Related papers: Real phase structures on matroid fans and matroid …
First, we examine the notion of nonrational convex polytope and nonrational fan in the context of toric geometry. We then discuss and interrelate some recent developments in the subject.
The control of structured waves has recently opened innovative scenarios in the perspective of radiation propagation and light-matter interaction. In particular, the transmission of customized electromagnetic fields is investigated for…
The relation between thermodynamic phase transitions in classical systems and topology changes in their configuration space is discussed for a one-dimensional, analytically tractable solid-on-solid model. The topology of a certain family of…
Quadrupole topological insulator, which supports robust corner states, has been recently demonstrated in two-dimensional (2D) spatial lattices. Here, we design the first photonic quadrupole topological insulator in fully synthetic spaces…
The precise theoretical characterization of a fractionalized phase in spatial dimensions higher than one is through the concept of ``topological order''. We describe a physical effect that is a robust and direct consequence of this hidden…
Atomically thin 2-dimensional heterostructures are a promising, novel class of materials with groundbreaking properties. The possiblity of choosing the many constituent components and their proportions allows optimizing these materials to…
For a long time a crystal structure of high-pressure epsilon-phase of solid oxygen was a mistery. Basing on the results of recent experiments that have solved this riddle we show that the magnetic and crystal structure of epsilon-phase can…
We propose an effective route to fully control the phase of plane waves reflected from electrically (optically) thin sheets. This becomes possible using engineered artificial full-reflection layers (metamirrors) as arrays of electrically…
A topological phase is a phase of matter which cannot be characterized by a local order parameter. It has been shown that gapped phases in 1D systems can be completely characterized using tools related to projective representations of the…
A consequence of the Folkman-Lawrence topological representation theorem is that the geometric realization of the order complex of the poset of non-zero covectors of a loopless rank $n-1$ oriented matroid on $[n]$ is homeomorphic to an…
We define a tropical version $\F_d(\trop X)$ of the Fano Scheme $\F_d(X)$ of a projective variety $X\subseteq \mathbb P^n$ and prove that $\F_d(\trop X)$ is the support of a polyhedral complex contained in $\trop \Grp(d,n)$. In general…
Topological superconductivity in quasi-one-dimensional systems is a novel phase of matter with possible implications for quantum computation. Despite years of effort, a definitive signature of this phase in experiments is still debated. A…
Microwave, submillimetre-wave, and far-infrared phased arrays are of considerable importance for astronomy. We consider the behaviour imaging phased arrays and interferometric phased arrays from a functional perspective. It is shown that…
We prove da Silva's 1987 conjecture that any positively oriented matroid is a positroid; that is, it can be realized by a set of vectors in a real vector space. It follows from this result and a result of the third author that the positive…
This paper generalises the homeomorphism theorem behind Viro's combinatorial patchworking of hypersurfaces in toric varieties to arbitrary codimension using tropical geometry. We first define the patchwork of a polyhedral space equipped…
A distinct electronic structure was observed in the single-layer FeSe which shows surprising high temperature superconductivity over 65k. Here we demonstrate that the electronic structure can be explained by the strain effect due to…
We describe a natural geometric relationship between matroids and underlying flag matroids by relating the geometry of the greedy algorithm to monotone path polytopes. This perspective allows us to generalize the construction of underlying…
Topological photonics revolutionizes some of the traditional approaches to light propagation and manipulation, and it provides unprecedented means for developing novel photonic devices. Recently discovered higher-order topological phases go…
Motivated by the authors' work on permuto-associahedra, which can be considered as a symmetrization of the associahedron using the symmetric group, we introduce and study the $\mathfrak{G}$-symmetrization of an arbitrary polytope $P$ for…
It is theoretically and numerically demonstrated that a mixture of two topologically distinct material phases is characterized by an anomalous "transparency window" in a spectral range wherein the individual material phases are strongly…