Related papers: Adelic descent for continuous localizing invariant…

We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.

We prove a stability theorem for spaces of smooth concordance embeddings. From it we derive various applications to spaces of concordance diffeomorphisms and homeomorphisms.

We define $k$-rationalized $G$-equivariant elliptic cohomology, for a field of characteristic zero $k$ and a compact Lie group $G$, via adelic descent. We also give adelic descriptions of rationalized $G$-equivariant singular cohomology and…

In this work, we analyze the regularizing property of the stochastic gradient descent for the efficient numerical solution of a class of nonlinear ill-posed inverse problems in Hilbert spaces. At each step of the iteration, the method…

In this short note, we will show that the metric of Deligne's pairing is continous.

Base on a conjecture, we prove that for any smooth separated stack of finite type over a number field, its descent obstruction equals its iterated descent obstruction. As a consequence, we show that for any algebraic stack over a number…

We introduce descent methods to the study of strong approximation on algebraic varieties. We apply them to two classes of varieties defined by P(t)=N_{K/k}(z): firstly for quartic extensions of number fields K/k and quadratic polynomials…

We construct the equivariant version of cd-structures, and we develop descent theory for topologies comes from equivariant cd-structures. In particular, we reprove several results of Cisinski-D\'eglies on the \'etale descent, qfh-descent,…

A proof of Sendov's conjecture is given.

Convergence of an adaptive collocation method for the stationary parametric diffusion equation with finite-dimensional affine coefficient is shown. The adaptive algorithm relies on a recently introduced residual-based reliable a posteriori…

We show that equivariant K-theory satisfies descent with respect to the isovariant Nisnevich topology. The main step is to show that the isovariant Nisnevich topology is a regular, complete and bounded cd topology.

In this note, we provide a short proof of Feige's conjecture for identically distributed random variables.

We prove some general theorems for preserving Dependent Choice when taking symmetric extensions, some of which are unwritten folklore results. We apply these to various constructions to obtain various simple consistency proofs.

We introduce a proximal version of dual coordinate ascent method. We demonstrate how the derived algorithmic framework can be used for numerous regularized loss minimization problems, including $\ell_1$ regularization and structured output…

We study algebras on which the Berenstein-Zelevinsky conjecture is true. In particular, we prove that this conjecture is true "up to localization".

We prove relative versions of many earlier results about almost invariant sets and splittings of groups. In particular, we prove a relative version of the algebraic torus theorem, and we prove the existence and uniqueness of relative…

Descent polynomials and peak polynomials, which enumerate permutations with given descent and peak sets respectively, have recently received considerable attention. We give several formulas for $q$-analogs of these polynomials which refine…

We revisit a subexponential bound for the $abc$ conjecture due to the first author, and we establish a variation of it using linear forms in logarithms. As an application, we prove an unconditional subexponential bound towards the $4$-terms…

We present a theory of Anderson localization on a one-dimensional lattice with translation-invariant hopping. We find by analytical calculation, the localization length for arbitrary finite-range hopping in the single propagating channel…

We determine conditions for the invariance of the gonality under base extension, depending on the numeric invariants of the curve. More generally, we study the Galois descent of morphisms of curves to Brauer-Severi varieties, and also of…