Spriger 刚刚出版了三卷本的 “Geometric Trilogy: Axiomatic, Algebraic and Differential Approaches to Geometry“, 作者 Francis Borceux.

Geometric Trilogy

• Focuses on historical aspects;
• Supports contemporary approaches of the three aspects of axiomatic geometry: Euclidean, non-Euclidean and projective;
• Includes full solutions to all famous historical problems of classical geometry and hundreds of figures.

## An Algebraic Approach to Geometry

Unified treatment of the various algebraic approaches of geometric spaces; Provides a full treatment, perfectly accessible at a bachelor level, of all algebraic ingredients necessary to develop all the major aspects of  the theory of algebraic curves.

## A Differential Approach to Geometry

Pays particular attention to historical development and preliminary approaches that support the contemporary geometrical notions; Links classical surface theory in the three dimensional real space to modern Riemannian geometry.

4.  Wilhelm Klingenberg, A Course in  Differential Geometry, GTM51

5.  Wolfgang Kühnel, Differential Geometry: Curves – Surfaces – Manifolds, Second Edition

Gang Tian(田刚) has just uploaded to the arXiv his paper “K-stability and Kähler-Einstein metrics“(Nov 20, 2012). The motivation of this paper is:
“In this paper, we prove that if a Fano manifold $$M$$ is K-stable, then it admits a Kähler-Einstein metrics. It affirms a folklore conjecture. Our result and its outlined proof were lectured on Oct. 25 of 2012 during the Blainefest at Stony Brook University.”

“This is the first of a series of three papers which provide proofs of results announced recently in arXiv:1210.7494.”

28 日, Xiu-Xiong Chen(陈秀雄), Simon Donaldson, Song Sun(孙崧, 很年轻, 曾在科大少年班就读) 在 arxiv 上传了一篇文章 “Kähler-Einstein metrics and stability“, 给出了一个证明 K-稳定的 Fano 流形容许 Kähler-Einstein 度量(Yau-Tian-Donaldson conjecture)的轮廓, 工具是 Donaldson 新发展的连续性方法:
“We annnounce a proof of the fact that a K-stable Fano manifold admits a Kähler-Einstein metric and give a brief outline of the proof.”

2002年, 安徽省怀宁中学读高二的孙崧获得全国高中学生化学竞赛二等奖.  同年他参加高考, 成为怀宁县考进科大少年班的第一人.