Related papers: The Minimal Genus Problem
The mapping class group of an orientable surface, which records its symmetries up to isotopy, plays a central role in low-dimensional topology. This chapter explores the foundational problem of determining minimal generating sets for these…
We give a survey of recent results, due mainly to the authors, concerning Bernstein-Markov type inequalities and connections with potential theory.
We provide a variational derivation of the limit shape of minimal difference partitions and discuss the link with exclusion statistics. Also see arXiv:0707.2312 for a related paper.
This document is a brief summary of progress that has been made on the problems posed in the document "Twenty Open Problems in Enumeration of Matchings" (also available from this server as math.CO/9801060). NOTE: This article has now been…
In this paper, we show that the low rank matrix completion problem can be reduced to the problem of finding the rank of a certain tensor.
The talk contains a brief introduction string theory, followed by a discussion of some of the recent developments.
Let $G$ be a finite group. In order to determine the smallest cardinality $d(G)$ of a generating set of $G$ and a generating set with this cardinality, one should repeat many times the test whether a subset of $G$ of small cardinality…
Baryogenesis via leptogenesis provides an appealing mechanism to explain the observed baryon asymmetry of the Universe. Recent refinements in the understanding of the dynamics of leptogenesis include detailed studies of the effects of…
We give a light introduction to some recent developments in Mori theory, and to our recent direct proof of the finite generation of the canonical ring.
In various research papers, such as [2], one will find the claim that the minLA is optimally solvable on outerplanar graphs, with a reference to [1]. However, the problem solved in that publication, which we refer to as the planar minimum…
This article reviews and discusses 1) the discovery and early work on the evolution of quasars and AGNs, 2) the different techniques used to find quasars and their suitability for evolutionary studies, 3) the current status of our knowledge…
A class of variational models describing ecological systems of k species competing for the same resources is investigated. The occurrence of coexistence in minimal energy solutions is discussed and positive results are proven for suitably…
We discover a family of closed, embedded minimal surfaces in the three-dimensional round sphere which includes new examples with low genus. The existence proof relies on an equivariant min-max procedure applied to a novel sweepout which is…
In a recent issue of this journal, Mordukhovich et al.\ pose and solve an interesting non-differentiable generalization of the Heron problem in the framework of modern convex analysis. In the generalized Heron problem one is given $k+1$…
In this paper we consider models for genus one curves of degree n for n = 2, 3 and 4, which arise in explicit n-descent on elliptic curves. We prove theorems on the existence of minimal models with the same invariants as the minimal model…
The minimum rank problem for a (simple) graph $G$ is to determine the smallest possible rank over all real symmetric matrices whose $ij$th entry (for $i\neq j$) is nonzero whenever $\{i,j\}$ is an edge in $G$ and is zero otherwise. This…
We give a short survey of recent LHC experiments and related theory topics concerning the Odderon problem.
We compare the minimal model of a log canonical pair with the minimal model of its reduced boundary. These results are then used to study the existence of the minimal model of a semi-log-canonical pair using its normalization.
We survey recent progress on the birational geometry of foliations on complex varieties. We focus on the MMP viewpoint: singularities, adjunction and applications to the MMP for foliations on surfaces and to the existence of flips on…
The population of distant dusty submm-luminous galaxies was first detected last year (Smail, Ivison and Blain 1997). Forms of evolution required to account for both this population and the intensity of background radiation have now been…