Related papers: Generalized topological state-sum constructions an…
We announce two breakthrough results concerning important questions in the Theory of Computational Complexity. In this expository paper, a systematic and comprehensive geometric characterization of the Subset Sum Problem is presented. We…
A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the classical theory of point-sets. In this paper, topologies…
We develop the formalism of universal torsors in equivariant birational geometry and apply it to produce new examples of nonbirational but stably birational actions of finite groups.
This paper reviews the construction of quantum field theory on a 4-dimensional spacetime by combinatorial methods, and discusses the recent developments in the direction of a combinatorial construction of quantum gravity.
We develop a generic spacetime model in General Relativity which can be used to build any gravitational model within General Relativity. The generic model uses two types of assumptions: (a) Geometric assumptions additional to the inherent…
With a simple generic approach, we develop a classification that encodes and measures the strength of completeness (or compactness) properties in various types of spaces and ordered structures. The approach also allows us to encode notions…
The integration of topological concepts into electronic energy band theory has been a transformative development in condensed matter physics. Since then, this paradigm has broadened its reach, extending to a variety of physical systems,…
In the literature, tensors have been effectively used for capturing the context information in language models. However, the existing methods usually adopt relatively-low order tensors, which have limited expressive power in modeling…
In this thesis we extend the formalism of tensor network algorithms to incorporate global internal symmetries. We describe how to both numerically protect the symmetry and exploit it for computational gain in tensor network simulations. Our…
We prove numerically and by dualities the existence of modulated, commensurate and incommensurate states of topological quantum matter in simple systems of parafermions, motivated by recent proposals for the realization of such systems in…
We present a detailed discussion of a general theory of phase-space distributions, introduced recently by the authors [J. Phys. A {\bf 31}, L9 (1998)]. This theory provides a unified phase-space formulation of quantum mechanics for physical…
We present an overview of some recent developments in the theory of generalized formal series, grounded in diffeological geometric framework. These constructions aim to offer new tools for understanding infinite-dimensional phenomena in…
A method is presented for imputing a topology for any chronological set, i.e., a set with a chronology relation, such as a spacetime or a spacetime with some sort of boundary. This topology is shown to have several good properties, such as…
The measurement based, or one-way, model of quantum computation for continuous variables uses a highly entangled state called a cluster state to accomplish the task of computing. Cluster states that are universal for computation are a…
Generalized Feller theory provides an important analog to Feller theory beyond locally compact state spaces. This is very useful for solutions of certain stochastic partial differential equations, Markovian lifts of fractional processes, or…
Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…
Recent advancements in generalized symmetries have drawn significant attention to gapped phases of matter exhibiting novel symmetries, such as noninvertible symmetries. By leveraging the duality transformations, the classification and…
Understanding quantum phases and phase transitions in the presence of symmetries is a central objective of quantum many-body physics. A powerful modern paradigm for investigating this problem is topological holography, which relates…
We formulate a theory of shape valid for objects of arbitrary dimension whose contours are path connected. We apply this theory to the design and modeling of viable trajectories of complex dynamical systems. Infinite families of…
A sum-and-distance system is a collection of finite sets of integers such that the sums and differences formed by taking one element from each set generate a prescribed arithmetic progression. Such systems, with two component sets, arise…