Authors:
mak
Abstract: We prove Turner’s conjecture, which describes the blocks of the Hecke algebras of the symmetric groups up to derived equivalence as certain explicit Turner double algebras. Turner doubles are Schur-algebra-like `local’ objects, which replace wreath products of Brauer tree algebras … Continue reading → PubDate: Sat, 02 Jun 2018 23:35:04 +000

Authors:
mak
Abstract: For any $\alpha < 1/3$, we construct weak solutions to the $3D$ incompressible Euler equations in the class $C_tC_x^\alpha$ that have nonempty, compact support in time on ${\mathbb R} \times {\mathbb T}^3$ and therefore fail to conserve the total kinetic … Continue reading → PubDate: Wed, 23 May 2018 16:58:06 +000

Authors:
mak
Abstract: We prove the hard Lefschetz theorem and the Hodge-Riemann relations for a commutative ring associated to an arbitrary matroid M. We use the Hodge-Riemann relations to resolve a conjecture of Heron, Rota, and Welsh that postulates the log-concavity of the … Continue reading → PubDate: Tue, 01 May 2018 15:55:49 +000

Authors:
mak
Abstract: We prove global existence of appropriate weak solutions for the compressible Navier–Stokes equations for more general stress tensor than those previously covered by P.–L. Lions and E. Feireisl’s theory. More precisely we focus on more general pressure laws which are … Continue reading → PubDate: Tue, 17 Apr 2018 16:43:12 +000

Authors:
mak
Abstract: We prove several results on (fractal) geometric properties of the classical Markov and Lagrange spectra. In particular, we prove that the Hausdorff dimensions of intersections of both spectra with half-lines always coincide, and may assume any real value in the … Continue reading → PubDate: Fri, 13 Apr 2018 15:53:02 +000

Authors:
mak
Abstract: We compute the algebraic hull of the Kontsevich–Zorich cocycle over any $\mathrm{GL}^+_2(\mathbb{R})$ invariant subvariety of the Hodge bundle, and derive from this finiteness results on such subvarieties. PubDate: Fri, 13 Apr 2018 01:37:24 +000

Authors:
mak
Abstract: The mapping torus of an endomorphism $\Phi$ of a group $G$ is the HNN-extension $G_{*G}$ with bonding maps the identity and $\Phi$. We show that a mapping torus of an injective free group endomorphism has the property that its finitely … Continue reading → PubDate: Wed, 11 Apr 2018 22:05:53 +000

Authors:
mak
Abstract: In this paper we determine the distributional behavior of sums of free (in the sense of Voiculescu) identically distributed, infinitesimal random variables. The theory is shown to parallel the classical theory of independent random variables, though the limit laws are … Continue reading → PubDate: Wed, 11 Apr 2018 22:04:14 +000

Authors:
mak
Abstract: We construct analytically the signature operator for a new family of topological manifolds. This family contains the quasi-conformal manifolds and the topological manifolds modeled on germs of homeomorphisms of $\mathbf{R}^n$ possessinga derivative which is in $L^p$, with $p> \frac{1}{2} … Continue reading → PubDate: Wed, 11 Apr 2018 22:03:02 +000

Authors:
mak
Abstract: Given ergodic $p$-invariant measures $\{\mu_i\}$ on the $1$-torus $\mathbb{T} = \mathbb{R}/\mathbb{Z}$, we give a sharp condition on their entropies, guaranteeing that the entropy of the convolution $\mu_1\ast\cdots\ast \mu_n$ converges to $\log p$. We also prove a variant of this result … Continue reading → PubDate: Wed, 11 Apr 2018 22:01:03 +000

Authors:
mak
Abstract: For stationary harmonic maps between Riemannian manifolds, we provide a necessary and sufficient condition for the uniform interior and boundary gradient estimates in terms of the total energy of maps. We also show that if analytic target manifolds do not … Continue reading → PubDate: Wed, 11 Apr 2018 22:00:15 +000

Authors:
mak
Abstract: We prove that every hyperbolic measure invariant under a $C^{1+\alpha}$ diffeomorphism of a smooth Riemannian manifold possesses asymptotically “almost” local product structure, i.e., its density can be approximated by the product of the densities on stable and unstable manifolds up … Continue reading → PubDate: Wed, 11 Apr 2018 22:00:01 +000

Authors:
mak
Abstract: We derive a formula connecting the derivatives of parallel section functions of an origin-symmetric star body in $\mathbb{R}^n$ with the Fourier transform of powers of the radial function of the body. A parallel section function (or $(n -1)$-dimensional X-ray) gives … Continue reading → PubDate: Wed, 11 Apr 2018 21:43:23 +000

Authors:
mak
Abstract: Thurston’s ending lamination conjecture proposes that a finitely generated Kleinian group is uniquely determined (up to isometry) by the topology of its quotient and a list of invariants that describe the asymptotic geometry of its ends. We present a proof … Continue reading → PubDate: Wed, 11 Apr 2018 21:43:05 +000

Authors:
mak
Abstract: We show the Williams Conjecture is false for irreducible shifts of finite type by examining relative sign-gyration numbers of conjugacies between shifts with no points of period one or two. DOI https://doi.org/10.2307/120975 PubDate: Wed, 11 Apr 2018 21:42:57 +000

Authors:
mak
Abstract: The main objective of this paper is to prove a new inequality for plurisubharmonic functions estimating their supremum over a ball by their supremum over a measurable subset of the ball. We apply this result to study local properties of … Continue reading → PubDate: Wed, 11 Apr 2018 21:42:29 +000

Authors:
mak
Abstract: In his 1974 thesis, Martin Scharlemann constructed a fake homotopy equivalence from a closed smooth manifold $f\colon Q \to S^3 \times S^1\#S^2 \times S^2$, and asked the question whether or not the manifold $Q$ itself is diffeomorphic to $S^3 \times … Continue reading → PubDate: Wed, 11 Apr 2018 21:42:22 +000

Authors:
mak
Abstract: We prove the Feigenbaum-Coullet-Tresser conjecture on the hyperbolicity of the renormalization transformation of bounded type. This gives the first computer-free proof of the original Feigenbaum observation of the universal parameter scaling laws. We use the Hyperbolicity Theorem to prove Milnor’s … Continue reading → PubDate: Wed, 11 Apr 2018 21:41:45 +000

Authors:
mak
Abstract: We construct a counterexample to the “hot spots” conjecture; there exists a bounded connected planar domain (with two holes) such that the second eigenvalue of the Laplacian in that domain with Neumann boundary conditions is simple and such that the … Continue reading → PubDate: Wed, 11 Apr 2018 21:18:04 +000

Authors:
mak
Abstract: We construct continuous families of Riemannian metrics on certain simply connected manifolds with the property that the resulting Riemannian manifolds are pairwise isospectral for the Laplace operator acting on functions. These are the first examples of simply connected Riemannian manifolds … Continue reading → PubDate: Wed, 11 Apr 2018 21:17:51 +000

Authors:
mak
Abstract: A necessary and sufficient condition is given for semi-ampleness of a numerically effective (nef) and big line bundle in positive characteristic. One application is to the geometry of the universal stable curve over $\overline M_g$, specifically, the semi-ampleness of the … Continue reading → PubDate: Wed, 11 Apr 2018 21:17:44 +000

Authors:
mak
Abstract: For the quasilinear wave equation \[ \partial_t^2 u-\Delta u = u_tu_{tt}, \] we analyze the long-time behavior of classical solutions with small (not rotationally invariant) data. We give a complete asymptotic expansion of the lifespan and describe the solution close … Continue reading → PubDate: Wed, 11 Apr 2018 21:16:50 +000

Authors:
mak
Abstract: We consider the system of $N$ ($\ge 2$) elastically colliding hard balls with masses $m+1,\ldots,m_N$, radius $r$, moving uniformly in the flat torus $\mathbb{T}_L^\nu = \mathbb{R}^\nu/L \cdot \mathbb{Z}^\nu$, $\nu \ge 2$. It is proved here that the relevant Lyapunov exponents … Continue reading → PubDate: Wed, 11 Apr 2018 21:16:40 +000

Authors:
mak
Abstract: Let $P$ be a locally finite disk pattern on the complex plane $\mathbb{C}$ whose combinatorics are described by the one-skeleton $G$ of a triangulation of the open topological disk and whose dihedral angles are equal to a function $\Theta\colon E\to … Continue reading → PubDate: Wed, 11 Apr 2018 21:16:31 +000

Authors:
mak
Abstract: Using a variational method, we exhibit a surprisingly simple periodic orbit for the newtonian problem of three equal masses in the plane. The orbit has zero angular momentum and a very rich symmetry pattern. Its most surprising feature is that … Continue reading → PubDate: Mon, 09 Apr 2018 18:47:59 +000

Authors:
mak
Abstract: Let $x(t)$ be a trajectory of the gradient of a real analytic function and suppose that $x_0$ is a limit point of $x(t)$. We prove the gradient conjecture of R. Thom which states that the secants of $x(t)$ at $x_0$ … Continue reading → PubDate: Mon, 09 Apr 2018 18:47:28 +000

Authors:
mak
Abstract: In this paper we will show that the assumption on the negative Schwarzian derivative is redundant in the case of $C^3$ unimodal maps with a nonflat critical point. The following theorem will be proved: For any $C^3$ unimodal map of … Continue reading → PubDate: Mon, 09 Apr 2018 18:47:15 +000

Authors:
mak
Abstract: Let $M$ be a compact, hyperbolizable $3$-manifold with nonempty incompressible boundary and let $AH(\pi_1(M)$ denote the space of (conjugacy classes of) discrete faithful representations of $\pi_1(M)$ into $\mathrm{PSL}_2(\mathbf{C})$. The components of the interior $MP(\pi_1(M))$ of $AH(\pi_1(M))$ (as a subset of … Continue reading → PubDate: Mon, 09 Apr 2018 18:47:04 +000

Authors:
mak
Abstract: The Poisson boundary of a group $G$ with a probability measure $\mu$ is the space of ergodic components of the time shift in the path space of the associated random walk. Via a generalization of the classical Poisson formula it … Continue reading → PubDate: Mon, 09 Apr 2018 18:46:56 +000

Authors:
mak
Abstract: We continue the study of the $A$-amplitude associated to a half-line Schrödinger operator, $-\frac{d^2}{dx^2} + q$ in $L^2((0,b))$, $b\le \infty$. $A$ is related to the Weyl-Titchmarsh $m$-function via $m(-\kappa^2) = -\kappa – \int_0^a A(\alpha)e^{-2\alpha\kappa}d\alpha+O(e^{-(2a-\varepsilon)\kappa})$ for all $\varepsilon>0$. We discuss … Continue reading → PubDate: Mon, 09 Apr 2018 18:13:25 +000

Authors:
mak
Abstract: Every nonconstant meromorphic function in the plane univalently covers spherical discs of radii arbitrarily close to arctan $\sqrt{8} \approx 70^{\circ}32’$. In in addition all critical points of the function are multiple, then a similar statement holds with $\pi/2$. These constants … Continue reading → PubDate: Mon, 09 Apr 2018 18:13:16 +000

Authors:
mak
Abstract: A Besicovitch set is a set which contains a unit line segment in any direction. It is known that the Minkowski and Hausdorff dimensions of such a set must be greater than or equal to $5/2$ in $\mathbb{R}^3$. In this … Continue reading → PubDate: Mon, 09 Apr 2018 18:12:41 +000

Authors:
mak
Abstract: A method of “algebraic estimates” is developed, and used to study the stability properties of integrals of the form $\int_B |f(z)|^{-\delta} dV$, under small deformations of the function $f$. The estimates are described in terms of a stratification of the … Continue reading → PubDate: Mon, 09 Apr 2018 17:50:38 +000

Authors:
mak
Abstract: One of the purposes of this paper is to prove that if $G$ is a noncompact connected semisimple Lie group of real rank one with finite center, then $$ L^{2,1}(G) \ast L^{2,1}(G) \subseteq L^{2,\infty}(G). $$ Let $K$ be a maximal … Continue reading → PubDate: Mon, 09 Apr 2018 17:50:29 +000

Authors:
mak
Abstract: Let $T$ be a complete, first-order theory in a finite or countable language having infinite models. Let $I(T,\kappa)$ be the number of isomorphism types of models of $T$ of cardinality $\kappa$. We denote by $\mu$ (respectively $\hat\mu$) the number of … Continue reading → PubDate: Mon, 09 Apr 2018 17:50:14 +000

Authors:
mak
Abstract: A strong version of the quantization conjecture of Guillemin and Sternberg is proved. For a reductive group action on a smooth, compact, polarized variety $(X,\mathcal{L})$, the cohomologies of $\mathcal{L}$ over the GIT quotient $X//G$ equal the invariant part of the … Continue reading → PubDate: Mon, 09 Apr 2018 17:49:05 +000

Authors:
mak
Abstract: Margulis shows that “most” arithmetic groups are superrigid. Platonov conjectured, conversely, that finitely generated linear groups which are superrigid must be of “arithmetic type.” We construct counterexamples to Platonov’s Conjecture. DOI https://doi.org/10.2307/121131 PubDate: Mon, 09 Apr 2018 16:47:07 +000

Authors:
mak
Abstract: For $\Gamma$ a countable amenable group consider those actions of $\Gamma$ as measure-preserving transformations of a standard probability space, written as $\{T_\gamma\}_{\gamma\in\Gamma}$ acting on $(X,\mathcal{F},\mu)$. We say $\{T_\gamma\}_{\gamma\in\Gamma}$ has completely positive entropy (or simply cpe for short) if for any … Continue reading → PubDate: Mon, 09 Apr 2018 16:46:59 +000

Authors:
mak
Abstract: We prove here that in the complement of the closure of the hyperbolic surface diffeomorphisms, the ones exhibiting a homoclinic tangency are $C^1$ dense. This represents a step towards the global understanding of dynamics of surface diffeomorphisms. DOI https://doi.org/10.2307/121127 PubDate: Mon, 09 Apr 2018 16:46:02 +000

Authors:
mak
Abstract: A fundamental goal of algebraic geometry is to do for singular varieties whatever we can do for smooth ones. Intersection homology, for example, directly produces groups associated to any variety which have almost all the properties of the usual homology … Continue reading → PubDate: Mon, 09 Apr 2018 16:31:39 +000

Authors:
mak
Abstract: The $\theta\colon \pi_1(R)\to \mathrm{PSL}(2,\mathbb{C})$ be a homomorphism of the fundamental group of an oriented, closed surface $R$ of genus exceeding one. We will establish the following theorem. THEOREM. Necessary and sufficient for $\theta$ to be the monodromy representation associated with … Continue reading → PubDate: Mon, 09 Apr 2018 16:31:07 +000

Authors:
mak
Abstract: The classical isoperimetric inequality in $\mathbb{R}^3$ states that the surface of smallest area enclosing a given volume is a sphere. We show that the least area surface enclosing two equal volumes is a double bubble, a surface made of two … Continue reading → PubDate: Mon, 09 Apr 2018 16:30:44 +000

Authors:
mak
Abstract: Let $\{b(n) \colon n \in \mathbf{N}\}$ be the sequence of coefficients in the Taylor expansion of a rational function $R(X) \in \mathbf{Q}(X)$ and suppose that $b(n)$ is a perfect $d^{\mathrm{th}}$ power for all large $n$. A conjecture of Pisot states … Continue reading → PubDate: Mon, 09 Apr 2018 16:10:16 +000

Authors:
mak
Abstract: In this paper we prove the topological uniqueness of maximal arrangements of a real plane algebraic curve with respect to three lines. More generally, we prove the topological uniqueness of a maximally arranged algebraic curve on a real toric surface. … Continue reading → PubDate: Mon, 09 Apr 2018 16:08:46 +000

Authors:
mak
Abstract: In the unit ball $B(0,1)$, let $u$ and $\Omega$ (a domain in $\mathbb{R}^N$) solve the following overdetermined problem: \[ \Delta u = \chi_{\Omega} \quad \mathrm{in}\; B(0,1),\qquad\qquad 0\; \in \partial\Omega, \qquad\qquad u = |\nabla u| = 0 \quad \mathrm{in}\; B(0,1) \backslash … Continue reading → PubDate: Mon, 09 Apr 2018 16:08:06 +000

Authors:
mak
Abstract: In this paper, we demonstrate a relation among Seiberg-Witten invariants which arises from embedded surfaces in four-manifolds whose self-intersection number is negative. These relations, together with Taubes’ basic theorems on the Seiberg-Witten invariants of symplectic manfiolds, are then used to … Continue reading → PubDate: Mon, 09 Apr 2018 16:06:35 +000

Authors:
mak
Abstract: The operator space analogue of the strong form of the principle of local reflexivity is shown to hold for any von Neumann algebra predual, and thus for any $C^\ast$-algebraic dual. This is in striking contrast to the situation for $C^\ast$-algebras, … Continue reading → PubDate: Mon, 09 Apr 2018 16:06:22 +000

Authors:
mak
Abstract: We prove that if a multiple trigonometric series is spherically Abel summable everywhere to an everywhere finite function $f(x)$ which is bounded below by an integrable function, then the series is the Fourier series of $f(x)$ if the coefficients of … Continue reading → PubDate: Mon, 09 Apr 2018 16:05:12 +000

Authors:
mak
Abstract: The classical Birkhoff conjecture claims that the boundary of a strictly convex integrable billiard table is necessarily an ellipse (or a circle as a special case). In this article we prove a complete local version of this conjecture: a small … Continue reading → PubDate: Wed, 04 Apr 2018 14:49:49 +000

Authors:
mak
Abstract: Given $k\in \mathbb{N}$, the $k$’th discrete Heisenberg group, denoted $ \mathbb{H}_{\scriptscriptstyle{\mathbb{Z}}}^{2k+1}$, is the group generated by the elements $a_1,b_1,\ldots,a_k,b_k,c$, subject to the commutator relations $[a_1,b_1]=\ldots=[a_k,b_k]=c$, while all the other pairs of elements from this generating set are required to commute, … Continue reading → PubDate: Wed, 14 Mar 2018 02:58:33 +000

Authors:
annadmin
Abstract: For almost all Riemannian metrics (in the $C^\infty $ Baire sense) on a closed manifold $M^{n+1}$, $3\leq (n+1)\leq 7$, we prove that the union of all closed, smooth, embedded minimal hypersurfaces is dense. This implies there are infinitely many minimal … Continue reading → PubDate: Thu, 08 Mar 2018 00:00:00 +000

Authors:
annadmin
Abstract: Given $M$ a Riemannian manifold with (possibly empty) boundary, we show that its volume spectrum $\{\omega _p(M)\}_{p\in \mathbb {N}}$ satisfies a Weyl law that was conjectured by Gromov. PubDate: Wed, 07 Mar 2018 00:00:00 +000

Authors:
annadmin
Abstract: The Möbius disjointness conjecture of Sarnak states that the Möbius function does not correlate with any bounded sequence of complex numbers arising from a topological dynamical system with zero topological entropy. We verify the logarithmically averaged variant of this conjecture … Continue reading → PubDate: Tue, 06 Mar 2018 00:00:00 +000