32 citations · 122 across the 43 of their papers we have counts for
7 papers · 1 filter
CAT(0) metrics on contractible manifolds
Karim A. Adiprasito, Louis Funar
We prove that an open manifold of dimension at least which admits a complete CAT(0) polyhedral metric is pseudo-collarable, its fundamental group at infinity is strongly pe…
Hodge Theory for Combinatorial Geometries
Karim Adiprasito, June Huh, Eric Katz
We prove the hard Lefschetz theorem and the Hodge-Riemann relations for a commutative ring associated to an arbitrary matroid M. We use the Hodge-Riemann relations to resolve a con…
A Geometric Lower Bound Theorem
Karim Adiprasito, Eran Nevo, José Alejandro Samper
We resolve a conjecture of Kalai relating approximation theory of convex bodies by simplicial polytopes to the face numbers and primitive Betti numbers of these polytopes and their…
A note on boundary manifolds of arrangements
Karim A. Adiprasito
We note an intimate connection between the Lefschetz Theorem for c-arrangements, and a theorem of Hironaka relating the complement of an arrangement to its boundary manifold. This…
Toric chordality
Karim Adiprasito
We study the geometric change of Chow cohomology classes in projective toric varieties under the Weil-McMullen dual of the intersection product with a Lefschetz element. Based on t…
Higher chordality: From graphs to complexes
Karim A. Adiprasito, Eran Nevo, Jose A. Samper
We generalize the fundamental graph-theoretic notion of chordality for higher dimensional simplicial complexes by putting it into a proper context within homology theory. We genera…
Face numbers of sequentially Cohen-Macaulay complexes and Betti numbers of componentwise linear ideals
Karim A. Adiprasito, Anders Björner, Afshin Goodarzi
A numerical characterization is given of the so-called h-triangles of sequentially Cohen-Macaulay simplicial complexes. This result characterizes the number of faces of various dim…