Related papers: A proof of the Gap Labeling Conjecture

Quasiperiodic systems show a universal gap structure due to quasiperiodicity which is analogous to gap openings at the Brillouin zone boundary in periodic systems. The integrated density of states (IDoS) below those energy gaps are…

We show that the In\"on\"u-Wigner contraction naturally associated to a reduction chain $\frak{s}\supset \frak{s}^{\prime}$ of semisimple Lie algebras induces a decomposition of the Casimir operators into homogeneous polynomials, the terms…

Inspired by the 1995 paper of Baake--Grimm--Pisani, we aim to explain the empirical observation that the distribution of Lee--Yang zeros corresponding to a one-dimensional Ising model appears to follow the gap labelling theorem. This…

The Bethe-Sommerfeld conjecture states that the spectrum of the stationary Schrodinger operator with a periodic potential in dimensions higher than 1 has only finitely many gaps. After work done by many authors, it has been proven by now in…

We are interested in characterizing which classes of finite graphs are well-quasi-ordered by the induced subgraph relation. To that end, we devise an algorithm to decide whether a class of finite graphs well-quasi-ordered by the induced…

We prove an index theorem for families of pseudodifferential operators generalizing those studied by C. Callias, N. Anghel and others. Specifically, we consider operators on a manifold with boundary equipped with an asymptotically conic…

Introduced by Goulden and Jackson in their 1996 paper, the matchings-Jack conjecture and the hypermap-Jack conjecture (also known as the $b$-conjecture) are two major open questions relating Jack symmetric functions, the representation…

In his book (II.5), Connes gives a proof of the Atiyah-Singer index theorem for closed manifolds by using deformation groupoids and appropiate actions of these on R^N. Following these ideas, we prove an index theorem for manifolds with…

A value of a CSP instance is typically defined as a fraction of constraints that can be simultaneously met. We propose an alternative definition of a value of an instance and show that, for purely combinatorial reasons, a value of an…

Underdoped Mott insulators provide us with a challenge of many-body physics. Recent renewed understanding is discussed in terms of the evolution of pole and zero structure of the single-particle Green's function. Pseudogap as well as Fermi…

Given a ring object $A$ in a symmetric monoidal category, we investigate what it means for the extension $\mathbb{1}\rightarrow A$ to be (quasi-)Galois. In particular, we define splitting ring extensions and examine how they occur.…

We consider the Dirichlet Laplacian in a straight planar strip perturbed by a bounded periodic symmetric operator. We prove the classical Bethe-Sommerfeld conjecture for this operator, namely, that this operator has finitely many gaps in…

In this paper, we study the K0-group of the C?-algebra associated to a pinwheel tiling. We prove that it is given by the sum of Z + Z^6 with a cohomological group. The C?-algebra is endowed with a trace that induces a linear map on its…

This paper presents a possible link between Cages and Expander Graphs by introducing three interconnected variants of the Bermond and Bollob\'as Conjecture, originally formulated in 1981 within the context of the Degree/Diameter Problem. We…

We provide a probabilistic proof of the fundamental gap estimate for Schr\"odinger operators in convex domains on the sphere, which extends the probabilistic proof of F. Gong, H. Li, and D. Luo for the Euclidean case. Our results further…

In this expository note we give proof of the Weierstrass gap theorem in Cohomology terminology. We analyze gap sequence for finding possible gaps and non-gaps on X.

The paper contains a proof of the Fontaine-Jannsen conjecture based on a crystalline version of the p-adic Poincar'e lemma (different proofs were found earlier by Faltings, Niziol and Tsuji).

We answer a question by Niederreiter concerning the enumeration of a class of subspaces of finite dimensional vector spaces over finite fields by proving a conjecture by Ghorpade and Ram.

This paper establishes several sharp spectral results for analytic quasiperiodic Schrodinger operators. Key contributions include: (1) exact exponential decay rates for spectral gaps of the almost Mathieu operator, addressing a question…

This is a detailed survey on the QWEP conjecture and Connes' embedding problem. Most of contents are taken from Kirchberg's paper [Invent. Math. 112 (1993)].