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

在今后三年期间将举行六次会议。这是非常成功的“华盛顿结”系列会议的延续，自1995年秋季以来，每学期在大华盛顿特区举行一次会议。该基金资助的第一次会议（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。报告将包括杰出研究人员的全体会议报告，以及各与会者的简短报告。研究生和博士研究生也将被鼓励参加。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，“华盛顿结”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），其中包含前沿的研究论文和课堂笔记，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。下一次会议将重点讨论Khovanov同调、分布结构同调、Yang-Baxter同调和量子计算之间的联系，以及分类的一般思想，包括绞链模块的分类。在过去的35年里，结论和3流形拓扑领域有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4维拓扑中与规范论类型不变量的关系（如Donaldson， Witten）。最近，量子拓扑的一个新发展以Khovanov同调的形式出现，将琼斯型多项式推广到链配合物的同调，显著地推广了不变量。此外，还提出了3-流形的Kauffman托架串模的分类，并对一些流形进行了发展。发现并研究了代数与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共同工作的场所。组织者将努力站在结理论及其分支新发展的前沿。杰出的研究人员将进行全体会谈，调查与霍万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小组的实力。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