Related papers: Packing, coding, and ground states
Basic issues of the general model-building framework of the mechanics of complex bodies are discussed. Attention is focused on the representation of the material elements, the conditions for the existence of ground states in conservative…
The development of Noncommutative Geometry is creating a reworking and new possibilities in physics. This paper identifies some of the commutation and derivation structures that arise in particle and field interactions and fundamental…
We illustrate how quantum information theory and free (i.e. noncommutative) semialgebraic geometry often study similar objects from different perspectives. We give examples in the context of positivity and separability, quantum magic…
Many physical systems are well modeled as collections of interacting particles. Nevertheless, a general approach to quantifying the absolute degree of order immediately surrounding a particle has yet to be described. Motivated thus, we…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
These lectures will address two questions. Is there a simple variational principle underlying the existence of secondary motifs in the native state of proteins? Is there a general approach which can qualitatively capture the salient…
We show that topological phases include disordered materials if the underlying invariant is interpreted as originating from coarse geometry. This coarse geometric framework, grounded in physical principles, offers a natural setting for the…
The main objective of the paper is to unveil an adequate mathematics hidden behind entanglement, that is Geometric Invariant Theory. More specifically relation between these two subjects can be described by the following theses. (i) Total…
This text is a short but comprehensive introduction to the basics of supergeometry and includes some of the recent advances in colored supergeometry. We do not aim for a standard text that states results and proves them more or less…
Codes in the projective space and codes in the Grassmannian over a finite field - referred to as subspace codes and constant-dimension codes (CDCs), respectively - have been proposed for error control in random linear network coding. For…
Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years the replica-symmetry-breaking mean field theory of spin glasses and the…
According to Peter Galison, the coordination of different ``subcultures'' within a scientific field happens through local exchanges within ``trading zones''. In his view, the workability of such trading zones is not guaranteed, and science…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…
We consider the line planning problem in public transport in the Parametric City, an idealized model that captures typical scenarios by a (small) number of parameters. The Parametric City is rotation symmetric, but optimal line plans are…
Elements of supergeometry are an ingredient in many contemporary classical and quantum field models involving odd fields. For instance, this is the case of SUSY field theory, BRST theory, supergravity. Addressing to theoreticians, these…
We present a simple physical model which demonstrates that the native state folds of proteins can emerge on the basis of considerations of geometry and symmetry. We show that the inherent anisotropy of a chain molecule, the geometrical and…
Group theory involves the study of symmetry, and its inherent beauty gives it the potential to be one of the most accessible and enjoyable areas of mathematics, for students and non-mathematicians alike. Unfortunately, many students never…
Many physical systems involve two types of orientational order, which are coupled together. For example, ferroelectric nematic liquid crystals have coupled polar and nematic order, and tilted hexatic phases have coupled polar and hexatic…
The color code is both an interesting example of an exactly solved topologically ordered phase of matter and also among the most promising candidate models to realize fault-tolerant quantum computation with minimal resource overhead. The…
Symmetry can be used to help solve many problems. For instance, Einstein's famous 1905 paper ("On the Electrodynamics of Moving Bodies") uses symmetry to help derive the laws of special relativity. In artificial intelligence, symmetry has…