Riemannian Manifolds with positive sectional curvature

TL;DR

This paper surveys recent mathematical results on Riemannian manifolds with positive sectional curvature, providing historical context and summarizing key developments in the field.

Contribution

It compiles and discusses recent advances and historical insights on manifolds with positive curvature from a series of lectures.

Findings

Summary of recent results in positive curvature manifolds

Historical comments on the development of the field

Highlights of key open problems and conjectures

Abstract

This is a survey of recent results on manifolds with positive curvature from a series of lecture given in Guanajuato, Mexico in 2010. It also contains some hitsorical comments.