Related papers: State Surfaces of Links
We show how networks of Wilson lines realize quantum groups U_q(sl(m)), for arbitrary m, in 3d SU(N) Chern-Simons theory. Lifting this construction to foams of surface operators in 4d theory we find that rich structure of junctions is…
In this thesis the formation and properties of a polymer gel on and at a surface are investigated. The gel under investigation is defined as a three-dimensional network of "phantom" macromolecules that form permanent links with one another…
We explore a novel method to generate and characterize complex networks by means of their embedding on hyperbolic surfaces. Evolution through local elementary moves allows the exploration of the ensemble of networks which share common…
The Jones polynomial and the Kauffman bracket are constructed, and their relation with knot and link theory is described. The quantum groups and tangle functor formalisms for understanding these invariants and their descendents are given.…
The electronic structure of iron pnictides is topologically nontrivial, leading to the appearance of Dirac cones in the band structure for the antiferromagnetic phase. Motivated by the analogy with Dirac cones in graphene, we explore the…
The state spaces of generalised coherent states associated with special unitary groups are shown to form rational curves and surfaces in the space of pure states. These curves and surfaces are generated by the various Veronese embeddings of…
Topological superconductors have become a subject of intense research due to their potential use for technical applications in device fabrication and quantum information. Besides fully gapped superconductors, unconventional superconductors…
The Jones polynomial of an alternating link is a certain specialization of the Tutte polynomial of the (planar) checkerboard graph associated to an alternating projection of the link. The Bollobas-Riordan-Tutte polynomial generalizes the…
The study of networks plays a crucial role in investigating the structure, dynamics, and function of a wide variety of complex systems in myriad disciplines. Despite the success of traditional network analysis, standard networks provide a…
Topological nodal line semimetals host stable chained, linked, or knotted line degeneracies in momentum space protected by symmetries. In this paper, we use the Jones polynomial as a general topological invariant to capture the global knot…
Circuit topology refers to the arrangement of interactions between objects belonging to a linearly ordered object set. Linearly ordered set of objects are common in nature and occur in a wide range of applications in economics, computer…
Topological photonics provides a powerful framework to describe and understand many nontrivial wave phenomena in complex electromagnetic platforms. The topological index of a physical system is an abstract global property that depends on…
We begin the study of completeness of affine connections, especially those on statistical manifolds as well as on affine hypersurfaces. We collect basic facts, prove new theorems and provide examples with remarkable properties.
Control of complex processes is a major goal of network analyses. Most approaches to control nonlinearly coupled systems require the network topology and/or network dynamics. Unfortunately, neither the full set of participating nodes nor…
We prove a Kauffman-Murasugi-Thistlethwaite theorem for alternating links in thickened surfaces. It states that any reduced alternating diagram of a link in a thickened surface has minimal crossing number, and any two reduced alternating…
We consider Ising models in two and three dimensions with nearest neighbor ferromagnetic interactions and long range, power law decaying, antiferromagnetic interactions. If the strength of the ferromagnetic coupling J is larger than a…
Tensor network states provide successful descriptions of strongly correlated quantum systems with applications ranging from condensed matter physics to cosmology. Any family of tensor network states possesses an underlying entanglement…
A key challenge in complex design problems that permeate science and engineering is the need to balance design objectives for specific design elements or subsystems with global system objectives. Global objectives give rise to competing…
A theory of self-induced transparency of surface TM-mode propagating along a interface separating conventional and left-handed metamaterials is developed. A transition layer sandwiched between connected media is described using a model of a…
This is a detailed study of the infinitesimal variation of the variety of lines through a point of a low degree hypersurface in pro jective space. The motion is governed by a system of partial differential equations which we describe…