Knots in Washington: Conferences on Knot Theory and its Ramifications 2008-2010

摘要奖：DMS-0817858主要研究员：Jozef H.Przytycki，龙永武，Alexander N.Shumakovitch，Hao Wu将于2008-2010年间举办一系列关于纽结理论及其影响的会议，延续自1995年秋季以来每学期在大华盛顿特区举行的“纽结在华盛顿”会议。全体会议将概述Khovanov同调、Heegard Floer同调和现有不变量的分类(如skein模)等领域的知识状况。投稿的演讲和课程致力于参与者之间的互动，为研究生和新近的博士提供了成为“华盛顿之结”的一部分的机会，组织者鼓励学生和初级研究人员参加这些会议。低维拓扑学研究三维和四维空间的形状。我们对这些维度特别感兴趣，因为它们是我们的空间和我们时空的维度。结点理论是低维拓扑学的一个子域，它研究我们空间中的结点。纽结理论的主要目的之一是区分纽结对象。这通常是通过所谓的“纽结不变量”来完成的，这些函数用更容易比较的几何对象来代替几何对象，如纽结。在过去的二十年里，在规范理论、量子代数和数学物理的思想的推动下，低维拓扑中的新不变量蓬勃发展。华盛顿会议的目的是将该领域的研究人员聚集在一起，包括著名的数学家以及研究生和新近的博士，讨论该学科的最新进展。会议网页ishttp://home.gwu.edu/~przytyck/knots/index.html.

AbstractAward: DMS-0817858Principal Investigator: Jozef H. Przytycki, Yongwu Rong,Alexander N. Shumakovitch, Hao WuA series of conferences devoted to knot theory and itsramifications will be held in 2008-2010, continuing the "Knots inWashington" conferences held every semester in the greaterWashington, D.C. area since fall 1995. Plenary talks willsurvey the state of knowledge in areas such as Khovanov homology,Heegard Floer homology, and categorification of existinginvariants such as skein modules. Contributed talks and periodsdevoted to interaction among participants provide opportunitiesfor graduate students and recent PhDs to be a part of "Knots inWashington," and the organizers encourage students and juniorresearchers to attend these meetings.Low dimensional topology studies shapes of three and fourdimensional spaces. These dimensions are of particular interestto us because they are the dimensions of our space and ourspace-time. Knot theory is a subfield of low dimensionaltopology, which studies the knottedness in our space. One of themain goals of knot theory is to distinguish knotted objects. Thisis often done by means of the so called "knot invariants,"functions that replace geometric objects, such as knots, withthose that are easier to compare. Over the past two decades,there have been a flourish of new invariants in low dimensionaltopology, boosted by ideas from gauge theory, quantum algebras,and mathematical physics. The purpose of the "Knots inWashington Conferences" is to bring together the researchers ofthe field, including established mathematicians as well asgraduate students and recent PhDs, to discuss the state of theart of the subject. The conference web page ishttp://home.gwu.edu/~przytyck/knots/index.html.