32 citations · 122 across the 43 of their papers we have counts for
57 papers
Degenerating orbits of the Longest Edge Bisection process
Karim A. Adiprasito, Daniel Kalmanovich, Yaar Solomon
We study the Longest Edge Bisection (LEB) process as a dynamical system on the projective shape space of simplices. A long-standing conjecture going back to Adler and Rivara-Levin…
Parseval-Rayleigh identities for homogeneous complete intersections
Karim Alexander Adiprasito, Ryoshun Oba, Stavros Argyrios Papadakis +1
We prove, in any positive characteristic, Parseval-Rayleigh identities for the residue map of a homogeneous complete intersection. As an application, we give a conceptual proof of…
Lattice polytopes and semigroup algebras: Generic Lefschetz properties and Parseval-Rayleigh identities
Karim Alexander Adiprasito, Stavros Argyrios Papadakis, Vasiliki Petrotou
We study semigroup algebras associated to lattice polytopes. We begin by generalizing and refining work of Hochster, and describe the volume maps of these algebras, that is, their…
The volume intrinsic to a commutative graded algebra
Karim Alexander Adiprasito, Stavros Argyrios Papadakis, Vasiliki Petrotou
Recent works of the authors have demonstrated the usefulness of considering moduli spaces of Artinian reductions of a given ring when studying standard graded rings and their Lefsc…
Polyhedral CAT(0) metrics on locally finite complexes
Karim A. Adiprasito, Louis Funar
We prove the arborescence of any locally finite complex that is with a polyhedral metric for which all vertex stars are convex. In particular locally finite cube…
Subadditivity of shifts, Eilenberg-Zilber shuffle products and homology of lattices
Karim Adiprasito, Anders Björner, Joel Hakavuori +2
We show that the maximal shifts in the minimal free resolution of the quotients of a polynomial ring by a monomial ideal are subadditive as a function of the homological degree. Th…
Beyond positivity in Ehrhart Theory
Karim Alexander Adiprasito, Stavros Argyrios Papadakis, Vasiliki Petrotou +1
We study semigroup algebras arising from lattice polytopes, compute their volume polynomials (particularizing work of Hochster), and establish strong Lefschetz properties (generali…
On the Schmidt and analytic ranks for trilinear forms
Karim Adiprasito, David Kazhdan, Tamar Ziegler
We discuss relations between different notions of ranks for multilinear forms. In particular we show that the Schmidt and the analytic ranks for trilinear forms are essentially pro…
Anisotropy, biased pairings, and the Lefschetz property for pseudomanifolds and cycles
Karim Adiprasito, Stavros Argyrios Papadakis, Vasiliki Petrotou
We prove the hard Lefschetz property for pseudomanifolds and cycles in any characteristic with respect to an appropriate Artinian reduction. The proof is a combination of Adiprasit…
A complete characterization of -pairs of 6-polytopes
Karim Adiprasito, Rémi Cocou Avohou
We completely characterize the first two entries, namely the -vector pairs, for -dimension polytopes. We also find the characterization for -dimension polytopes w…
Sparse handlebody decompositions and non-finiteness of
Karim Adiprasito, Bruno Benedetti
We prove that a PL manifold admits a handle decomposition into handles of index if and only if is -stacked, i.e., it admits a PL triangulation in which all …
A subexponential size triangulation of
Karim Adiprasito, Sergey Avvakumov, Roman Karasev
We address a long-standing and long-investigated problem in combinatorial topology, and break the exponential barrier for triangulations of real projective space, constructing a tr…
The Partition Complex: an invitation to combinatorial commutative algebra
Karim Adiprasito, Geva Yashfe
We provide a new foundation for combinatorial commutative algebra and Stanley-Reisner theory using the partition complex introduced in [Adi18]. One of the main advantages is that i…
Normal crossing immersions, cobordisms and flips
Karim Adiprasito, Gaku Liu
We study various analogues of theorems from PL topology for cubical complexes. In particular, we characterize when two PL homeomorphic cubulations are equivalent by Pachner moves b…
On the realization space of the cube
Karim Adiprasito, Daniel Kalmanovich, Eran Nevo
We consider the realization space of the -dimensional cube, and show that any two realizations are connected by a finite sequence of projective transformations and normal transf…
Unstable blueprints can be shared
Karim Adiprasito
This expository note illustrates toric perturbation and biased pairing theory to show that Artinian reductions of face rings of -spheres that do not satisfy the Lefschetz proper…
FAQ on the g-theorem and the hard Lefschetz theorem for face rings
Karim Adiprasito
This short review is the result of a minicourse at the Sapienza University of Rome the author gave about the proof of the -theorem. We review the hard Lefschetz theorem for simp…
The Hard Lefschetz Theorem for PL spheres
Karim Adiprasito, Johanna K. Steinmeyer
We provide a simpler proof of the hard Lefschetz Theorem for face rings of PL spheres: While the algebraic theory remains the same, we replace the geometric constructions by Pachne…
Combinatorial Lefschetz theorems beyond positivity
Karim Adiprasito
Consider a simplicial complex that allows for an embedding into . How many faces of dimension or higher can it have? How dense can they be? This basic q…
Semistable reduction in characteristic 0
Karim Adiprasito, Gaku Liu, Michael Temkin
In 2000 Abramovich and Karu proved that any dominant morphism of varieties of characteristic zero can be made weakly semistable by replacing by a smooth alteration…
Log smoothness and polystability over valuation rings
Karim Adiprasito, Gaku Liu, Igor Pak +1
Let be a valuation ring of height one of residual characteristic exponent and with algebraically closed field of fractions. Our main result provides a best possib…
Theorems of Carathéodory, Helly, and Tverberg without dimension
Karim Adiprasito, Imre Bárány, Nabil H. Mustafa +1
We prove a no-dimensional version of Carathédory's theorem: given an -element set , a point $a \in \conv P$, and an integer , , there is a subse…
Rigidity with few locations
Karim Adiprasito, Eran Nevo
Graphs triangulating the -sphere are generically rigid in -space, due to Gluck-Dehn-Alexandrov-Cauchy. We show there is a \emph{finite} subset in -space so that the ve…
QGLBT for polytopes
Karim Adiprasito, Mikhail Burens, Eran Nevo
We extend the assertion of the Generalized Lower Bound Theorem (GLBT) to general polytopes under the assumption that their low dimensional skeleton is simplicial, with partial resu…