Knots in Poland III; the conference on Knot Theory and its Ramifications

波兰的结 III;

基本信息

  • 批准号:
    1034753
  • 负责人:
  • 金额:
    $ 2.8万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2010
  • 资助国家:
    美国
  • 起止时间:
    2010-07-01 至 2011-06-30
  • 项目状态:
    已结题

项目摘要

AbstractAward: DMS-1034753Principal Investigator: Jozef H. Przytycki, Mikhail G. KhovanovThis proposal asks for financial support for US based participants, for a 3-week long summer program devoted to Knot Theory: Knots in Poland III: conference on Knot Theory and its Ramifications. It will be a conference interspersed with specialized workshops and tutorials. It will be third conference in the series of large, very successful international conferences ``Knots in Poland". The conferences will take place in Warsaw July 18-25 and in Banach Center in Bedlewo July 25-August 4, 2010. Specifically, we propose to support about 15 graduate students and 10 mathematicians without grant. As part of the conference we will have a series of 3 talks by Tom Mrowka on his proof that Khovanov homology can be understood as a page in a spectral sequence converging to a version of Instanton Floer homology. A consequence of this is that Khovanov homology detects the unknot. Knots have fascinated people from the dawn of the human history. Much of the early knot theory was motivated by physics and chemistry (e.g. Kelvin theory of vortex atoms). The fundamental problem in knot theory is to be able to distinguish non-equivalent knots. There have been exciting new developments in the area of Knot Theory in recent years. From the Jones, Homflypt, and Kauffman polynomials, through quantum invariants of 3-manifolds, Topological Quantum Field Theories, to relations with gauge theory type invariants in 4-dimensional topology (Donaldson, Witten, etc). More recently, Khovanov introduced homology theory of links which categorifies the Jones polynomial (a chain complex is build on the Kauffman model of the Jones polynomial). Soon after, Ozsvath and Szabo developed Heegaard-Floer homology, that lifts the Alexander polynomial. These two significantly different theories are closely related and the dependencies are the object of intensive study. One can mention here Khovanov-Rozansky categorification of Homflypt polynomial, categorification of the Kauffman bracket skein module of some 3-dimensional manifolds, and the result of T.Mrowka that Khovanov homology detects the unknot.The subject has significant applications and relations withbiology, physics, chemistry and the theory of computation. Wefeel that a conference on this subject is highly appropriate atthis time, and we strive to be in the frontier of new developmentin knot theory and its ramifications. The project has broaderimpact in several aspects. Knots in Poland conference bringstogether from all over the word, third-world countries, formerSoviet Union, minorities, women, and provides an opportunity forresearchers and students to share their latest ideas and tocollaborate with each other. The knowledge obtained on thisoccasion will be disseminated by participants throughout theworld. Distinguished researchers (including about 10 woman) willdeliver plenary talks surveying the state of knowledge related toKnot Theory and its Ramifications. PhD students and fresh PhD'swill be encouraged to attend. We expect to publish conferenceproceedings (as we did in the past) containing cutting-edgeresearch papers and lecture notes which will be suitable forresearch mathematicians, students and readers with background inother exact sciences, including biology, chemistry, computerscience, and physics. Conference Web Page:http://www.mimuw.edu.pl/~traczyk/knotpol2010/http://www.mimuw.edu.pl/%7Etraczyk/knotpol2010/
摘要奖:DMS-1034753主要研究者:Jozef H. Przytycki,Mikhail G. Khovanov此提案要求为美国的参与者提供财政支持,为3个星期的夏季计划,致力于结理论:结在波兰III:结理论及其分支会议。 这将是一个会议穿插专业研讨会和教程。 这将是“波兰结”系列大型、非常成功的国际会议中的第三次会议。 会议将于2010年7月18日至25日在华沙和7月25日至8月4日在Bedlewo的巴拿赫中心举行。具体而言,我们建议支持约15名研究生和10名数学家没有补助金。 作为会议的一部分,我们将有一系列的3会谈汤姆Mrowka对他的证明,Khovanov同源性可以理解为一个页面的频谱序列收敛到一个版本的Instanton Floer同源性。 这样的结果是Khovanov同源性检测到解结。 结从人类历史的黎明就吸引了人们。 许多早期的纽结理论是由物理和化学激发的(例如开尔文涡旋原子理论)。纽结理论的基本问题是能够区分不等价的纽结。近年来,纽结理论领域出现了令人兴奋的新发展。从琼斯,Homflypt和考夫曼多项式,通过量子不变量的3流形,拓扑量子场论,关系与规范理论类型不变量的4维拓扑(唐纳森,维滕等)。 最近,Khovanov引入了链接的同调理论,将琼斯多项式归类(链复合体建立在琼斯多项式的考夫曼模型上)。 不久之后,Ozsvath和Szabo开发了Heegaard-Floer同源性,提升了亚历山大多项式。这两个显著不同的理论是密切相关的,依赖关系是深入研究的对象。这里可以提到Homflypt多项式的Khovanov-Rozansky范畴化,某些三维流形的Kauffman括号skein模的范畴化,以及T.Mrowka关于Khovanov同调检测unknot的结果,该课题与生物学、物理学、化学和计算理论有着重要的应用和联系。 我们认为,在这个时候召开一个关于这个主题的会议是非常合适的,我们努力站在纽结理论及其分支新发展的前沿。 该项目在几个方面具有广泛的影响。 波兰的节点会议带来了来自世界各地的人,第三世界国家,前苏联,少数民族,妇女,并为研究人员和学生提供了一个机会,分享他们的最新想法,并相互合作。在这次会议上获得的知识将由世界各地的与会者传播。 杰出的研究人员(包括约10名妇女)将提供全体会议的讲话,调查有关知识的状态tokot理论及其分支。 博士生和新博士将被鼓励参加。 我们希望出版会议记录(就像我们过去所做的那样),其中包含尖端的研究论文和演讲稿,这些论文和演讲稿适合于研究数学家,学生和具有其他精确科学背景的读者,包括生物学,化学,计算机科学和物理学。 会议网页:http://www.mimuw.edu.pl/~traczyk/knotpol2010/http://www.mimuw.edu.pl/%7Etraczyk/knotpol2010/

项目成果

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Jozef Przytycki其他文献

Linking numbers in rational homology 3-spheres, cyclic branched covers and infinite cyclic covers
有理同源 3 球体、循环分支覆盖和无限循环覆盖中的连接数

Jozef Przytycki的其他文献

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{{ truncateString('Jozef Przytycki', 18)}}的其他基金

Knots in Washington XLI: a Conference Series on Knot Theory and its Ramifications; November 13-15, 2015
华盛顿的结 XLI:关于结理论及其衍生的会议系列;
  • 批准号:
    1543617
  • 财政年份:
    2015
  • 资助金额:
    $ 2.8万
  • 项目类别:
    Standard Grant
Knots in Washington: Conferences on Knot Theory and its Ramifications
华盛顿的结:结理论及其影响的会议
  • 批准号:
    1137422
  • 财政年份:
    2011
  • 资助金额:
    $ 2.8万
  • 项目类别:
    Standard Grant
Knots in Washington: Conferences on Knot Theory and its Ramifications 2008-2010
华盛顿结:结理论及其影响 2008-2010 年会议
  • 批准号:
    0817858
  • 财政年份:
    2008
  • 资助金额:
    $ 2.8万
  • 项目类别:
    Standard Grant
Knots in Washington XXI: Skein Modules, Khovanov Homology and Hochschild Homology
华盛顿结 XXI:绞纱模块、Khovanov 同源性和 Hochschild 同源性
  • 批准号:
    0555648
  • 财政年份:
    2006
  • 资助金额:
    $ 2.8万
  • 项目类别:
    Standard Grant
Knots in Washington XVIII: Khovanov homology
华盛顿结十八:霍瓦诺夫同源性
  • 批准号:
    0432284
  • 财政年份:
    2004
  • 资助金额:
    $ 2.8万
  • 项目类别:
    Standard Grant
Topics in Algebraic Topology Based on Knots
基于结的代数拓扑专题
  • 批准号:
    9808955
  • 财政年份:
    1999
  • 资助金额:
    $ 2.8万
  • 项目类别:
    Standard Grant

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