## Eran NevoInstitute of Mathematics, Hebrew University, Givat Ram, Jerusalem 91904, Israel. E-mail: nevo[at]math.huji.ac.il TL: +972-2-6586871 ## Teaching 2023/24:- Introduction to Mathematics research (Fall 2023/24) [website]
- Discrete Mathematics (Spring 2024) [website]
## Research- Combinatorics - with connections to commutative algebra, topology, geometry and convexity.
- 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. -
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), 259279.[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), 243248[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), 15271538.[pdf]. - On the generalized lower bound conjecture for polytopes and spheres, with: S. Murai,
*Acta Math.***210**(2013), 185202[pdf]. - On r-stacked triangulated manifolds, with: S. Murai,
*J. Algebraic Combin.***39**(2014), 373388.[pdf]. - Stellar theory for flag complexes, with: F. Lutz,
*Math. Scand.***118**(2016), 7082.[pdf]. - Bipartite rigidity, with: G. Kalai and I. Novik,
*Trans. Amer. Math. Soc.***368**(2016), 55155545.[pdf]. - Polyhedrons and PBIBDs from hyperbolic manifolds,
*Geom. Ded.***178**(2015), 103110.[pdf]. - Bipartite minors, with: M. Chudnovsky, G. Kalai, I. Novik and P. Seymour,
*J. Combin. Theory Ser. B***116**(2016), 219228[pdf]. - Generalized Tchebyshev triangulations, with G. Hetyei,
*J. Algebraic Combin.***137**(2016), 88125[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), 359378[pdf]. - On vanishing patterns in j-strands of edge ideals, with A. Abedelfatah,
*J. Algebraic Combin.***46**(2017), 287295. [pdf]. - Bounds for entries of ?-vectors of flag homology spheres, with J.P. Labbe,
*SIAM J. Discrete Math.***31**(2017), 20642078. [pdf]. - Lefschetz properties of balanced 3-polytopes, with David Cook II, Martina Juhnke-Kubitzke and Satoshi Murai,
*Rocky Mountain Journal of Mathematics***48**(2018), 769790[pdf]. - Pach's selection theorem does not admit a topological extension, with Imre Barany, Roy Meshulam and Martin Tancer,
*Discrete Comput. Geom.***60**(2018), 420429[pdf]. - On the reconstruction of polytopes, with Joseph Doolittle, Guillermo Pineda-Villavicencio, Julien Ugon and David Yost,
*Discrete Comput. Geom.***61**(2019), 285302[pdf]. - A lower bound theorem for centrally symmetric simplicial polytopes, with
Steven Klee, Isabella Novik and Hailun Zheng,
*Discrete Comput. Geom.***61**(2019), 541561[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), 18511866.[pdf]. - Turan, involution and shifting, with Gil Kalai,
*Algebr. Combin.***2**(2019), 367378[pdf]. - Almost simplicial polytopes: The lower and upper bound theorems, with G. Pineda-Villavicencio, J. Ugon and D. Yost,
*Canad. J. Math.***72**(2020) 537556[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) 711723 [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), 261273. 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), 297303. [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, 490501. [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,
to appear in*Discrete Comput. Geom.*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,
to appear in*Algebraic Combinatorics*[pdf]. - Volume rigidity and algebraic shifting, with Denys Bulavka and Yuval Peled, submitted.
An extended abstract at
*S?m. Lothar. Combin.***89B**(2023), Art. 14, 12 pp. [pdf]. - QGLBT for polytopes, with Karim Adiprasito, submitted [pdf].
- Rigidity expander graphs, with Alan Lew, Yuval Peled and Orit E. Raz, 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, arXived [pdf].
- Exterior Shifting of Low Genus Surfaces, with Aaron Keehn, arXived [pdf].
## Interests## Projects (students are welcome to join!)## Papers published or accepted## PreprintsLast update: 23. 05. 2024. |