Discrete Projective Differential Geometry: Comprehensive Theory and Integrable Structure

微分几何已经发展了几个世纪的最杰出的数学家和它的适用性在数学和物理科学是毫无疑问的。然而，自然和人造结构本质上都是离散的。离散微分几何构成了一个相对较新的和活跃的研究领域位于纯数学和应用数学之间，它比微分几何更基本，因为它的目的是建立一个自治的离散模拟，微分几何可以通过适当的连续极限导出。尽管离散微分几何已经达到了高度的复杂性，这个项目旨在提供在这一领域的第一个全面的理论。

Differential geometry has been developed over centuries by the most distinguished of mathematicians and its applicability in the mathematical and physical sciences is beyond doubt. However, both natural and man-made structures are inherently discrete. Discrete differential geometry constitutes a relatively new and active research area located between pure and applied mathematics which is more fundamental than differential geometry in that it aims to establish an autonomous discrete analogue from which differential geometry may be derived via an appropriate continuum limit. Even though discrete differential geometry has reached a high degree of sophistication, this project seeks to deliver the first comprehensive theory in this area.