p****o
发帖数: 13 | 1 分析：Non-linear PDE. Toughest of the toughest. Obviously beyond human
ability.
代数：Let's check the buzzwords... Motivic Stuff，Quantum Stuff，Non-
commutative Stuff，Homotopic Stuff，Categorified Stuff. So, how about
Derived Motivic Non-commutative Homotopic Chromatic Higher q-Algebra?
几何：See algebra and analysis.
逻辑：This is not really a very "mathematical" topic...
数论：Stuffs related to the zeta function. On the other hand, everything is
related to the zeta function. |
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g****t
发帖数: 31659 | 2 逻辑和代数接近的那部分还是很有用的。
好猛得的线性PDE书上就有一些基本结论是逻辑的定理证明的。
分析：Non-linear PDE. Toughest of the toughest. Obviously beyond human
ability.
代数：Let's check the buzzwords... Motivic Stuff，Quantum Stuff，Non-
commutative Stuff，Homotopic Stuff，Categorified Stuff. So, how about
Derived Motivic Non-commutative Homotopic Chromatic Higher q-Algebra?
几何：See algebra and analysis.
逻辑：This is not really a very "mathematical" topic...
数论：Stuffs related to the zeta function. On the other hand, everything is
related to the |
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s*****V
发帖数: 21731 | 3 http://site.douban.com/130104/widget/notes/5389697/note/1820952
2011-11-03 23:35:00
我想谈谈过去五十年和我预测未来一百年的代数几何,我将一次次分开讨论,如果有兴趣
请支持:
1940-1965
代数几何在1900年以前,已经有了代数曲面的部分理论和代数曲线上的Riemann-Roch定
理,但是语言和概念处于一个混乱的状态.在1950到1965年间出现了三个巨大的革命.奠
定了代数几何的秩序描述了重要的问题,提供了未来发展的方向.她们是Hodge(加一堆人
)开创复几何, Kodaira的三大工作和Grothendieck的抽象语言及新定义(问题):
让我先讲第一项工作.
Hodge+Lefschetz+Kaehler考虑了复流形的定义和一般的性质,Kaehler引入了Kaehler度
量,Hodge利用了分析中着名的Elliptic regularity对Kaehler流形的上同调群作了至今
仍然神秘的Hodge分解,并且提出着名的Hodge猜想,Lefschetz证明了Hodge猜想的非常特
殊情形... 阅读全帖 |
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m******0
发帖数: 33 | 4 weyl conjecture,mordel conjecture, Milnor conjecture说明玄学还是有价值的啊
。不是太玄，是不够玄，我们要更玄,现在的什么非交换代数几何，homotopical
algebraic geometry，都没有脱离Grothendieck的思想，没有新的突破，derived
algebraic geometry是一场革新，新观念的引入才能 help solving old unsolved
problems，
Dennis Gaitsgory,Kevin Costello，Mike Hopkins这样的牛人，最近的工作也要受
Jacob Lurie 工作的启发。
some |
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h******3
发帖数: 1 | 5 不知哪位大侠有下面这本书的电子版：
Homotopic Topology
A. T. Fomenko , D. B. Fukes , V. L. Gutenmacher
仿佛这本名著绝版了...要有的话麻烦发到
y****[email protected]
万分感谢！ |
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D**o
发帖数: 2653 | 6 注意作者 \author{YHBKJ}
Atiyah-Bott Localization 1
2012-09-05 09:24:19
\documentclass[a4paper,12pt]{article}
\usepackage{amsfonts}
\usepackage{amsmath,amsthm,amssymb}
\usepackage{CJK,graphicx}
\usepackage{amscd}
\usepackage{amssymb}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}{Corollary}[section]
\newtheorem{definition}{Definition}[section]
\newtheorem{lemma}{Lemma}[section]
\begin{document}
\title{\textbf{\Huge{Atiyah-Bott Localization 1}}}\author{YHBKJ}\date{}\
maketitle
\begin{ab... 阅读全帖 |
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R**********n
发帖数: 523 | 7 http://lesniewski.us/papers/presentations/Bloomberg112505.pdf
page 34
or
http://arxiv.org/abs/0910.1671
We have embedded the classical theory of stochastic finance into a
differential geometric framework called Geometric Arbitrage Theory and show
that it is possible to:
--Write arbitrage as curvature of a principal fibre bundle.
--Parameterize arbitrage strategies by its holonomy.
--Give the Fundamental Theorem of Asset Pricing a differential homotopic
characterization.
--Characterize Geometric ... 阅读全帖 |
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