Related papers: Weil-Petersson Metric Geometry Quick Overview

The goal of this article is to survey recent developments in the theory of contact structures in dimension three.

Some of the most important theoretical and phenomenological aspects of the pinch technique are presented, and several recent developments are briefly reviewed.

We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the…

We review recent results and ongoing investigations of the symplectic and Poisson geometry of derived moduli spaces, and describe applications to deformation quantization of such spaces.

We chart out the landscape of $\Winfty$-type algebras using $\Wkpq$---a recently discovered one-parameter deformation of $\W_{\rm KP}$. We relate all hitherto known $\Winfty$-type algebras to $\Wkpq$ and its reductions, contractions, and/or…

In this paper, we mainly discuss some generalized metric properties and the character of the free paratopological groups, and extend several results valid for free topological groups to free paratopological groups.

We examine relations between geometry and the associated curvature decompositions in Weyl geometry.

Ways to access transversity through asymmetry measurements are reviewed. The recent first extraction and possible near future extractions are discussed.

A review of recent developments in the analyses of supersymmetric dark matter is given.

A brief introduction to geometric valuation theory is given. The focus is on classification results for valuations on convex bodies and on function spaces.

The notion of a spectral geometry on a compact metric space X is introduced. This notion serves as a discrete approximation of X motivated by the notion of a spectral triple from non-commutative geometry. A set of axioms charaterising…

This paper will appear in the Proceedings of the 1995 Santa Cruz Summer Institute. The paper is a survey of recent developments in the theory of toric varieties, including new constructions of toric varieties and relations to symplectic…

A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.

This article provides a survey on some main results and recent developments in the mathematical theory of water waves. More precisely, we briefly discuss the mathematical modeling of water waves and then we give an overview of local and…

These notes are an expanded version of an introductory lecture on contact geometry given at the 2001 Georgia Topology Conference. They are intended to present some of the "topological" aspects of three dimensional contact geometry.

We propose a unifying framework for generalising the Wasserstein-1 metric to a discrepancy measure between nonnegative measures of different mass. This generalization inherits the convexity and computational efficiency from the…

We survey some recent geometric methods for studying Heegaard splittings of 3-manifolds

Nonlinear analysis has played a prominent role in the recent developments in geometry and topology. The study of the Yang-Mills equation and its cousins gave rise to the Donaldson invariants and more recently, the Seiberg-Witten invariants.…

We compute the p-widths, $\{\omega_p\}$, for the real projective plane with the standard metric.

In this expository paper we present a brief introduction to the geometrical modeling of some quantum computing problems. After a brief introduction to establish the terminology, we focus on quantum information geometry and ZX-calculus,…