Related papers: Finite Gap Jacobi Matrices, II. The Szeg\H{o} Clas…

Let I be a dense linear order with a left endpoint but no right endpoint. We consider the lattice L(I) of finite unions of closed intervals of I. This lattice arises naturally in the setting of o-minimality, as these are precisely the…

For non-uniformly expanding maps inducing with a general return time to Gibbs Markov maps, we provide sufficient conditions for obtaining higher order asymptotics for the correlation function in the infinite measure setting. Along the way,…

In analogy to complex function theory we introduce a Szeg\"o metric in the context of hypercomplex function theory dealing with functions that take values in a Clifford algebra. In particular, we are dealing with Clifford algebra valued…

Recent numerical and theoretical studies on the two-dimensional $J$-$Q_3$ model suggests that the deconfined quantum critical point is actually a $SO(5)$-symmetry-enhanced first-order phase transition that is spontaneously broken to $O(4)$.…

Let $F$ be a Siegel cusp form of degree 2, even weight $k \geq 2$ and odd squarefree level $N$. We undertake a detailed study of the analytic properties of Fourier coefficients $a(F,S)$ of $F$ at fundamental matrices $S$ (i.e., with $-4…

We establish an uncertainty principle for functions $f: \mathbb{Z}/p \rightarrow \mathbb{F}_q$ with constant support (where $p \mid q-1$). In particular, we show that for any constant $S > 0$, functions $f: \mathbb{Z}/p \rightarrow…

In the nested limit of the spin-fermion model for the cuprates, one-dimensional physics in the form of half-filled two-leg ladders emerges. We show that the renormalization group flow of the corresponding ladder is towards the d-Mott phase,…

In this paper, we are interested in matrix valued orthogonal polynomials on the real line with respect to exponential weights. We obtain strong asymptotics as the degree tends to infinity in different regions of the complex plane, as well…

In this paper, inspired by the elegant work of Good and Meddaugh \cite{GM} and the graph models for zero-dimensional systems developed by several authors, like Gambaudo and Martens \cite{GM06}, Shimomura \cite{Sh14}. We try to discover a…

We consider an abstract compact orientable Cauchy-Riemann manifold endowed with a Cauchy-Riemann complex line bundle. We assume that the manifold satisfies condition Y(q) everywhere. In this paper we obtain a scaling upper-bound for the…

We study absolute continuity of harmonic measure with respect to surface measure on domains $\Omega$ that have large complements. We show that if $\Gamma\subset \mathbb{R}^{d+1}$ is $d$-Ahlfors regular and splits $ \mathbb{R}^{d+1}$ into…

We study the family of quadratic maps f_a(x) = 1 - ax^2 on the interval [-1,1] with a between 0 and 2. When small holes are introduced into the system, we prove the existence of an absolutely continuous conditionally invariant measure using…

Let K be a self-similar or self-affine set in R^d, let \mu be a self-similar or self-affine measure on it, and let G be the group of affine maps, similitudes, isometries or translations of R^d. Under various assumptions (such as separation…

We prove almost Lipshitz continuity of spectra of singular quasiperiodic Jacobi matrices and obtain a representation of the critical almost Mathieu family that has a singularity. This allows us to prove that the Hausdorff dimension of its…

We study the superconducting state of Sr$_2$RuO$_4$ on the bases of a phenomenological but orbital specific description of the electron-electron attraction and a realistic quantitative account of the electronic structure in the normal…

Quantum cat maps are toy models in quantum chaos associated to hyperbolic symplectic matrices $A\in \operatorname{Sp}(2n,\mathbb{Z})$. The macroscopic limits of sequences of eigenfunctions of a quantum cat map are characterized by…

We study the harmonically weighted one-level density of low-lying zeros of $L$-functions in the family of holomorpic newforms of fixed even weight $k$ and prime level $N$ tending to infinity. For this family, Iwaniec, Luo and Sarnak proved…

Given a representation of the circle group by semiclassical Fourier integral operators, we construct an algebra of semiclassical pseudodifferential operators that are a quantum analogue of the notion of symplectic cutting of Lerman, and we…

Self-similar sets require a separation condition to admit a nice mathematical structure. The classical open set condition (OSC) is difficult to verify. Zerner proved that there is a positive and finite Hausdorff measure for a weaker…

We discuss the proof of and systematic application of Case's sum rules for Jacobi matrices. Of special interest is a linear combination of two of his sum rules which has strictly positive terms. Among our results are a complete…