This is a tutorial on some aspects of toric varieties related to their potential use in geometric modeling. We discuss projective toric varieties and their ideals, as well as real toric varieties and the moment map. In particular, we explain the relation between linear precision and the moment map.

We trace progress and thinking about the Strominger-Yau-Zaslow conjecture since its introduction in 1996. In particular, we aim to explain how the conjecture led to the algebro-geometric program developed by myself and Siebert, whose objective is to explain mirror symmetry by studying degenerations of Calabi-Yau manifolds. We end by outlining how tropical curves arise in the mirror symmetry story.

We show that a recently proposed password authentication scheme based on geometric hashing has several security weaknesses, and that the use of this scheme should be avoided in practice.

This paper explores the use of assumptions to build multiple models about sustainable development in a compositional way. It presents a model aiming at supporting stakeholders to improve their understanding about a water basin system under the pressure of changes in land use. Domain knowledge is approached from three perspectives: urban, semi-urban and rural. Simulations explore sustainability ...

We show how the Gaussian min-max theorem provides direct proofs of several famous results in asymptotic geometric analysis, such as, the Dvoretzky theorem, the Johnson-Lindenstrauss Lemma, Gluskin’s theorem on embedding in `1 , and others.

The subject of geometric analysis evolves according to our understanding of geometry and analysis. However, one should say that ideas of algebraic geometry and representation theory have been extremely powerful in both global and local geometry. In fact, the spectacular idea of using geometry to understand Diophantine problem has already widened our concept of space. The desire to find suitable...

A functional composition of the cumulative distribution function of one probability distribution with the inverse cumulative distribution function of another is called the transmutation map. In this article, we will use the quadratic rank transmutation map (QRTM) in order to generate a flexible family of probability distributions taking Lindley-geometric distribution as the base value distribut...

Motivated by the problem of efficiently collecting data from wireless sensor networks via a mobile sink, we present an accelerated random walk on Random Geometric Graphs. Random walks in wireless sensor networks can serve as fully local, lightweight strategies for sink motion that significantly reduce energy dissipation but introduce higher latency in the data collection process. In most cases ...

We develop the theory of the nonadiabatic geometric phase, in both the Abelian and non-Abelian cases, in quaternionic Hilbert space.