Authors:
mak
Abstract: We determine exact exponential asymptotics of eigenfunctions and of corresponding transfer matrices of the almost Mathieu operators for all frequencies in the localization regime. This uncovers a universal structure in their behavior, governed by the continued fraction expansion of the … Continue reading → PubDate: Thu, 23 Nov 2017 01:33:18 +000

Authors:
mak
Abstract: We consider the Neumann Laplacian acting on square-integrable functions on a triangle in the hyperbolic plane that has one cusp. We show that the generic such triangle has no eigenvalues embedded in its continuous spectrum. To prove this result we … Continue reading → PubDate: Fri, 03 Nov 2017 19:42:57 +000

Authors:
mak
Abstract: Weighted orbital integrals are distributions on reductive groups over local fields appearing both in the local and global trace formulas. There are associated invariant distributions, which play the same role in the invariant trace formulas. In the case of real … Continue reading → PubDate: Wed, 25 Oct 2017 01:59:08 +000

Authors:
mak
Abstract: Let $E$ be a semistable rank two vector bundle of degree $d$ on a Riemann surface $C$ of genus $g\ge 1$, i.e. such that the minimal degree $s$ of a tensor product of $E$ with a line bundle having a … Continue reading → PubDate: Wed, 25 Oct 2017 01:58:54 +000

Authors:
mak
Abstract: Let $G/H$ be an affine symmetric space of split rank $r$. Let $\mathbf{D}$ be a preferred polynomial algebra of $G$-invariant differential operators on $G/H$ generated by $r$ elements. We show that the space of $K$-finite joint eigenfunctions of $\mathbf{D}$ on … Continue reading → PubDate: Wed, 25 Oct 2017 01:58:41 +000

Authors:
mak
Abstract: The following theorem is the main result of the paper. THEOREM. Let $R$ and $T$ be somewhat commutative algebras with the same holonomic number and let $\varphi \colon R\to T$ be an algebra homomorphism. Then every holonomic $T$-module $M$ is … Continue reading → PubDate: Wed, 25 Oct 2017 01:58:27 +000

Authors:
mak
Abstract: This article describes a conjectural $p$-adic analytic construction of global points on (modular) elliptic curves, points which are defined over the ring class fields of real quadratic fields. The resulting conjectures suggest that the classical Heegner point construction, and the … Continue reading → PubDate: Wed, 25 Oct 2017 01:58:03 +000

Authors:
mak
Abstract: Let $F$ be a field of characteristic $\ne 2$. The $u$-invariant of the field $F$ is defined as the maximum dimension of anisotropic quadratic forms over $F$. It is well-known that the $u$-invariant cannot be equal to $3$, $5$, or … Continue reading → PubDate: Wed, 25 Oct 2017 01:57:50 +000

Authors:
mak
Abstract: This work is concerned with the validity of Weyl law for hyperbolic surfaces on the asymptotic counting of the Laplace eigenvalues. Following Phillips-Sarnak, we show that the Weyl law is false for generic hyperbolic surfaces under the standard multiplicity assumption … Continue reading → PubDate: Wed, 25 Oct 2017 01:57:04 +000

Authors:
mak
Abstract: In this paper we show that the cohomology of a connected CW-complex is periodic if and only if it is the base space of a spherical fibration with total space that is homotopically finite dimensional. As applications we characterize those … Continue reading → PubDate: Wed, 25 Oct 2017 01:56:45 +000

Authors:
mak
Abstract: Let $G$ be a finite simple group and let $S$ be a normal subset of $G$. We determine the diameter of the Cayley graph $\Gamma(G,S)$ associated with $G$ and $S$, up to a multiplicative constant. Many applications follow. For example, … Continue reading → PubDate: Wed, 25 Oct 2017 01:56:27 +000

Authors:
mak
Abstract: The first isospectral pairs are constructed on the most simple simply connected domains, namely, on balls and spheres. This long-standing problem, concerning the existence of such pairs, has been solved by a new method call “anticommutator technique”. Among the wide … Continue reading → PubDate: Wed, 25 Oct 2017 01:55:56 +000

Authors:
mak
Abstract: The authors prove the 1990 conjecture of Guralnick and Thompson on composition factors of monodromy groups. Using Riemann’s existence theorem, the conjecture translates into a problem on primitive permutation groups. This group theoretic problem had been reduced to a question … Continue reading → PubDate: Wed, 25 Oct 2017 01:55:42 +000

Authors:
mak
Abstract: We prove that given $\alpha$ in a set of total (Haar) measure in $\mathbf{T}^1 =\mathbf{R}/\mathbf{Z}$, the set of $A\in C^\infty(\mathbf{T}^1,\mathrm{SU}(2))$ for which the skew-product system $(\alpha,A): \mathbf{T}^1 \times \mathrm{SU}(2) \to \mathbf{T}^1 \times \mathrm{SU}(2)$, $(\alpha,A)(\theta,y) = (\theta+\alpha,A(\theta)y)$ is reducible — that … Continue reading → PubDate: Wed, 25 Oct 2017 01:55:29 +000

Authors:
mak
Abstract: We estimate the expected number of limits cycles of a planar polynomial vetor field situated in a neighbourhood of the origin provided that the field in a large neighbourhood is close enough to a linear center. Our main tool is … Continue reading → PubDate: Wed, 25 Oct 2017 01:54:59 +000

Authors:
mak
Abstract: is not available for this article. DOI : 10.2307/3062117 Original article: DOI : 10.2307/120982 PubDate: Wed, 25 Oct 2017 01:54:36 +000

Authors:
mak
Abstract: We prove (a weak version of) Arnold’s Chord conjecture in [2] using Gromov’s “classical” idea in [9] to produce holomorphic disks with boundary on a Lagrangian submanifold. In this paper we prove the following theorem which was conjectured by Arnold … Continue reading → PubDate: Wed, 25 Oct 2017 01:54:22 +000

Authors:
mak
Abstract: We show that every deformation of a divergence-type Fuchsian group has a limit set which is either a circle or has dimension strictly larger than $1$. This is known to be false for all convergence-type groups, and hence solves Bowen’s … Continue reading → PubDate: Wed, 25 Oct 2017 01:54:09 +000

Authors:
mak
Abstract: In this paper we consider various regularity results for discrete quasi-periodic Schrödinger equations $$ -\psi_{n+1} – \psi_{n-1} +V(\theta +n\omega)\psi_n E\psi_n $$ with analytic potential $V$. We prove that on intervals of positivity for the Lyapunov exponent the integrated density of … Continue reading → PubDate: Wed, 25 Oct 2017 01:53:57 +000

Authors:
mak
Abstract: We prove that the answer to the “zero-in-the-spectrum” conjecture, in the form suggested by J. Lott, is negative. Namely, we show that for any $n\ge 6$ there exists a closed $n$-dimensional smooth manifold $M^n$, so that zero does not belong … Continue reading → PubDate: Wed, 25 Oct 2017 01:51:10 +000

Authors:
mak
Abstract: Let $X$ be a finite group, and denote its integral group ring by $\mathbb{Z}X$. A group basis of $\mathbb{Z}X$ is a subgroup $Y$ of the group of units of $\mathbb{Z}X$ of augmentation $1$ such that $\mathbb{Z}X = \mathbb{Z}Y$ and $|X| … Continue reading → PubDate: Wed, 25 Oct 2017 01:50:55 +000

Authors:
mak
Abstract: In this paper we prove a conjecture of J. Palis according to which the arithmetic difference of generic pairs of regular Cantor sets on the line either has zero Lebesgue measure or contains an interval. More precisely, we prove that … Continue reading → PubDate: Wed, 25 Oct 2017 01:50:26 +000

Authors:
mak
Abstract: We prove the Goldman-Parker Conjecture: A complex hyperbolic ideal triangle group is discretely embedded in $\mathrm{PU}(2,1)$ if and only if the product of its three standard generators is not elliptic. We also prove that such a group is indiscrete if … Continue reading → PubDate: Wed, 25 Oct 2017 01:49:38 +000

Authors:
mak
Abstract: Let $d$ be a square free positive integer and $O_d$ the ring of integers in $\mathbf{Q}(\sqrt{-d})$. The main result of this paper is that the groups $\mathrm{PSL}(2,O_d)$ are subgroup separable on geometrically finite subgroups. DOI : 10.2307/2661363 PubDate: Wed, 25 Oct 2017 01:48:43 +000

Authors:
mak
Abstract: We exhibit a $3$-manifold which admits no tight contact structure. DOI : 10.2307/2661367 PubDate: Wed, 25 Oct 2017 01:48:31 +000

Authors:
mak
Abstract: We consider Diophantine inequalities of the kind $|F(\mathrm{x})| \le m$, where $F(\mathbf{X})\in \mathbb{Z}[\mathbf{X}]$ is a homogeneous polynomial which can be expressed as a product of $d$ homogeneous linear forms in $n$ variables with complex coefficients and $m\ge 1$. We say … Continue reading → PubDate: Wed, 25 Oct 2017 01:48:16 +000

Authors:
mak
Abstract: For $a>0$, let $W^a(t)$ be the $a$–neighbourhood of standard Brownian motion in $\mathbb{R}^d$ starting at $0$ and observed until time $t$. It is well-known that $E|W^a(t)| \sim \kappa_at(t\to \infty)$ for $d\ge 3$, with $\kappa_a$ the Newtonian capacity of the … Continue reading → PubDate: Wed, 25 Oct 2017 01:47:26 +000

Authors:
mak
Abstract: Let $M$ be a closed compact $n$-dimensional manifold with $n$ odd. We calculate the first and second variations of the zeta-regularized determinants $\det’ \Delta$ and $\det L$ as the metric on $M$ varies, where $\Delta$ denotes the Laplacian on functions … Continue reading → PubDate: Wed, 25 Oct 2017 01:47:01 +000

Authors:
mak
Abstract: We consider discrete orthogonal polynomial ensembles which are discrete analogues of the orthogonal polynomial ensembles in random matrix theory. These ensembles occur in certain problems in combinatorial probability and can be thought of as probability measures on partitions. The Meiner … Continue reading → PubDate: Wed, 25 Oct 2017 01:46:13 +000

Authors:
mak
Abstract: Given the Hermitian, symmetric and symplectic ensembles, it is shown that the probability that the spectrum belongs to one or several intervals satisfies a nonlinear PDE. This is done for the three classical ensembles: Gaussian, Laguerre and Jaocbi. For the … Continue reading → PubDate: Wed, 25 Oct 2017 01:45:48 +000

Authors:
mak
Abstract: Hilbert’s 17th problem concerns expression of polynomials on $R^n$ as a sum of squares. It is well known tha tmany positive polynomials are not sums of squares; see [Re], [D’A] for excellent surveys. In thsi paper we consider symmetric noncommutative … Continue reading → PubDate: Sat, 21 Oct 2017 20:06:59 +000

Authors:
mak
Abstract: We prove the Kato conjecture for elliptic operators on $\mathbb{R}^n$. More precisely, we establish that the domain of the square root of a uniformly complex elliptic operator $L = -\mathrm{div} (A\nabla)$ with bounded measurable coefficients in $\mathbb{R}^n$ is the Sobolev … Continue reading → PubDate: Sat, 21 Oct 2017 20:06:15 +000

Authors:
mak
Abstract: We solve the Kato problem for divergence form elliptic operators whose heat kernels satisfy a pointwise Gaussian upper bound. More precisely, given the Gaussian hypothesis, we establish that the domain of the square root of a complex uniformly elliptic operator … Continue reading → PubDate: Sat, 21 Oct 2017 20:05:58 +000

Authors:
mak
Abstract: We consider a connected semisimple Lie group $G$ with finite center, an admissible probability measure $\mu$ on $G$, and an ergodic $(G,\mu)$-space $(X,\nu)$. We first note (Lemma 0.1) that $(X,\nu)$ has a unique maximal projective factor of the form $(G/Q,\nu_0)$, … Continue reading → PubDate: Sat, 21 Oct 2017 20:05:16 +000

Authors:
mak
Abstract: We prove that the word problem of a finitely generated group $G$ is in NP (solvable in polynomial time by a nondeterministic Turing machine) if and only if this group is a subgroup of a finitely presented group $H$ with … Continue reading → PubDate: Sat, 21 Oct 2017 20:04:37 +000

Authors:
mak
Abstract: This is the first of two papers devoted to connections between asymptotic functions of groups and computational complexity. In particular, we show how to construct a finitely presented group with NP-complete word problem. One of the main results of this … Continue reading → PubDate: Sat, 21 Oct 2017 20:04:16 +000

Authors:
mak
Abstract: Let $G$ be an arbitrary finite group and fix a prime number $p$. The McKay conjecture asserts that $G$ and the normalizer in $G$ of a Sylow $p$-subgroup have equal numbers of irreducible characters with degrees not divisible by $p$. … Continue reading → PubDate: Sat, 21 Oct 2017 20:00:10 +000

Authors:
mak
Abstract: Let $k$ denote a field with nontrivial discrete valuation. We assume that $k$ is complete with perfect residue field. Let $G$ be the group of $k$-rational points of a reductive, linear algebraic group defined over $k$. Let $\frak g$ denote … Continue reading → PubDate: Sat, 21 Oct 2017 19:59:52 +000

Authors:
mak
Abstract: Through the study of the degenerate complex Monge-Ampère equation, we establish the optimal regularity of the extremal function associated to intrinsic norms of Chern-Levine-Nirenberg and Bedford-Taylor. We prove a conjecture of Chern-Levine-Nirenberg on the extended intrinsic norms on complex manifolds … Continue reading → PubDate: Sat, 21 Oct 2017 19:59:21 +000

Authors:
mak
Abstract: This paper is concerned with proving superlogarithmic estimates for the operator $\square_b$ on pseudoconvex CR manifolds and using them to establish hypoellipticity of $\square_b$ and of the $\overline\partial$-Neumann problem. These estimates are established under the assumption that subellipticity degenerates in … Continue reading → PubDate: Sat, 21 Oct 2017 19:59:06 +000

Authors:
mak
Abstract: In this paper we prove a formula, conjectured by Bloch and Srinivas [S2], which describes the Chow group of zero cycles of a normal quasi-projective surface $X$ over a field, as an inverse limit of relative Chow groups of a … Continue reading → PubDate: Sat, 21 Oct 2017 19:58:52 +000

Authors:
mak
Abstract: Freire, Lopes and Mañé proved that for any rational map $f$ there exists a natural invariant measure $\mu_f$ [5]. Mañé showed there exists an $n>0$ such that $(f^n,\mu_f)$ is measurably conjugate to the one-sided $d^n$-shift , with Bernoulli measure $(\frac{1}{d^n},\ldots,\frac{1}{d^n})$ … Continue reading → PubDate: Sat, 21 Oct 2017 19:58:26 +000

Authors:
mak
Abstract: A uniformly $p$-to–one endomorphism is a measure-preserving map with entropy log $p$ which is almost everywhere $p$-to–one and for which the conditional expectation of each preimage is precisely $1/p$. The standard example of this is a one-sided $p$-shift with uniform … Continue reading → PubDate: Sat, 21 Oct 2017 19:58:07 +000

Authors:
mak
Abstract: In this paper we complete a program to study measurable dynamics in the real quadratic faily. Our goal was to prove that almost any real quadratic map $P_c \colon z\mapsto x^2 +c$, $c\in [-2,1/4]$, has either an attracting cycle or … Continue reading → PubDate: Sat, 21 Oct 2017 19:57:52 +000

Authors:
mak
Abstract: We show that the usual Hodge conjecture implies the general Hodge conjecture for certain abelian varieties of type III, and use this to deduce the general Hodge structure for all powers of certain $4$-dimensional abelian varieties of type III. We … Continue reading → PubDate: Sat, 21 Oct 2017 19:55:53 +000

Authors:
mak
Abstract: DOI : 10.2307/3062133 Let $K$ be a field of characteristic $0$ and let $n$ be a natural number. Let $\Gamma$ be a subgroup of the multiplicative group $(K^\ast)^n$ of finite rank $r$. Given $a_1,\ldots,a_n\in K^\ast$ write $A(a_1,\ldots,a_n\Gamma)$ for the number of … Continue reading → PubDate: Sat, 21 Oct 2017 19:55:24 +000

Authors:
mak
Abstract: We solve the problem of Duffin and Schaeffer (1952) of characterizing those sequences of real frequencies with generate Fourier frames. Equivalently, we characterize the sampling sequences for the Paley-Wiener space. The key step is to connect the problem with de … Continue reading → PubDate: Sat, 21 Oct 2017 19:55:08 +000

Authors:
mak
Abstract: We formulate natural conformally invariant conditions on a $4$-manifold for the existence of a metric whose Schouten tensor satisfies a quadratic inequality. This inequality implies that the eigenvalues of the Ricci tensor are positively pinched. DOI : 10.2307/3062131 PubDate: Sat, 21 Oct 2017 19:54:54 +000

Authors:
mak
Abstract: I prove the existence, and describe the structure, of moduli space of pairs $(P,\Theta)$ consisting of a projective variety $P$ with semiabelian group action and an ample Cartier divisor on it satisyfing a few simple conditions. Every connected component of … Continue reading → PubDate: Sat, 21 Oct 2017 19:54:40 +000

Authors:
mak
Abstract: This paper proves that classical minimal surfaces of arbitrary topological type with total boundary curvature at most $4\pi$ must be smoothly embedded. Related results are proved for varifolds and for soap film surfaces. DOI : 10.2307/3062155 PubDate: Sat, 21 Oct 2017 19:48:27 +000

Authors:
mak
Abstract: In this paper we prove an analogue in the discrete setting of $\mathbb{Z}^d$, of the spherical maximal theorem for $\mathbb{R}^d$. The methods used are two-fold: the application of certain “sampling” techniques, and ideas arising in the study of the number … Continue reading → PubDate: Sat, 21 Oct 2017 19:48:08 +000

Authors:
mak
Abstract: Suppose that $2d-2$ tangent lines to the rational nomal surve $z\mapsto (1 : z : \ldots : z^d)$ in $d$-dimensional complex projective space are given. It was known that the number of codimension $2$ subspaces intersecting all these lines is … Continue reading → PubDate: Sat, 21 Oct 2017 19:47:49 +000

Authors:
mak
Abstract: In a previous work [11], the author considered a representation of the braid group $\rho\colon B_n \to \mathrm{GL}_m(\mathbb{Z}[q^{\pm 1},t^{\pm 1}]) (m = n(n-1)/2)$, and proved it to be faithful for $n=4$. Bigelow [3] then proved the same representation to be … Continue reading → PubDate: Sat, 21 Oct 2017 19:47:17 +000

Authors:
mak
Abstract: We produce explicit elliptic curves over $\mathbb{F}_p(t)$ whose Mordell-Weil groups have arbitrarily large rank. Our method is to prove the conjecture of Birch and Swinnteron-Dyer for these curves (or rather the Tate conjecture for related elliptic surfaces) and then use … Continue reading → PubDate: Sat, 21 Oct 2017 19:46:59 +000

Authors:
mak
Abstract: The main contribution of this work is a new type of graph product, which we call the zig-zag product. Taking a product of a large graph with a small graph, the resulting graph inherits (roughly) its size from the large … Continue reading → PubDate: Sat, 21 Oct 2017 19:46:41 +000

Authors:
mak
Abstract: We study the geometry and topology of immersed surfaces in Euclidean 3-space whose Gauss map satisfies a certain two-piece property, and solve the “shadow problem” formulated by H. Wente. DOI : 10.2307/3062157 PubDate: Sat, 21 Oct 2017 19:46:04 +000

Authors:
mak
Abstract: The generalized Korteweg-de Vries equations are a class of Hamiltonian systems in infinite dimension derived from the KdV equation where the quadratic term is replaced by a higher order power term. These equations have two conservation laws in the energy … Continue reading → PubDate: Sat, 21 Oct 2017 19:45:20 +000

Authors:
mak
Abstract: We give a proof of the André-Oort conjecture for $\mathcal{A}_g$ – the moduli space of principally polarized abelian varieties. In particular, we show that a recently proven `averaged’ version of the Colmez conjecture yields lower bounds for Galois orbits of … Continue reading → PubDate: Sun, 08 Oct 2017 15:12:16 +000

Authors:
mak
Abstract: Building on work by Kontsevich, Soibelman, Nagao and Efimov, we prove the positivity of quantum cluster coefficients for all skew–symmetric quantum cluster algebras, via a proof of a conjecture first suggested by Kontsevich on the purity of mixed Hodge structures … Continue reading → PubDate: Wed, 04 Oct 2017 14:15:31 +000