Related papers: Crystallography Without Periodicity
Recent ideas based on the properties of assemblies of frictionless particles in mechanical equilibrium provide a perspective of amorphous systems different from that offered by the traditional approach originating in liquid theory. The…
This is the written version of a talk I gave at the 35th Symposium Ahrenshoop in Berlin, Germany, August 2002. It is an exposition of joint work with S. Doplicher, K. Fredenhagen, and Gh. Piacitelli [1]. The violation of unitarity found in…
Twenty years ago, in October 1990, I found myself attending a workshop on Theoretical Physics in Chernomorka (Ukraine) intended only for Soviet physicists. That trip to the USSR/CCCP as well as the preceding months at CERN were highly…
The question of the nature of galaxy clustering and the possible homogeneity of galaxy distribution is one of the fundamental problem of cosmology. It is well established that galaxy structures are characterized, up to a certain scale, by…
We refute the arguments by Anton in cond-mat/0004390, which set out to disprove the existence of a collapse transition for a randomly forced inelastic particle.
The random first-order transition (RFOT) theory of the structural glass transition is reviewed in a pedagogical fashion. The rigidity that emerges in crystals and glassy liquids is of the same fundamental origin. In both cases, it…
Talk given at ICM '98, Berlin, reviewing some of the recent developments in understanding of string theory for a mathematical audience (to appear in Documenta Mathematica).
Let $U$ be an arbitrary word in letters $x_1^{\pm 1}, ..., x_m^{\pm 1}$ and $m \ge 2$. We prove that the group presentation $<x_1, ..., x_m \|\ U x_i U^{-1} = x_{i+1}, i=1,..., m-1>$ is aspherical. The proof is based upon prior partial…
This is a copy of the talk given at the conference ``Methods in Field Theory'' at Stara Lesna, The Slovak Republic, Sepemeber 22-26, 1997. An introduction to the noncommutative sphere and a summary of the results of articles q-alg/9703038…
This paper gives an overview from the perspective of Lie group theory of some of the recent advances in the rapidly expanding research area of quantum entanglement. This paper is a written version of the last of eight one hour lectures…
The spontaneous breaking of time translation symmetry has led to the discovery of a new phase of matter - the discrete time crystal. Discrete time crystals exhibit rigid subharmonic oscillations, which result from a combination of many-body…
A new quantum ontology of quantum mechanics has been proposed recently. This ontology is based on impossible to realize measurements which need to be performed repeatedly on the same single physical system or on the same pair of physical…
Talks given at the V Taller de Particulas y Campos (V-TPyC) and V Taller Latinoam. de Fenomenologia de las Interac. Fundam. (V-TLFIF), Puebla, Mexico, 10/30 - 11/3 1995. These lectures are devoted to elementary particle physicists and…
Random quantum circuits continue to inspire a wide range of applications in quantum information science and many-body quantum physics, while remaining analytically tractable through probabilistic methods. Motivated by an interest in…
This paper introduces the idea of pseudo-group. Applications of pseudo-groups in Group Theory and Symmetry Breaking in Particle Physics and Cosmology are considered.
Coalescent theory is the study of random processes where particles may join each other to form clusters as time evolves. These notes provide an introduction to some aspects of the mathematics of coalescent processes and their applications…
Part of the title of this article is taken from writings of Einstein, which argue that we need to exercise our ability to analyse familiar concepts, to demonstrate the conditions on which their justification and usefulness depend, and the…
This is an expository paper, based on by a talk given at the AWM Research Symposium 2017. It is intended as a gentle introduction to geometric group theory with a focus on the notion of hyperbolicity, a theme that has inspired the field…
This is a brief note to comment on some recent papers addressing the Monoceros ring. In our view, nothing new was delivered on the matter: No new evidence or arguments are presented which lead to think that the over-densities in Monoceros…
A physical theory without interpretation is mathematics. Since there are no paradoxes in science, only incorrect interpretations of phenomena or inadequate theories, it is necessary to use a consistent interpretation of quantum mechanics…