25 citations · 181 across the 41 of their papers we have counts for
51 papers
On the uniqueness of collections of pennies and marbles
Sean Dewar, Georg Grasegger, Kaie Kubjas +2
In this note we study the uniqueness problem for collections of pennies and marbles. More generally, consider a collection of unit -spheres that may touch but not overlap. Given…
Identifiability of Points and Rigidity of Hypergraphs under Algebraic Constraints
James Cruickshank, Fatemeh Mohammadi, Anthony Nixon +1
The identifiability problem arises naturally in a number of contexts in mathematics and computer science. Specific instances include local or global rigidity of graphs and unique c…
Rational tensegrities through the lens of toric geometry
Fatemeh Mohammadi, Xian Wu
A classical tensegrity model consists of an embedded graph in a vector space with rigid bars representing edges, and an assignment of a stress to every edge such that at every vert…
Tensors in statistics and rigidity theory
Fatemeh Mohammadi
This is a short report on the discussions of appearance of tensors in algebraic statistics and rigidity theory, during the semester ``AGATES: Algebraic Geometry with Applications t…
K-polynomials of multiplicity-free varieties
Federico Castillo, Yairon Cid-Ruiz, Fatemeh Mohammadi +1
We describe the twisted -polynomial of multiplicity-free varieties in a multiprojective setting. More precisely, for multiplicity-free varieties, we show that the support of the…
Progress on Infinite Cluster Categories Related to Triangulations of the (Punctured) Disk
Fatemeh Mohammadi, Job Daisie Rock, Francesca Zaffalon
In this mostly expository paper, we present recent progress on infinite (weak) cluster categories that are related to triangulations of the disk, with and without a puncture. First…
Template-based Program Synthesis using Stellensätze
Amir Kafshdar Goharshady, S. Hitarth, Fatemeh Mohammadi +1
Template-based synthesis, also known as sketching, is a localized approach to program synthesis in which the programmer provides not only a specification, but also a high-level ``s…
Combinatorial Mutations of Gelfand-Tsetlin Polytopes, Feigin-Fourier-Littelmann-Vinberg Polytopes, and Block Diagonal Matching Field Polytopes
Oliver Clarke, Akihiro Higashitani, Fatemeh Mohammadi
The Gelfand-Tsetlin and the Feigin-Fourier-Littelmann-Vinberg polytopes for the Grassmannians are defined, from the perspective of representation theory, to parametrize certain bas…
Phase transition and fractionalization in superconducting Kondo lattice model
Fatemeh Mohammadi, Amirhossein Saedpanah, Abolhassan Vaezi +1
Topology, symmetry, electron correlations, and the interplay between them have formed the cornerstone of our understanding of quantum materials in recent years and are used to iden…
Global Rigidity of Line Constrained Frameworks
James Cruickshank, Fatemeh Mohammadi, Harshit J Motwani +2
We consider the global rigidity problem for bar-joint frameworks where each vertex is constrained to lie on a particular line in . In our setting we allow multiple ver…
Computing positroid cells in the Grassmannian of lines, their boundaries and their intersections
Susama Agarwala, Fatemeh Mohammadi, Francesca Zaffalon
Positroids are families of matroids introduced by Postnikov in the study of non-negative Grassmannians. In particular, positroids enumerate a CW decomposition of the totally non-ne…
Toric degenerations of partial flag varieties and combinatorial mutations of matching field polytopes
Oliver Clarke, Fatemeh Mohammadi, Francesca Zaffalon
We study toric degenerations arising from Gröbner degenerations or the tropicalization of partial flag varieties. We produce a new family of toric degenerations of partial flag var…
Designing and topological orders in networks of Majorana bound states
Fatemeh Mohammadi, Mehdi Kargarian
Topological orders have been intrinsically identified in a class of systems such as fractional quantum Hall states and spin liquids. Accessing such states often requires extreme co…
A study of nonlinear multiview varieties
Yairon Cid-Ruiz, Oliver Clarke, Fatemeh Mohammadi
We study the nonlinear generalization of the classical multiview variety, which is a fundamental concept in computer vision. In this paper, we take the first comprehensive step to…
Toric and tropical Bertini theorems in positive characteristic
Francesca Gandini, Milena Hering, Diane Maclagan +4
We generalize the toric Bertini theorem of Fuchs, Mantova, and Zannier to positive characteristic. A key part of the proof is a new algebraically closed field containing the field…
Double Schubert polynomials do have saturated Newton polytopes
Federico Castillo, Yairon Cid-Ruiz, Fatemeh Mohammadi +1
We prove that double Schubert polynomials have the Saturated Newton Polytope property. This settles a conjecture by Monical, Tokcan and Yong. Our ideas are motivated by the theory…
Lattice Conditional Independence Models and Hibi Ideals
Peter Caines, Fatemeh Mohammadi, Eduardo Sáenz de Cabezón +1
Lattice Conditional Independence models are a class of models developed first for the Gaussian case in which a distributive lattice classifies all the conditional independence stat…
Multigraded algebras and multigraded linear series
Yairon Cid-Ruiz, Fatemeh Mohammadi, Leonid Monin
This paper is devoted to the study of multigraded algebras and multigraded linear series. For an -graded algebra , we define and study its volume function $F_A:\ma…
Standard monomial theory and toric degenerations of Richardson varieties in the Grassmannian
Narasimha Chary Bonala, Oliver Clarke, Fatemeh Mohammadi
Richardson varieties are obtained as intersections of Schubert and opposite Schubert varieties. We provide a new family of toric degenerations of Richardson varieties inside Grassm…
Matroid stratifications of hypergraph varieties, their realization spaces, and discrete conditional independence models
Oliver Clarke, Kevin Grace, Fatemeh Mohammadi +1
We study varieties associated to hypergraphs from the point of view of projective geometry and matroid theory. We describe their decompositions into matroid varieties, which may be…
Standard monomial theory and toric degenerations of Richardson varieties in flag varieties
Narasimha Chary Bonala, Oliver Clarke, Fatemeh Mohammadi
We study standard monomial bases for Richardson varieties inside the flag variety. In general, writing down a standard monomial basis for a Richardson variety can be challenging, a…
Conditional probabilities via line arrangements and point configurations
Oliver Clarke, Fatemeh Mohammadi, Harshit J. Motwani
We study the connection between probability distributions satisfying certain conditional independence (CI) constraints, and point and line arrangements in incidence geometry. To a…
Combinatorial Mutations and Block Diagonal Polytopes
Oliver Clarke, Akihiro Higashitani, Fatemeh Mohammadi
Matching fields were introduced by Sturmfels and Zelevinsky to study certain Newton polytopes and more recently have been shown to give rise to toric degenerations of various famil…
Triangulations and Canonical Forms of Amplituhedra: a fiber-based approach beyond polytopes
Fatemeh Mohammadi, Leonid Monin, Matteo Parisi
Any totally positive matrix induces a map from the positive Grassmannian to the Grassmannian , whose image is the amplituhe…