Showing papers in "Advances in Mathematics in 2017"

TL;DR: In this article, the authors developed a direct method of moving planes for the fractional Laplacian operator, instead of using the conventional extension method introduced by Caffarelli and Silvestre.

TL;DR: In this article, a one-parameter family of knots Floer homologies tHFK for knots in S 3 has been constructed, and these invariants can be used to give homomorphisms from the smooth concordance group C to Z, giving bounds on the four-ball genus of knots.

TL;DR: In this article, the affine Yangian of gl 1 has been shown to be an additivization of the quantum toroidal algebra of g in the same way as the Yangian Y h ( g ) is an additiivisation of U q ( L g ) for a simple Lie algebra g.

TL;DR: Spectral Mackey functors as mentioned in this paper are homotopy-coherent versions of ordinary Mackeyfunctors as defined by Dress and can be described as excisive functors on a suitable ∞-category, and they use this to show that universal examples of these objects are given by algebraic K-theory.

TL;DR: In this paper, the homotopy theory of motivic spaces and spectra parametrized by quotient stacks [X / G ], where G is a linearly reductive linear algebraic group, is studied.

TL;DR: In this article, the authors introduce a class of G-equivariant spectra called F -nilpotent, which is defined as the class of spectra that are complete, torsion, complete, and nilpotent objects in a symmetric monoidal stable ∞-category.

TL;DR: In this article, a family of symmetric rational functions that form a one-parameter generalization of the classical Hall-Littlewood polynomials is introduced, which is closely related to the half-infinite volume, finite magnon sector limit of the higher spin six-vertex (or XXZ) model.

TL;DR: In this paper, a family of groups admitting a braided monoidal structure is constructed, and the authors show that homological stability holds with both polynomial and abelian twisted coefficients, with no further assumptions.

TL;DR: In this paper, it has been shown that a Calderon-Zygmund operator T is pointwise controlled by a finite number of dyadic operators of a very simple structure (called the sparse operators).

TL;DR: In this paper, it was shown that for p ≥ 2, solutions of equations modeled by the fractional p-Laplacian improve their regularity on the scale of fractional Sobolev spaces.

TL;DR: For projective klt pairs of dimension 3 over an algebraically closed field of characteristic p > 5, the cone theorem, base point free theorem, contraction theorem, finiteness of minimal models, termination with scaling, existence of Mori fibre spaces, etc.

TL;DR: In this article, the authors considered left non-degenerate set-theoretic solutions to the Yang-Baxter equation, a class of algebraic structures encompassing groups, racks, and cycle sets.

TL;DR: In this paper, an L q (L p ) -theory for the semilinear fractional equations of the type (0.1) ∂ t α u ( t, x ) was introduced.

TL;DR: In this paper, it was shown that every irreducible V G -module occurs in an irreducerible g-twisted V-module for some g ∈ G.

TL;DR: In this paper, the sharp remainder terms of L p and weighted Hardy and Rellich inequalities on the class of homogeneous groups were derived and a number of identities were derived including weighted and higher order types.

TL;DR: In this paper, the authors studied the relationship between properties of the action, of the groupoid and of the C*-algebra, with an emphasis on situations in which O G, E is a Kirchberg algebra.

TL;DR: In this article, the analogues of boundary layer potentials for the sub-Laplacian on homogeneous Carnot groups/stratified Lie groups were proposed and proved.

TL;DR: In this article, pointwise gradient bounds for heat semigroups associated to general (possibly unbounded) Laplacians on infinite graphs satisfying the curvature dimension condition CD (K, ∞ ) were proved.

TL;DR: In this article, it was shown that any Newhouse open set in the space of C r -diffeomorphisms on a closed surface is contained in the closure of the set of diffeomorphisms which have non-trivial wandering domains whose forward orbits have historic behavior.

TL;DR: In this article, the authors established the global existence and uniqueness of smooth solutions to the two-dimensional compressible magnetohydrodynamic system when the initial data is close to an equilibrium state.

TL;DR: Several applications to algebraic complexity theory are discussed, such as a deterministic polynomial time algorithm for non-commutative rational identity testing, and the existence of small division-free formulas for Non-Commutative polynomials.

TL;DR: In this article, the authors prove wave breaking in the nonlinear nonlocal equation which combines the dispersion relation of water waves and a nonlinearity of the shallow water equations, provided that the slope of the initial datum is sufficiently negative.

TL;DR: In this article, Boyer and Clay showed that an oriented three-manifold with torus boundary admits either no L-space Dehn filling, a unique L-Space filling, or an interval of fillings.

TL;DR: In this article, the authors established upper bounds on the blow-up rate of the gradients of solutions of the Lame system with partially infinite coefficients in dimensions greater than two as the distance between the surfaces of discontinuity of the coefficients of the system tends to zero.

TL;DR: In this article, the Hausdorff dimension of the set of real numbers having a unique expansion has been studied, and it has been shown that the dimension function D : ( 1, ∞ ) → [ 0, 1 ] is continuous and has bounded variation.

TL;DR: In this paper, the authors studied barycenters in the space of probability measures on a Riemannian manifold, equipped with the Wasserstein metric, and established absolute continuity of the barycenter of general measures Ω ∈ P(P(M))Ω∈P(P (M)).

TL;DR: In this article, a general framework for lax and oplax transformations and their higher analogs between strong ( ∞, n ) -functors is developed, motivated by the challenge of defining twisted quantum field theories in the context of higher categories.

TL;DR: The upper-tail problem in the sparse regime of p → 0 as n → ∞ with p ≥ n − α for an explicit α = α H > 0, which was thereafter asymptotically solved by two of the authors in this article.

TL;DR: In this article, the mirror of a hypersurface of general type (and more generally varieties of non-negative Kodaira dimension) is described as the critical locus of the zero fibre of a certain Landau-Ginzburg potential.

TL;DR: In this article, the unstable metric entropy and unstable topological entropy of partially hyperbolic diffeomorphisms are defined and a variational principle for the unstable topology is established.