2008-02-05
年
还是对自己有个计划吧，不然生活少了目标，很枯燥的。
①看能否在同学给我的免费空间上安装好Wordpress，用Latex发布一系列的高等数学各章总结，希望对所有想把高等数学学好的朋友有所帮助。（这项工作比较困难）
②专业课也应该有所涉及，对实变函数和常微分方程希望也能做到各章总结
③学点经济学方面知识，看有否机会买点基金玩玩
④期待Gphone的出现，到时候就换手机
⑤丰富单身生活，多看看文学方面的书籍，自己这方面太缺乏了
⑥还有一些经典的电影，多看，多想。老觉得现在脑子已经没有那么灵活老
⑦暑假出去休息，看看祖国大好河山
⑧最后当然不能忘的是把本职工作做好，教好书
我这个人比较懒，呼呼……
就这些吧，新年新气象，新年新希望，新年新目标，新年……
2008-02-04
2008-02-03
THE 2008 WOLF FOUNDATION PRIZE IN MATHEMATICS
The Prize Committee for Mathematics has unanimously decided that the 2008 Wolf Prize will be jointly awarded to:
Pierre R. Deligne
Institute for Advanced Study
Princeton, New Jersey, USA
for his work on mixed Hodge theory; the Weil conjectures; the Riemann-Hilbert correspondence; and for his contributions to arithmetic.
Phillip A. Griffiths
Institute for Advanced Study
Princeton, New Jersey, USA
for his work on variations of Hodge structures; the theory of periods of abelian integrals; and for his contributions to complex differential geometry.
David B. Mumford
Brown University
Providence, Rhode Island, USA
for his work on algebraic surfaces; on geometric invariant theory; and for laying the foundations of the modern algebraic theory of moduli of curves and theta functions.
Central to modern algebraic geometry is the theory of moduli, i.e., variation of algebraic or analytic structure. This theory was traditionally mysterious and problematic. In critical special cases, i.e., curves, it made sense, i.e., the set of curves of genus greater than one had a natural algebraic structure. In dimensions greater than one, there was some sort of structure locally, but globally everything remained mysterious. The two main (and closely related) approaches to moduli were invariant theory on the one hand and periods of abelian integrals on the other. This key problem was tackled and greatly elucidated by Deligne, Griffiths, and Mumford.
Professor David B. Mumford revolutionized the algebraic approach through invariant theory, which he renamed 'geometric invariant theory.' With this approach, he provided a complicated prescription for the construction of moduli in the algebraic case. As one application he proved that there were a set of equations defining the space of curves, with integer coefficients. Most important, Mumford showed that moduli spaces, though often very complicated, exist except for what, after his work, are well-understood exceptions. This framework is critical for the work by Griffiths and Deligne. Classically, the moduli space of curves was parameterized by using periods of the abelian integrals on them. Mathematicians, e.g., the Wolf Prize winner Andre Weil, have unsuccessfully tried to generalize the periods to higher dimensions.
Professor Phillip A. Griffiths had the fundamental insight that the Hodge filtration measured against the integer homology generalizes the classical periods of integrals. Moreover, he realized that the period mapping had a natural generalization as a map into a classifying space for variations of Hodge structure, with a new non-classical restriction imposed by the Kodaira-Spencer class action. This led to a great deal of work in complex differential geometry, e.g., his basic work with Deligne, John Morgan, and Dennis Sullivan on rational homotopy theory of compact Kaehler manifolds.
Building on Mumford's and Griffiths' work, Professor Pierre R. Deligne demonstrated how to extend the variation of Hodge theory to singular varieties. This advance, called mixed Hodge theory, allowed explicit calculation on the singular compactification of moduli spaces that came up in Mumford's geometric invariant theory, which is called the Deligne-Mumford compactification. These ideas assisted Deligne in proving several other major results, e.g., the Riemann-Hilbert correspondence and the Weil conjectures.