Knots in Washington XLI: a Conference Series on Knot Theory and its Ramifications; November 13-15, 2015

在接下来的三年时间里，将举行六次会议。这是一个非常成功的系列会议“在华盛顿的结”的延续，自1995年秋季以来，每学期在大华盛顿特区举行一次会议。由这笔赠款资助的第一次会议(也是该系列的第51次会议)将于2015年秋季举行。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演讲，以及不同参与者的简短演讲。研究生和新近毕业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。在大华盛顿特区地区，该系列活动有助于将相关研究人员聚集在一起，并促进该地区的研究活动。在国际上，《华盛顿的纽结》吸引了来自世界各地的研究人员，现在被认为是纽结理论和低维拓扑学的一次重大会议。我们希望发表会议记录(就像我们过去做的那样)，其中包含尖端的研究论文和课堂讲稿，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、计算机科学、生物和化学。下一次会议将集中讨论Khovanov同调、分配结构同调、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模的分类。在过去的35年里，纽结理论和三维流形拓扑学领域有了令人振奋的新发展--从琼斯多项式和三维流形的量子不变量，到Vassiliev不变量，拓扑量子场论，到四维拓扑中与规范理论类型不变量的关系(例如，Donaldson，Witten)。最近，量子拓扑学的新发展以Khovanov同调的形式出现，Khovanov同调是Jones类型多项式到链复合体的同调的推广，它显著地推广了不变量。同时，对于某些流形，提出并发展了3维流形的Kauffman括号斜切模范型。发现并研究了与代数的Hochschild同调的关系。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合作的场所。组织者将努力站在纽结理论及其分支的新发展的前沿。杰出的研究人员将举行全体会议，概述与霍瓦诺夫同调有关的知识状况。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：http://home.gwu.edu/~przytyck/knots/index.html

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