## Eran Nevo

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

• [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: spheres triangulations) and polytopes (for example: cubical polytopes).
Tools include for example: the Stanley-riesner ring, toric varieties, framework rigidity.
• 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. [ps] (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: [ps]. 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 Björner 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].
• Linear resolutions of powers of 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, to appear in Discrete Comput. Geom. [pdf].
• A lower bound theorem for centrally symmetric simplicial polytopes, with Steven Klee, Isabella Novik and Hailun Zheng, to appear in Discrete Comput. Geom. [pdf].
• On Betti numbers of flag complexes with forbidden induced subgraphs, with K. A. Adiprasito and M. Tancer, to appear in Mathematical Proceedings Cambridge Philosophical Society.[pdf].
• On the cone of f-vectors of cubical polytopes, with Ron M. Adin and Daniel Kalmanovich, to appear in Proc. AMS.[pdf].
• Turan, involution and shifting, with Gil Kalai, to appear in Alger. Combin.[pdf].

### Preprints

• Almost simplicial polytopes: The lower and upper bound theorems, with G. Pineda-Villavicencio, J. Ugon and D. Yost, submitted [pdf].
• QGLBT for polytopes, with Karim Adiprasito, arXived [pdf].
• Rigidity with few locations, with Karim Adiprasito, submitted [pdf].
• Circulant matrices and Galois-Togliatti systems, with Pietro De Poi, Emilia Mezzetti, Mateusz Michalek and Rosa Maria Miro-Roig, arXived [pdf].

Last update: 27. 09. 2018.