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
• 负责人: Jozef Przytycki
• 金额: $ 8.4万
• 依托单位: George Washington University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-09-01 至 2019-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1543617&HistoricalAwards=false
• 关键词: Knots; Washington; XLI; Conference; Series

There will be six conferences over the next three-year period. This is a continuation of a very successful conference series "Knots in Washington", with a conference held every semester in the greater Washington DC area since Fall 1995. The first conference funded under this grant (and the 51st conference in the series) will be held in Fall 2015. The series will provide opportunity for researchers in the area to share their latest ideas and to collaborate with each other. The presentations will include plenary talks by distinguished researchers, as well as short talks by various participants. Graduate students and recent PhDs will also be encouraged to attend. Over the years, we have attracted a large number of postdocs, graduate students, and even some undergraduate students. In the greater Washington DC area, the series helps to bring together the relevant researchers, and to boost research activities in the region. Internationally, "Knots in Washington" has attracted researchers from all over the world, and is now considered a major conference in knot theory and low-dimensional topology. We expect to publish conference proceedings (as we did in the past) containing cutting-edge research papers and lecture notes that will be suitable for research mathematicians, students, and readers with background in other exact sciences, including physics, computer science, biology, and chemistry. The next conference will focus on the connections between Khovanov homology, homology of distributive structures, Yang-Baxter homology, and Quantum Computing, as well as on the general idea of categorification, including categorification of skein modules. There have been exciting new developments in the area of knot theory and 3-manifold topology in the last 35 years -- from Jones polynomial and quantum invariants of 3-manifolds, through Vassiliev invariants, topological quantum field theories, to relations with gauge theory type invariants in 4-dimensional topology (e.g., Donaldson, Witten). More recently, a new development in quantum topology has emerged in the form of Khovanov homology, a generalization of the Jones type polynomials to homology of chain complexes that significantly generalizes the invariants. Also, the categorification of the Kauffman bracket skein module of 3-manifolds has been proposed and developed for some manifolds. The relation to Hochschild homology of algebras has been discovered and studied. The (quantum) complexity of computing the Jones polynomial and Turaev-Viro invariants have been analyzed. Knots in Washington will provide a place for researchers in the above mentioned areas to communicate with each other and work together. The organizers will strive to be at the frontier of new developments in knot theory and its ramifications. Distinguished researchers will give plenary talks surveying the state of knowledge related to Khovanov homology. The choice of conference topics will also reflect the strength of the topology group at the George Washington University. Conference Web Page: http://home.gwu.edu/~przytyck/knots/index.html

在今后三年期间将举行六次会议。这是一个非常成功的会议系列"结在华盛顿"的延续，自1995年秋季以来，每学期在大华盛顿特区地区举行一次会议。第一次会议资助下，该赠款（和该系列的第51次会议）将在秋季2015年举行。该系列将为该领域的研究人员提供机会，分享他们的最新想法并相互合作。演讲将包括杰出研究人员的全体会议，以及各种与会者的简短演讲。研究生和最近的博士也将被鼓励参加。多年来，我们吸引了大量的博士后，研究生，甚至一些本科生。在大华盛顿地区，该系列有助于汇集相关研究人员，并促进该地区的研究活动。在国际上，"结在华盛顿"吸引了来自世界各地的研究人员，现在被认为是结理论和低维拓扑学的主要会议。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，适合研究数学家，学生和具有其他精确科学背景的读者，包括物理学，计算机科学，生物学和化学。下一次会议将集中讨论Khovanov同调，分配结构的同调，Yang-Baxter同调和量子计算之间的联系，以及分类的一般思想，包括skein模块的分类。在过去的35年里，纽结理论和3-流形拓扑领域取得了令人兴奋的新发展--从琼斯多项式和3-流形的量子不变量，到瓦西里耶夫不变量、拓扑量子场论，再到与规范理论的关系-维拓扑中的类型不变量（例如，唐纳森，维滕）。最近，量子拓扑学的一个新发展以霍瓦诺夫同调的形式出现，这是琼斯型多项式到链复合物同调的推广，它显著地推广了不变量。此外，我们还提出了三维流形的Kauffman括号skein模的分类，并对某些流形进行了推广。代数与Hochschild同调的关系已被发现和研究。分析了计算Jones多项式和Turaev-Viro不变量的量子复杂性。华盛顿的Knots将为上述领域的研究人员提供一个相互交流和共同工作的场所。组织者将努力在纽结理论及其分支的新发展的前沿。杰出的研究人员将给全体会议的报告调查有关Khovanov同源性的知识状态。会议主题的选择也将反映乔治华盛顿大学拓扑组的实力。会议网页：www.example.com