Related papers: Sym\'etrie et th\'eorie des groupes \`a travers la…
We introduce a notion of topological property (T) for \'etale groupoids. This simultaneously generalizes Kazhdan's property (T) for groups and geometric property (T) for coarse spaces. One main goal is to use this property (T) to prove the…
The concept of space group has long served as the fundamental framework to describe the physical properties of crystalline materials, from electronic bands to photonic dispersions. The recent progress of spatiotemporal control, such as…
We introduce a theory of "patterns" in order to study geodesics in a certain class of group presentations. Using patterns we show that there does not exist a geodesic automatic structure for certain group presentations, and that certain…
The thesis is devoted to abstract, geometric and symmetric aspects of modern elementary particle theories. A new direction in constructing supersymmetric and superstring models based on consequent and strong consideration and inclusion of…
We prove combination theorems in the spirit of Klein and Maskit in the context of discrete convergence groups acting geometrically finitely on their limit sets. As special cases, we obtain combination theorems for geometrically finite…
Using unitarity, analyticity and crossing symmetry, we derive universal sum rules for scattering amplitudes in theories invariant under an arbitrary symmetry group. The sum rules relate the coefficients of the energy expansion of the…
Dynamical quantum field theories (QFTs), such as those in which spacetimes are equipped with a metric and/or a field in the form of a smooth map to a target manifold, can be formulated axiomatically using the language of…
Resource theories constitute a powerful theoretical framework and a tool that captures, in an abstract structure, pragmatic aspects of the most varied theories and processes. For physical theories, while this framework deals directly with…
Symmetry plays a fundamental role in understanding natural phenomena and mathematical structures. This work develops a comprehensive theory for studying the persistent symmetries and degree of asymmetry of finite point configurations over…
In this review, the fundamental concepts of group theory and representation theory are introduced. Special emphasis is placed on the unitary irreducible representations of the $SU(N)$ Lie group, the Poincare group, Little Group, discrete…
This book provides a self-contained introduction to geometric group theory. The topics range from an introduction of Cayley and Schreier graphs to Gromov's theorem on groups of polynomial growth and amenability. We discuss the ping-pong…
The theory of plasma physics offers a number of nontrivial examples of partial differential equations, which can be successfully treated with symmetry methods. We propose three different examples which may illustrate the reciprocal…
Frame theory has been a popular subject in the design of structured signals and codes in recent years, with applications ranging from the design of measurement matrices in compressive sensing, to spherical codes for data compression and…
Group field theories are particular quantum field theories defined on D copies of a group which reproduce spin foam amplitudes on a space-time of dimension D. In these lecture notes, we present the general construction of group field…
In this work we study spontaneous symmetry breaking patterns in tensor models. We focus on the patterns which lead to effective matrix theories transforming in the adjoint of $U(N)$. We find the explicit form of the Goldstone bosons which…
We use group theoretic methods to obtain the extended Lie point symmetries of the equations of motion for a charged particle in the field of a monopole. Cases with certain model magnetic fields and potentials are also studied. Our analysis…
It is shown that the correct mathematical implementation of symmetry in the geometric formulation of classical field theory leads naturally beyond the concept of Lie groups and their actions on manifolds, out into the realm of Lie group…
In this paper we consider Tyler's robust covariance M-estimator under group symmetry constraints. We assume that the covariance matrix is invariant to the conjugation action of a unitary matrix group, referred to as group symmetry. Examples…
We develop a geometric scattering theory for a geometrically finite group acting on (a vector bundle over) a symmetric space of negative curvature. In particular, we obtain the meromorphic continuation of Eisenstein series and scattering…
Generalized symmetries (also known as categorical symmetries) is a newly developing technique for studying quantum field theories. It has given us new insights into the structure of QFT and many new powerful tools that can be applied to the…