Institute of Mathematics,
Givat Ram, Jerusalem 91904, Israel.
Current Teaching: Linear Algebra 2.
- Combinatorics - with connections to commutative algebra, topology, geometry and convexity.
- 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 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].
- Linear resolutions of powers of 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.
- Lefschetz properties of balanced 3-polytopes, with David Cook II, Martina Juhnke-Kubitzke and Satoshi Murai, to appear in Rocky Mountain Journal of Mathematics[pdf].
- Pach's selection theorem does not admit a topological extension, with Imre Barany, Roy Meshulam and Martin Tancer, to appear in Discrete Comput. Geom. [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].
- Almost simplicial polytopes: The lower and upper bound theorems, with G. Pineda-Villavicencio, J. Ugon and D. Yost, submitted [pdf].
- On Betti numbers of flag complexes with forbidden induced subgraphs, with K. A. Adiprasito and M. Tancer, submitted [pdf].
- On the cone of f-vectors of cubical polytopes, with
Ron M. Adin and Daniel Kalmanovich, submitted [pdf].
- Turan, involution and shifting, with Gil Kalai, submitted [pdf].
- QGLBT for polytopes, with Karim Adiprasito, arXived [pdf].
- Rigidity with few locations, with Karim Adiprasito, arXived [pdf].
Last update: 13. 06. 2018.