Showing papers in "Advances in Mathematics in 2016"

TL;DR: In this paper, a quasisymmetric refinement of Stanley's chromatic symmetric function is introduced, and a conjectural refinement of the power sum basis expansion is shown in special cases.

TL;DR: In this article, a variant of the multigrade efficient congruencing method was applied to estimate Vinogradov's integral of degree 3 for moments of order 2 s, establishing strongly diagonal behaviour for 1 ⩽ s ⌽ 6.

TL;DR: In this article, the integrality of multiplicities is proved using a small generalisation of Sturm's Theorem, while positivity involves a modification of a method of Hooley, for finding an effective bound on a family of Selberg-Kloosterman zeta functions at s = 3 / 4.

TL;DR: In this paper, a general technique for computing large deviations of nonlinear functions of independent Bernoulli random variables is presented, which is applied to compute the large deviation rate functions for subgraph counts in sparse random graphs.

TL;DR: In this paper, it was shown that the world of all geometric noncommutative schemes is closed under an operation of a gluing of differential graded categories via bimodules.

TL;DR: In this paper, supercongruences between terminating hypergeometric series and quotients of p-adic Gamma functions are proved using classical hypergeometrical transformation formulae.

TL;DR: In this paper, it was shown that a cobordism between sutured manifolds induces a TQFT in the sense of Atiyah, which is a common generalization of the hat version of the closed 3-manifold map in Heegaard Floer theory, and the contact gluing map defined by Honda, Kazez and Matic.

TL;DR: In this paper, the authors study the dynamics of the interface between two incompressible fluids in a two-dimensional porous medium whose flow is modeled by the Muskat equations, and show that solutions to the solution instantaneously become infinitely smooth.

TL;DR: In this paper, the authors proved the existence of solutions to the viscous, non-resistive magnetohydrodynamics (MHD) equations on the whole of Rn, n = 2, 3, for divergence-free initial data in certain Besov spaces.

TL;DR: In this paper, it was shown that the representation type of the Jacobian algebra P (Q, S ) associated to a 2-acyclic quiver with non-degenerate potential S is invariant under QP-mutations.

TL;DR: In this paper, it was shown that the Stanley depth of a monomial ideal is always at least its depth, which disproved the conjecture that every Cohen-Macaulay simplicial complex is partitionable.

TL;DR: In this paper, the Galois groups of stable homotopy theory have been studied in the context of finite etale algebra objects and the notion of a stable module category of a finite group.

TL;DR: In this article, the authors improved the L p bounds of eigenfunctions of the Laplacian on negatively curved manifolds by a power of logarithm, and derived improvements on the size of the nodal sets.

TL;DR: In this paper, the authors extend the notion of tree-like paths to the setting of weakly geometric rough paths in a Banach space and define a new definition for reduced path and a lemma identifying the reduced path group with the space of signatures.

TL;DR: In this paper, it was shown that continuous expansive flows with specification have unique equilibrium states for potentials with the Bowen property, and this conclusion remains true using weaker non-uniform versions of specification, expansivity, and the Bowen properties.

TL;DR: In this article, the spectral instability of general symmetric shear flows of the incompressible Navier-Stokes equations at a high Reynolds number in a two-dimensional channel was shown.

TL;DR: In this article, it was shown that convex hypersurfaces in R n + 1 contracting under the flow by any power α > 1 n + 2 of the Gauss curvature converge to a smooth, uniformly convex self-similar contracting solution of the flow.

TL;DR: In this paper, a classification of continuous time, nearest neighbor Markov dynamics on the space of interlacing arrays that act nicely on Macdonald processes is presented, which unifies known examples of such dynamics and also yields many new ones.

TL;DR: In this paper, it was shown that the relative singularity category Δ R ( A ) of A has a number of pleasant properties, such as being hom-finite, and that it determines the classical singularity categories D s g ( R ) of Buchweitz and Orlov as a certain canonical quotient category.

TL;DR: In this paper, it was shown that the valuation of a non-zero rational function is piecewise linear on a skeleton S ( X, H ) in a strictly semistable K ∘ -model X of X plus a suitable horizontal divisor H in the analytification of X. This generalizes Berkovich's original construction by admitting unbounded faces in the directions of the components of H.

TL;DR: In this article, it was shown that every sufficiently large K 3 -divisible graph with minimum degree at least 3 n/4 + o (n) has an approximate K 3-decomposition.

TL;DR: This paper contains a proof of the cavity method conjecture that the satisfiability threshold in the random k-SAT problem is r k - SAT = 2 k ln ⁡ 2 − 1 2 ( 1 + ln⁡ 2 ) + e k, with lim k → ∞⁡ e k = 0.

TL;DR: In this article, the existence of adjoints in this bicategory and formulas for the evaluation and coevaluation maps in terms of Atiyah classes and homological perturbation are presented.

TL;DR: The free homotopy coherent adjunction (FHJ) as discussed by the authors is a simplicial category that extends a quasi-category of algebras to a coherent monad.

TL;DR: In this article, an elementary construction of colored sl n link homology is given, where 2-morphisms are given by foams, singular cobordisms between sl n webs; applying a (TQFT-like) representable functor recovers (colored) Khovanov-Rozansky homology.

TL;DR: In this paper, the authors study VB-groupoids and VB algebroids and elucidate the Lie theory relating these objects, i.e., their relation via differentiation and integration.

TL;DR: In this paper, it was shown that the cone-volume measure of a convex body with centroid at the origin satisfies the subspace concentration condition, which extends the results obtained in the discrete case and implies a conjectured best possible inequality for the U-functional of the body.

TL;DR: In this article, the Kazhdan-Lusztig polynomials of representable matroids are shown to be non-negative, and they are interpreted as intersection cohomology Poincare polynomorphisms.

TL;DR: In this article, the analog of the QUE conjecture for Eisenstein series restricted to the infinite geodesic connecting 0 and ∞ inside the modular surface is shown. But the analog is restricted to finite families of sets.

TL;DR: Balogh, Morris and Samotij as discussed by the authors used the hypergraph container method to show that there are at most 2 O(n 1 + 1/l ) -free graphs on n vertices for some c > 0 and infinitely many values of n ∈ N, disproving a well-known and natural conjecture of Erdős.