- Algebraic and geometric combinatorics,
especially combinatorics of polytopes
- Connections between combinatorics, commutative algebra and algebraic
Upper Bound Theorems
for homology manifolds,
Israel Journal of Mathematics, 108 (1998), 45-82.
The Lower Bound Theorem for centrally symmetric simple polytopes,
Mathematika, 46 (1999), 231-240.
A note on geometric embeddings of simplicial complexes in
a Euclidean space,
Discrete and Computational Geometry, 23 (2000),
Lower bounds for the cd-index of odd-dimensional simplicial
European Journal of Combinatorics 21 (2000), 533-541.
Syzygies of oriented matroids
(with Alex Postnikov and Bernd Sturmfels),
Duke Mathematical Journal, 111 (2002), 287-317.
Lyubeznik's resolution and rooted complexes,
Journal of Algebraic Combinatorics, 16 (2002), 97-101.
A short simplicial h-vector and the Upper Bound Theorem
(with Patricia Hersh) ,
Discrete and Computational Geometry,
28 (2002), 283-289.
Remarks on the Upper Bound Theorem
Journal of Combinatorial Theory Ser. A, 104
Symmetric iterated Betti numbers
(with Eric Babson and Rekha Thomas),
Journal of Combinatorial Theory Ser. A, 105 (2004),
- Face numbers and nongeneric initial ideals (with Eric Babson),
Electronic J. Combin., 11 (2004/06), no.2,
Research Paper 25, 23pp.
On face numbers of manifolds with symmetry
Advances in Math., 192 (2005), 183-208.
- Reverse Lexicographic and lexicographic shifting,
(with Eric Babson and Rekha Thomas),
Journal of Algebraic Combinatorics, 23 (2006), 107-123.
- How neighborly can a centrally symmetric polytope be? (with Nati Linial),
Discrete and Computational Geometry 36 (2006), no. 2, 273--281.
- Face ring multiplicity via CM-connectivity
sequences (with Ed Swartz),
Canadian Journal of Mathematics 61 (2009), no.4, 888-903.
- A centrally symmetric version of the cyclic polytope
(with Alexander Barvinok),
Discrete and Computational Geometry, 39 (2008), 76-99.
- Socles of Buchsbaum modules, complexes and posets (with Ed Swartz),
Advances in Mathematics 222 (2009), 2059-2084.
- Applications of Klee's Dehn-Sommerville relations (with Ed Swartz),
Discrete and Computational Geometry, 42, Issue 2 (2009), 261-276.
- Gorenstein rings through face rings of manifolds (with Ed Swartz),
Compositio Mathematica, 145, Issue 4 (2009), 993-1000.
- Balanced complexes and complexes without large missing faces (with Michael Goff
and Steve Klee), Arkiv fur Matematik, 49, Issue 2 (2011), 335-350.
- Face numbers of generalized balanced Cohen-Macaulay complexes (with Jonathan Browder),
Combinatorica, 31(6) (2011), 669-689. [PDF]
- Face rings of simplicial complexes with singularities
(with Ezra Miller and Ed Swartz), Mathematische Annalen, 351,
Issue 4 (2011), 857-875.
- Face numbers of pseudomanifolds with isolated singularities
(with Ed Swartz), Mathematica Scandinavica, 110 (2012), 198-222.
- Centrally symmetric manifolds with few vertices (with Steve Klee),
Advances in Mathematics, 229 (2012), 487-500.
- Neighborliness of the symmetric moment curve (with Alexander Barvinok and Seung Jin Lee),
Mathematika, 59 (2013), 223-249. [PDF]
- Centrally symmetric polytopes with many faces
(with Alexander Barvinok and Seung Jin Lee),
Israel Journal of Mathematics, 195 (2013), no. 1,
- Explicit constructions of centrally symmetric k-neighborly
polytopes and large strictly antipodal sets
(with Alexander Barvinok and Seung Jin Lee), Discrete and Computational Geometry,
49, Issue 3 (2013), 429-443.
- From flag complexes to banner complexes (with Steve Klee), SIAM J. Discrete Math,
27 (2013), no. 2, 1146-1158.
- Bipartite Rigidity (with Gil Kalai and Eran Nevo),
Trans. Amer. Math. Soc., 368 (2016), no. 8, 5515-5545.[PDF]
- Bipartite Minors (with Maria Chudnovsky, Gil Kalai, Eran Nevo, and Paul Seymour),
Journal Combinatorial Theory, Ser. B 116 (2016), 219-228.[PDF]
- Lower Bound Theorems and a Generalized Lower Bound Conjecture for balanced simplicial complexes
(with Steve Klee), Mathematika, 62 (2016) 441-477.[PDF]
- Face enumeration on simplicial complexes (with Steve Klee). Recent Trends in Combinatorics, 653-686, IMA Vol. Math. Appl., 159, Springer, 2016.
- Face numbers of manifolds with boundary (with Satoshi Murai), Int. Math. Res. Not. IMRN, 2017, No. 12, 3603-3646.
- Simplicial moves on balanced complexes (with Ivan Izmestiev and Steve Klee), Advances in Mathematics, 320C (2017), 82-114.
- A Duality in Buchsbaum rings and triangulated manifolds (with Satoshi Murai and Ken-ichi Yoshida),
Algebra & Number Theory, 11-3 (2017), 635-656.
- Face numbers and the fundamental group (with Satoshi Murai), Israel Journal of Mathematics, to appear.
- A generalized lower bound theorem for balanced manifolds (with Martina Juhnke-Kubitzke, Satoshi Murai, and Connor Sawaske), Mathematische Zeitschrift, to appear.
- A lower bound theorem for centrally symmetric simplicial polytopes (with Steve Klee, Eran Nevo, and Hailun Zheng), submitted.[PDF]
I am on the editorial boards of
Journal of Algebraic Combinatorics
and SIAM Journal on Discrete Mathematics
I am also co-organizing the
Combinatorics and Geometry Seminar
at the University of Washington together with
Lectures from Jerusalem Spring School, May 2007: