相关论文: Vanishing lines in Adams spectral sequences are ge…

We consider special multiclass spectral, discrepancy, degree, and codegree properties of expanding graph sequences. As we can prove equivalences and implications between them and the definition of the generalized quasirandomness of…

We prove generalized ABC theorems for vanishing sums of non-Archimedean entire functions of several variables in arbitrary characteristic.

We prove the genericity of the shadowing and periodic shadowing properties for both conservative and dissipative homeomorphisms on a compact connected manifold. Our proof is valid for topological manifolds and still holds in the dissipative…

The normal modes of a continuum solid endowed with a random distribution of line defects that behave like elastic strings are described. These strings interact with elastic waves in the bulk, generating wave dispersion and attenuation. As…

Generalized symmetry extends the usual notion of symmetry to ones that are of higher-form, acting on subsystems, non-invertible, etc. The concept was originally defined in the field theory context using the idea of topological defects. On…

In this article, we review and discuss different aspects of stability and genericity of some properties of space-times which occur in various contexts in the General Theory of Relativity. We also give argument supporting the conclusion that…

This paper reproves a general form of the Green-Lazarsfeld 'generic vanishing' theorem and more recent strengthenings, as well as giving some new applications.

Line congruences are $2$-dimensional families of lines in $3$-space. The singularities that appear in generic line congruences are folds, cusps and swallowtails. In this paper we give a geometric description of these singularities. The main…

The point symmetry group is studied for the generalized Webster-type equation describing non-linear acoustic waves in lossy channels with variable cross sections. It is shown that, for certain types of cross section profiles, the admitted…

We consider the asymptotic behaviour of the solution of one dimensional stochastic differential equations and Langevin equations in periodic backgrounds with zero average. We prove that in several such models, there is generically a non…

We prove the generic existence of spectral networks for a large class of spectral data.

We report conditions on a switching signal that guarantee that solutions of a switched linear systems converge asymptotically to zero. These conditions are apply to continuous, discrete-time and hybrid switched linear systems, both those…

We show that there exist smooth surfaces violating Generic Vanishing in any characteristic $p \geq 3$. As a corollary, we recover a result of Hacon and Kov\'acs, producing counterexamples to Generic Vanishing in dimension 3 and higher.

We show that geometric disorder leads to purely singular continuous spectrum generically. The main input is a result of Simon known as the ``Wonderland theorem''. Here, we provide an alternative approach and actually a slight strengthening…

We study the variable-length ensemble of self-avoiding walks on the complete graph. We obtain the leading order asymptotics of the mean and variance of the walk length, as the number of vertices goes to infinity. Central limit theorems for…

We establish a hidden extension in the Adams spectral sequence converging to the stable homotopy groups of spheres at the prime 2 in the 54-stem. This extension is exceptional in that the only proof we know proceeds via Pstragowski's…

A supersymmetry anomaly is found in the presence of non-perturbative fields. When the action is expressed in terms of the correct quantum variables, anomalous surface terms appear in its supersymmetric variation - one per each collective…

Vortex singularities in speckle patterns formed from random superpositions of waves are an inevitable consequence of destructive interference and are consequently generic and ubiquitous. Singularities are topologically stable, meaning they…

We prove persistence of absolutely continuous spectrum for the Anderson model on a general class of tree-like graphs.

A spectral singularity is a mathematical notion with an intriguing physical realization in terms of certain zero-width resonances. In optics it manifests as lasing at the threshold gain. We explore the application of their…