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The activation and subsequent covalent coupling of polycyclic aromatic hydrocarbons (PAHs) are of great interest in fields like chemistry, energy, biology, or health, among others. However, this is not a trivial process. So far, it is based…
We use rewriting systems to spell out cup-products in the (twisted) cohomology groups of a product of surface groups. This allows us to detect a non-trivial obstruction bounding from below the effective topological complexity of an…
Light can mediate effective dipole-dipole interactions between atoms or quantum emitters coupled to a common environment. Exploiting them to tailor a desired effective Hamiltonian can have major applications and advance the search for…
We highlight a general theory to engineer arbitrary Hermitian tight-binding lattice models in electrical LC circuits, where the lattice sites are replaced by the electrical nodes, connected to its neighbors and to the ground by capacitors…
Topological materials present unconventional electronic properties that make them attractive for both basic science and next-generation technological applications. The majority of currently known topological materials have been discovered…
We develop topological methods for characterizing the relationship between polymer chain entanglement and bulk viscoelastic responses. We introduce generalized Linking Number and Writhe characteristics that are applicable to open linear…
Topological band theory provides a conceptual framework to predict or even engineer robust metallic states at the boundaries of topologically distinct phases. The bulk-boundary correspondence requires that a topological electronic phase…
We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform. We apply this understanding to modify the computations so as to (a) speed…
The azide-alkyne Huisgen cycloaddition has a key role in click chemistry and configures as powerful tool in pharmaceutical and medicinal chemistry. Although this reaction has already been largely studied, there is an ongoing debate about…
This survey of topological cyclic homology is a chapter in the Handbook on Homotopy Theory. We give a brief introduction to topological cyclic homology and the cyclotomic trace map following Nikolaus-Scholze, followed by a proof of…
The Adler-Konheim-McAndrew type definitions and the Bowen-Dinaburg-Hood type definitions of parametric topological entropy will be considered on orbits and coincidence orbits of nonautonomous multivalued maps in compact Hausdorff spaces.…
Over the last few years, crystalline topology has been used in photonic crystals to realize edge- and corner-localized states that enhance light-matter interactions for potential device applications. However, the band-theoretic approaches…
The topological Anderson and Mott insulators are two phases that have so far been separately and widely explored beyond topological band insulators. Here we combine the two seemingly different topological phases into a system of spin-1/2…
Topological excitons are superpositions of electron-hole pair states, characterized by an envelope function with finite vorticity in momentum space. This vorticity is determined by the underlying topology of the electronic bands. We derive…
Modeling molecules as undirected graphs and chemical reactions as graph rewriting operations is a natural and convenient approach tom odeling chemistry. Graph grammar rules are most naturally employed to model elementary reactions like…
Going beyond the conventional classification rule of Altland-Zirnbauer symmetry classes, $PT$ symmetric topological phases are classified by $(PT)^2=1$ or $-1$. The interconversion between the two $PT$-symmetric topological classes is…
Point-contact spectroscopy of several non-superconducting topological materials reveals a low temperature phase transition that is characterized by a Bardeen-Cooper-Schrieffer-type of criticality. We find such a behavior of differential…
We derive a series of quantitative bulk-boundary correspondences for 3D bosonic and fermionic symmetry-protected topological (SPT) phases under the assumption that the surface is gapped, symmetric and topologically ordered, i.e., a…
Topological indices are graph invariants numeric quantities, which are utilized by researchers to analyze a variety of physiochemical aspects of molecules. The goal of developing topological indices is to give each chemical structure a…
The introduction of Su-Schrieffer-Heeger model has led to a major breakthrough in the area of one-dimensional topological insulators, even though this model was primarily formulated on an organic polymer called $trans$-polyacetylene in…