[pdf].
    • C_4-free edge ideals, with: I. Peeva,
      J. Algebraic Combin. 37 (2013), 243–248[pdf].
    • Nonpolytopal nonsimplicial lattice spheres with nonnegative toric g-vector, with: L. J. Billera,
      Discrete Comput. Geom. 48 (2012), 1048-1057.[pdf].
    • The flag f-vectors of Gorenstein* order complexes of dimension 3, with: S. Murai,
      Proc. Amer. Math. Soc. 142(2014), 1527–1538.[pdf].
    • On the generalized lower bound conjecture for polytopes and spheres, with: S. Murai,
      Acta Math. 210 (2013), 185–202[pdf].
    • On r-stacked triangulated manifolds, with: S. Murai,
      J. Algebraic Combin.39 (2014), 373–388.[pdf].
    • Stellar theory for flag complexes, with: F. Lutz,
      Math. Scand. 118 (2016), 70–82.[pdf].
    • Bipartite rigidity, with: G. Kalai and I. Novik,
      Trans. Amer. Math. Soc. 368 (2016), 5515–5545.[pdf].
    • Polyhedrons and PBIBDs from hyperbolic manifolds,
      Geom. Ded. 178 (2015), 103–110.[pdf].
    • Bipartite minors, with: M. Chudnovsky, G. Kalai, I. Novik and P. Seymour,
      J. Combin. Theory Ser. B 116(2016), 219–228[pdf].
    • Generalized Tchebyshev triangulations, with G. Hetyei,
      J. Algebraic Combin. 137 (2016), 88–125[pdf].
    • Many triangulated odd-dimensional spheres, with F. Santos and S. Wilson,
      Math. Annalen 364 (2016), 737-762[pdf].
    • Higher chordality: from graphs to complexes, with K. A. Adiprasito, and J. A. Samper,
      Proc. Amer. Math. Soc. 144 (2016), 3317-3329[pdf].
    • On the maximum order of graphs embedded in surfaces, with: G. Pineda-Villavicencio, D. R. Wood,
      J. Combin. Theory Ser. B 119 (2016), 28-41[pdf].
    • A Geometric Lower Bound Theorem, with K. A. Adiprasito and J. A. Samper,
      Geom. Funct. Anal. 26 (2016), 359–378[pdf].
    • On vanishing patterns in j-strands of edge ideals, with A. Abedelfatah,
      J. Algebraic Combin. 46 (2017), 287–295. [pdf].
    • Bounds for entries of ?-vectors of flag homology spheres, with J.P. Labbe,
      SIAM J. Discrete Math. 31 (2017), 2064–2078. [pdf].
    • Lefschetz properties of balanced 3-polytopes, with David Cook II, Martina Juhnke-Kubitzke and Satoshi Murai,
      Rocky Mountain Journal of Mathematics 48 (2018), 769–790[pdf].
    • Pach's selection theorem does not admit a topological extension, with Imre Barany, Roy Meshulam and Martin Tancer,
      Discrete Comput. Geom. 60 (2018), 420–429[pdf].
    • On the reconstruction of polytopes, with Joseph Doolittle, Guillermo Pineda-Villavicencio, Julien Ugon and David Yost,
      Discrete Comput. Geom. 61 (2019), 285–302[pdf].
    • A lower bound theorem for centrally symmetric simplicial polytopes, with Steven Klee, Isabella Novik and Hailun Zheng,
      Discrete Comput. Geom. 61 (2019), 541–561[pdf].
    • On Betti numbers of flag complexes with forbidden induced subgraphs, with K. A. Adiprasito and M. Tancer,
      Mathematical Proceedings Cambridge Philosophical Society, 168 (2020) 567--600[pdf].
    • On the cone of f-vectors of cubical polytopes, with Ron M. Adin and Daniel Kalmanovich,
      Proc. Amer. Math. Soc. 147(2019), 1851–1866.[pdf].
    • Turan, involution and shifting, with Gil Kalai,
      Algebr. Combin. 2(2019), 367–378[pdf].
    • Almost simplicial polytopes: The lower and upper bound theorems, with G. Pineda-Villavicencio, J. Ugon and D. Yost,
      Canad. J. Math. 72 (2020) 537–556[pdf].
    • Complexity yardsticks for f-vectors of polytopes and spheres,
      Discrete Comput. Geom. 64 (2020), 347-354 [pdf].
    • Rigidity with few locations, with Karim Adiprasito,
      Isr. J. Math. 240 (2020) 711–723 [pdf].
    • Circulant matrices and Galois-Togliatti systems, with Pietro De Poi, Emilia Mezzetti, Mateusz Michalek and Rosa Maria Miro-Roig,
      J. Pure Appl. Algebra 224 (2020), 106404, 14 pp. [pdf].
    • Induced equators in flag spheres, with Maria Chudnovsky,
      J. Combin. Theory Ser. A 176 (2020), 105283, 14 pp. [pdf].
    • Flag complexes and homology, with K.F.E. Chong,
      J. Combin. Theory Ser. A 182 (2021), 105466, 21 pp. [pdf].
    • On the realization space of the cube, with Karim Adiprasito and Daniel Kalmanovich,
      JEMS 26 (2024), 261–273. An extended abstract at Sem. Lothar. Combin. 84B (2020), Art. 80, 12 pp. [pdf].
    • Embedding Divisor and Semi-Prime Testability in f-vectors of polytopes,
      Discrete Comput. Geom. 70 (2023), 297–303. [pdf].
    • Sharp threshold for rigidity of random graphs, with Alan Lew, Yuval Peled and Orit E. Raz,
      Bull. London Math. Soc. 55 (2023), no. 1, 490–501. [pdf].
    • Stable sets in flag spheres, with Maria Chudnovsky,
      European J. Combin. 110 (2023), Paper No. 103699, 9 pp. An extended abstract at Sem. Lothar. Combin. 86B (2022), Art. 10, 11 pp. [pdf].
    • Vertex spanning planar Laman graphs in triangulated surfaces, with Simion Tarabykin,
      Discrete Comput. Geom. 72 (2024), 912–927. An extended abstract at Sem. Lothar. Combin. 86B (2022), Art. 43, 12 pp. [pdf].
    • On the d-dimensional algebraic connectivity of graphs, with Alan Lew, Yuval Peled and Orit E. Raz,
      Isr. J. Math. 256 (2023), 479-511. [pdf].
    • Regularity of Edge Ideals Via Suspension, with A. Banerjee,
      Algebraic Combinatorics 6 (2023), 1687–1695. [pdf].
    • Volume rigidity and algebraic shifting, with Denys Bulavka and Yuval Peled,
      J. Combin. Theory Ser. B 170 (2023), (2025), 189–202. An extended abstract at Sem. Lothar. Combin. 89B (2023), Art. 14, 12 pp. [pdf].
    • Rigidity expander graphs, with Alan Lew, Yuval Peled and Orit E. Raz, to appear in
      Combinatorica [pdf].

    Preprints

    • QGLBT for polytopes, with Karim Adiprasito, submitted [pdf].
    • On colorings of hypergraphs embeddable in R^d, with Seunghun Lee, submitted [pdf].
    • On flag-no-square 4-manifolds, with Daniel Kalmanovich and Gangotryi Sorcar, submitted [pdf].
    • Exterior Shifting of Low Genus Surfaces, with Aaron Keehn, submitted [pdf].
    • On the k-volume rigidity of a simplicial complex in R^d, with Alan Lew, Yuval Peled, Orit E. Raz, arXived [pdf].



    Last update: 11. 03. 2025.