Related papers: Adelic descent for continuous localizing invariant…

We prove the Invariant Subspace Conjecture for separable Hilbert spaces.

We prove an adelic descent result for localizing invariants: for each Noetherian scheme $X$ of finite Krull dimension and any localizing invariant $E$, e.g., algebraic K-theory of Bass-Thomason, there is an equivalence $E(X)\simeq \lim…

We give here a proof of the convergence of the Stochastic Gradient Descent (SGD) in a self-contained manner.

We provide a new proof of Alesker's Irreducibility Theorem. We first introduce a new localization technique for polynomial valuations on convex bodies, which we use to independently prove that smooth and translation invariant valuations are…

We prove inversion of adjunction on log canonicity.

We prove descent theorems for semiorthogonal decompositions using techniques from derived algebraic geometry. Our methods allow us to capture more general filtrations of derived categories and even marked filtrations, where one descends not…

In this article we give a totally new proof of the integral localization formula for equivariantly closed differential forms (Theorem 7.11 in [BGV]). We restate it here as Theorem 2. This localization formula is very well known, but the…

The paper proposes and motivates a conjecture on the invariance of cohomological support loci under derived equivalence. It contains a proof in the case of surfaces, and explains further developments and consequences.

In this article some explicit estimates on the decay of the convolutive inverse of a sequence are proved. They are derived from the functional calculus for Sobolev algebras. Applications include localization in spline-type spaces and…

We derive a simple lower bound for the multi-version coding problem formulated in [1]. We also propose simple algorithms that almost match the lower bound derived. Another lower bound is proven for an extended version of the multi-version…

We establish a convergence theorem for a certain type of stochastic gradient descent, which leads to a convergent variant of the back-propagation algorithm

In this expository article, we explain how to use localization to compute Gromov-Witten invariants of smooth toric varieties and orbifold Gromov-Witten invariants of smooth toric Deligne-Mumford stacks.

We prove a stability version of the Pr\'ekopa-Leindler inequality.

We provide a proof of a variant of the Landau-Siegel Zeros conjecture.

The characteristic feature of the adeles is that they involve localizations of products (or equivalently restricted products of localizations). The point of this paper is to introduce an adelic style cohomological invariant of a partially…

We propose some adaptive mirror descent dethods for convex programming problems with delta-subgradients and prove some theoretical results.

A lower bound for the interleaving distance on persistence vector spaces is given in terms of rank invariants. This offers an alternative proof of the stability of rank invariants.

We prove that the construction of our previous paper math.QA/0103190 yields an invariant of tangle cobordisms.

In this paper, we present a fast and effective method for solving the Poisson-modified total variation model proposed in [9]. The existence and uniqueness of the model are again proved using different method. A semi-implicit difference…

We present a method for hedging in continuous time.