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There are several topological spaces associated to a complex hyperplane arrangement: the complement and its boundary manifold, as well as the Milnor fiber and its own boundary. All these spaces are related in various ways, primarily by a…
This paper is a letter-type version of hep-th/9806236. We discuss properties of non-linear equations of motion which describe higher-spin gauge interactions for massive spin-0 and spin-1/2 matter fields in 2+1 dimensional anti-de Sitter…
This paper provides an overview of selected results and open problems in the theory of hyperplane arrangements, with an emphasis on computations and examples. We give an introduction to many of the essential tools used in the area, such as…
We describe two major string topology operations, the Chas-Sullivan product and the Goresky-Hingston coproduct, from geometric and algebraic perspectives. The geometric construction uses Thom-Pontrjagin intersection theory while the…
An earlier model for substrate strain mediated interactions between monomer adatoms is extended to the interaction of monomers with dimers and the interaction of dimers. While monomers (sitting on high symmetric sites) are supposed to…
In many real world datasets arising from social networks, there are hidden higher order relations among data points which cannot be captured using graph modeling. It is natural to use a more general notion of hypergraphs to model such…
Two distinct non-singular interior models that describe anisotropic spherical configurations are presented in this work. We develop the Einstein field equations and the associated mass function in accordance with a static spherical…
In this paper we review some recent results on nonlocal interaction problems. The focus is on interaction kernels that are anisotropic variants of the classical Coulomb kernel. In other words, while preserving the same singularity at zero…
Anisotropy at the level of the inter-particle interaction provides the particles with specific instructions for the self-assembly of target structures. The ability to synthesize non-spherical colloids, together with the possibility of…
In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and…
We study the ground-state entanglement of one-dimensional harmonic chains that are coupled to each other by a collective interaction as realized e.g. in an anisotropic ion crystal. Due to the collective type of coupling, where each chain…
Modeling higher-order interactions (HOI) has emerged as a crucial challenge in complex systems analysis, as many phenomena cannot be fully captured by pairwise relationships alone. Hypergraphs, which generalize graphs by allowing…
We extend the entanglement bootstrap approach to (3+1)-dimensions. We study knotted excitations of (3+1)-dimensional liquid topological orders and exotic fusion processes of loops. As in previous work in (2+1)-dimensions, we define a…
We develop classical globally supersymmetric theories. As much as possible, we treat various dimensions and various amounts of supersymmetry in a uniform manner. We discuss theories both in components and in superspace. Throughout we…
We study the holographic entanglement entropy for singular surfaces in theories described holographically by hyperscaling violating backgrounds. We consider singular surfaces consisting of cones or creases in diverse dimensions. The…
In complex systems research, the study of higher-order interactions has exploded in recent years. Researchers have formalized various types of group interactions, such as public goods games, biological contagion, and information…
These notes are loosely based on lectures given at the CERN Winter School on Supergravity, Strings and Gauge theories, February 2009 and at the IPM String School in Tehran, April 2009. I have focused on a few concrete topics and also on…
A recently proposed mechanism for large-scale structure in string cosmology --based on massless axionic seeds-- is further analyzed and extended to the acoustic-peak region. Existence, structure, and normalization of the peaks turn out to…
The holographic representation of the entanglement entropy of four dimensional conformal field theories is studied. By generalizing the replica trick the anomalous terms in the entanglement entropy are evaluated. The same terms in the…
The stress profile and reorientation of grains, in response to a point force applied to a preloaded two dimensional granular system, are calculated in the context of a continuum theory that incorporates the texture of the packing. When high…