Related papers: Prismatic crystals and $q$-Higgs fields

We describe one-dimensional photonic crystals that support a guided mode suitable for atom trapping within a unit cell, as well as a second probe mode with strong atom-photon interactions. A new hybrid trap is analyzed that combines optical…

The embedding of a given point set with non-crystallographic symmetry into higher-dimensional space is reviewed, with special emphasis on the Minkowski embedding known from number theory. This is a natural choice that does not require an a…

The Higgs program is relevant to many of the open fundamental questions in particle physics and in cosmology. Thus, when discussing future collider experiments, one way of comparing them is by assessing their potential contributions to…

In this article, we introduce infinitesimal cohomology for rigid analytic spaces that are not necessarily smooth, with coefficients in a p-adic field or Fontaine's de Rham period ring.

We give a criterion for extending a generically semisimple (not necessarily conformal) Frobenius manifold locally near a smooth point of the discriminant to a cohomological field theory. As an application, we show that a large set of…

We place the representation variety in the broader context of abelian and nonabelian cohomology. We outline the equivalent constructions of the moduli spaces of flat bundles, of smooth integrable connections, and of holomorphic integrable…

Let $\mathfrak{q}$ denote an ideal of a local ring $(A,\mathfrak{m})$. For a system of elements $\underline{a} = a_1,\ldots,a_t$ such that $a_i \in \mathfrak{q}^{c_i}, i = 1, \ldots,t,$ and $n \in \mathbb{Z}$ we investigate a subcomplex…

The two-dimensional one-component plasma, i.e. the system of point-like charged particles embedded in a homogeneous neutralizing background, is studied on the surface of a cylinder of finite circumference, or equivalently in a semiperiodic…

We use the fusion construction in the twisted quantum affine algebras to obtain a unified method to deform the wedge product for classical Lie algebras. As a byproduct we uniformly realize all non-spin fundamental modules for quantized…

We define the unit circle for global function fields. We demonstrate that this unit circle (endearingly termed the \emph{$q$-unit circle}, after the finite field $\mathbb{F}_q$ of $q$ elements) enjoys all of the properties akin to the…

The classical Simpson correspondence describes complex linear representations of the fundamental group of a smooth complex projective variety in terms of linear algebra objects, namely Higgs bundles. Its p-adic analogue, introduced by G.…

For a semisimple real Lie group $G$, we study topological properties of moduli spaces of polystable parabolic $G$-Higgs bundles over a Riemann surface with a divisor of finitely many distinct points. For a split real form of a complex…

In this article, we construct two kinds of de Rham-like complexes which compute the cohomology of complete crystals on the higher-level $q$-crystalline site, which was introduced in a previous article of the author. One complex is the…

It is shown that tiling in icosahedral quasicrystals can also be properly described by cyclic twinning at the unit cell level. The twinning operation is applied on the primitive prolate golden rhombohedra, which can be considered a result…

The atomic structure of the icosahedral Ti-Zr-Ni quasicrystal is determined by invoking similarities to periodic crystalline phases, diffraction data and the results from ab initio calculations. The structure is modeled by decorations of…

This works extends the recent study on the dielectric permittivity of crystals within the Hartree model [E. Cances and M. Lewin, Arch. Rational Mech. Anal., 197 (2010) 139--177] to the time-dependent setting. In particular, we prove the…

The Higgs field is a central point of the Standard Model supplying masses to other fields through the symmetry breaking mechanism. However, it is associated with an elementary particle which is not yet discovered experimentally. In this…

Today, both particle physics and cosmology are described by few parameter Standard Models, i.e. it is possible to deduce consequence of particle physics in cosmology and vice verse. The former is examined in this lecture, in light of the…

In this paper, we develop the theory of abstract crystals for quantum Borcherds-Bozec algebras. Our construction is different from the one given by Bozec. We further prove the crystal embedding theorem and provide a characterization of…

The macroscopic surface electric susceptibility determines the linear optical properties of an insulating single-layer two-dimensional atomic crystal, and can be expressed in terms of the microscopic polarizability of the atoms. We compute…