Showing papers in "Advances in Mathematics in 2020"

TL;DR: In this article, the stability and log canonical thresholds of a Q-Fano variety are studied in terms of the moment polytope of the bundle of valuations on the bundle.

TL;DR: Markov categories are developed as a framework for synthetic probability and statistics, following work of Golubtsov as well as Cho and Jacobs, and provides a uniform treatment of various types of probability theory.

TL;DR: In this paper, Li, Wei and Zhang proved the linear inviscid damping and vorticity depletion phenomena for the linearized Euler equations around the Kolmogorov flow, which confirmed Bouchet and Morita's predictions based on numerical analysis.

TL;DR: In this article, the Grassmannian X = G r n − k (C n ) was considered and a mirror dual Landau-Ginzburg model was proposed.

TL;DR: In this article, the authors define and study the quantum equivariant K-theory of cotangent bundles over Grassmannians and prove that the spectrum of operators of quantum multiplication by these quantum classes is governed by the Bethe ansatz equations for the inhomogeneous XXZ spin chain.

TL;DR: The leading order of the exponential rate function for the probability that the number of copies of H in the Erdős-Renyi graph G ( n, p ) exceeds its expectation by a factor 1 + u, assuming n − κ ( H ) ≪ p ≪ 1, with κ( H ) = 1 / ( 2 Δ ), where Δ ≥ 1 is the maximum degree of H.

TL;DR: In this paper, Carando et al. showed that the multivariable Rubio de Francia extrapolation theorem for the multilinear Muckenhoupt classes A p →, r → can be extended to bilinear rough singular integral operators.

TL;DR: In this paper, a sliding method for the fractional p-Laplacian is proposed to obtain monotonicity of solutions in non-local problems with more general operators and more general nonlinearities.

TL;DR: In this article, it was shown that the moduli space M P Spin (7 ) ⊂ B P of irreducible Spin ( 7 ) -instanton connections on P modulo gauge, as a manifold or derived manifold, is orientable.

TL;DR: In this article, the precise late-time asymptotics for solutions to the wave equation on extremal Reissner-Nordstrom black holes were derived based on purely physical space techniques.

TL;DR: For each integer n ⩾ 2, the authors describes the space of stability conditions on the derived category of the n-dimensional Ginzburg algebra associated to the A 2 quiver.

TL;DR: In this article, the L p -Brunn-Minkowski inequality conjecture for convex bodies close to the unit ball in Hausdorff distance has been verified.

TL;DR: In this paper, a linear response for random compositions of maps, chosen independently according to a distribution P, is studied for a wide class of one dimensional random maps, including Gauss-Renyi maps and Pomeau-Manneville maps.

TL;DR: In this paper, the authors derived exact and asymptotic formulae for the expected number of k-faces for arbitrary k ∈ { 0, 1, …, d − 1 }.

TL;DR: In this paper, the cone of deformations of a Coxeter permutahedron is defined as the finite cone of the toric variety associated to the Coxeter complex, a class of polytopes containing important families such as weight, signed graphic zonotopes, Coxeter matroids, root cones, and Coxeter associahedra.

TL;DR: In this paper, it was shown that the quantum toroidal algebra U q, q (gl n ) is isomorphic to the double shuffle algebra of Feigin and Odesskii for the cyclic quiver.

TL;DR: In this article, the authors studied the joint convexity/concavity of trace functions and showed that the trace functions are monotone under completely positive trace preserving maps.

TL;DR: In this article, the authors introduce symmetric monoidal functors on stratified and decorated bordisms, which capture the algebraic essence of defect TQFTs and give precise meaning to the fusion of line and surface defects as well as their duality operations.

TL;DR: For a finite group G and a 4-cocycle ω ∈ Z 4 (G, k × ), the center of the monoidal 2-category 2Vec G ω of ω-twisted G-graded 1-categories of finite dimensional k-vector spaces was shown explicitly in this article.

TL;DR: In this article, a classification of representation types of the subcategories of representations of an m × n rectangular grid with monomorphisms (dually, epimorphisms) in one or both directions is given.

TL;DR: In this article, a general form of the wall-crossing formula was proposed to compute the disk potentials of monotone Lagrangian submanifolds with their Floer-theoretic behavior away from a Donaldson divisor.

TL;DR: The Erdős-Hajnal conjecture of as mentioned in this paper states that for every forest H there exists a constant c > 0 such that every graph G that does not contain H as an induced subgraph has a clique or stable set of cardinality at least | G | c.

TL;DR: In this paper, the authors prove a conjecture of Kahn-Saito-Yamazaki [8, Conj.1(1)] by extending Voevodsky's fundamental results on homotopy invariant (pre)sheaves with transfers to its generalizations, reciprocity sheaves and cube-invariant sheaves.

TL;DR: In this paper, the authors study the higher regularity of free boundaries in obstacle problems for integro-differential operators and establish optimal boundary regularity estimates for solutions to linear nonlocal equations in C k, α domains.

TL;DR: Recently, Cao-Maulik-Toda et al. as mentioned in this paper considered curve counting invariants of X using Hilbert schemes of curves and conjecture a DT/PT correspondence which relates these to stable pair invariants for toric Calabi-Yau 4-folds.

TL;DR: In this article, the authors studied the parabolic G-Higgs bundles over a compact Riemann surface with fixed punctures, and established a correspondence between these objects and representations of the fundamental group of the punctured surface in G with arbitrary holonomy around the punctures.

TL;DR: In this article, the authors give a systematic construction of (weakly) d-representation-finite self-injective algebras of the repetitive categories of finite global dimension satisfying a certain finiteness condition for the Serre functor.

TL;DR: In this article, the spectral theory of periodic Jacobi matrices on trees is studied and the most significant result is that these operators have no singular continuous spectrum, which is the first result that has been confirmed in the literature.

TL;DR: In this paper, the authors construct virtual fundamental classes on nested Hilbert schemes of points and curves in complex nonsingular projective surfaces, and derive explicit formulas for some of these integrals by relating them to Carlsson-Okounkov's vertex operator formulas.

TL;DR: In this article, the authors studied energy propagation along line-defects (edges) in two-dimensional continuous, energy preserving periodic media, where the edge operator is a small perturbation of the bulk and models a transition (via a domain wall) between distinct periodic, P or C breaking perturbations.