相关论文: Techniques for the Analytic Proof of the Finite Ge…

Controlled topology is one of the main tools for proving the isomorphism conjecture concerning the algebraic $K$-theory of group rings. In this article we dive into this machinery in two examples: when the group is infinite cyclic and when…

This paper is a follow-up to our joint paper with I. Agol, P. Storm and K. Whyte "Finiteness of arithmetic hyperbolic reflection groups". The main purpose is to investigate the effective side of the method developed there and its possible…

It is well-known that every regular language admits a unique minimal deterministic acceptor. Establishing an analogous result for non-deterministic acceptors is significantly more difficult, but nonetheless of great practical importance. To…

For a projective curve $C$ and the canonical divisor $K_C$ on $C$, it is classically known that the canonical ring $R(C) = \oplus_{m=0}^\infty H^0(C, m K_C)$ is finitely generated in degree at most three. In this article, we study whether…

A novel approach is introduced to a very widely occurring problem, providing a complete, explicit resolution of it: minimisation of a convex quadratic under a general quadratic, equality or inequality, constraint. Completeness comes via…

In PODS'21, Hu presented an algorithm in the massively parallel computation (MPC) model that processes any acyclic join with an asymptotically optimal load. In this paper, we present an alternative analysis of her algorithm. The novelty of…

The computation of the fundamental group of the complement of an algebraic plane curve has been theoretically solved since Zariski-van Kampen, but actual computations are usually cumbersome. In this work, we describe the notion of Wirtinger…

Conjecturing and theorem proving are activities at the center of mathematical practice and are difficult to separate. In this paper, we propose a framework for completing incomplete conjectures and incomplete proofs. The framework can turn…

We discuss the relationship among various conjectures in the minimal model theory including the finite generation conjecture of the log canonical rings and the abundance conjecture. In particular, we show that the finite generation…

Let $U$ be an open relatively compact subanalytic subset of a real analytic manifold. We show that there exists a finite linear covering (in the sense of Guillermou and Schapira) of $U$ by subanalytic open subsets of $U$ homeomorphic to a…

Compact sets in constructive mathematics capture our intuition of what computable subsets of the plane (or any other complete metric space) ought to be. A good representation of compact sets provides an efficient means of creating and…

We discuss the relative log minimal model theory for log surfaces in the analytic setting. More precisely, we show that the minimal model program, the abundance theorem, and the finite generation of log canonical rings hold for log pairs of…

This paper presents an alternative proof of the Fundamental Theorem of Algebra that has several distinct advantages. The proof is based on simple ideas involving continuity and differentiation. Visual software demonstrations can be used to…

We give a necessary and sufficient condition on a $d$-dimensional affine subspace of $\mathbb{R}^n$ to be characterized by a finite set of patterns which are forbidden to appear in its digitization. This can also be stated in terms of local…

This article discusses the recent transcendental techniques used in the proofs of the following three conjectures. (1)~The plurigenera of a compact projective algebraic manifold are invariant under holomorphic deformation. (2)~There exists…

In this chapter we describe a selection of mathematical techniques and results that suggest interesting links between the theory of gratings and the theory of homogenization, including a brief introduction to the latter. By no means do we…

The aim of this paper is to extend the structure theory for infinitely generated modules over tame hereditary algebras to the more general case of modules over concealed canonical algebras. Using tilting, we may assume that we deal with…

Some of the more powerful results of mathematical statistics are becoming of increasing importance in statistical mechanics. Here the use of the central limit theorem in conjunction with the canonical ensemble is shown to lead to an…

This paper develops techniques for producing presentations of upper cluster algebras. These techniques are suited to computer implementation, and will always succeed when the upper cluster algebra is totally coprime and finitely generated.…

We construct canonical frames and find all maximally symmetric models for a natural generic class of corank 2 distributions on manifolds of odd dimension greater or equal to 7. This class of distributions is characterized by the following…