Related papers: The Minimal Genus Problem

Given its briefness and predictability, the minimal seesaw -- a simplified version of the canonical seesaw mechanism with only two right-handed neutrino fields -- has been studied in depth and from many perspectives, and now it is being…

We study a variational problem motivated by models of species population density in a nonhomogeneous environment. We first analyze local minimizers and the structure of the saturated region (where the population attains its maximal density)…

During the last years, low-rank tensor approximation has been established as a new tool in scientific computing to address large-scale linear and multilinear algebra problems, which would be intractable by classical techniques. This survey…

In this short note, we construct a minimally intersecting pair of simple closed curves that fill a genus 2 surface with an odd, greater than 3, number of punctures. This finishes the determination of minimally intersecting filling pairs for…

We introduce the notion of evolution on sets and study several sets endowed with this structure and obtain some results about this new notion.

In this paper we consider convergence of approximate solutions of conservation laws. We start with an overview over the historical developments since the 1950s, and the analytical tools used in this context. Then we present some of our own…

These lecture notes introduce key concepts of mathematical population genetics within the most elementary setting and describe a few recent applications to microbial evolution experiments. Pointers to the literature for further reading are…

We discuss various recent advances on weak forms of the Twin Prime Conjecture.

The aim of this survey article is to cover most of the recent research on preopen sets. I try to present majority of the results on preopen sets that I am aware of.

In this note we investigate the complexity of the Minimum Label Alignment problem and we show that such a problem is APX-hard.

We consider numerical approximation to the solution of non-autonomous evolution equations. The order of convergence of the simplest possible Magnus method will be investigated.

This is a survey of recent and classical results concerning various types of homogeneity, such as n-homogeneity, discrete homogeneity, and countable dense homogeneity. Some new results are also presented, and several problems are posed.

Some simple nonlinear recursions which can be completely managed are identified and the behaviour of all their solutions is ascertained.

We survey recent results on Calderon's inverse problem with partial data, focusing on three and higher dimensions.

This article studies the possible degenerations of plane Cremona transformations of some degree into maps of smaller degree.

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…

I address the need for deep blazar surveys by showing that our current understanding of blazars is based on a relatively small number of intrinsically luminous sources. I then review the on-going deeper surveys, addressing in particular…

By a recent result obtained by R. Howlett and the author considerable progress has been made towards a complete solution of the isomorphism problem for Coxeter groups. In this paper we give a survey on the isomorphism problem and explain in…

We survey the history of the capset problem in the context of related results on progression-free sets, discuss recent progress, and mention further directions to explore.

By some new recursive algorithms, in this paper, we will give some improvements on Waring's problem.