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

项目负责人：Jozef H. Przytycki, Yongwu Rong,Alexander N. Shumakovitch， Hao WuA将于2008-2010年举行一系列关于结理论及其分支的会议，延续自1995年秋季以来每学期在大华盛顿特区举行的“结在华盛顿”会议。全体会议将调查知识的状态，如Khovanov同调，Heegard Floer同调和现有不变量的分类，如绞模。参与者之间的互动为研究生和刚获得博士学位的学生提供了成为“华盛顿结”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时空的维度。结理论是低维拓扑学的一个分支，主要研究空间中的结性。结理论的主要目标之一是区分结的物体。这通常是通过所谓的“结不变量”来实现的，这种函数用更容易比较的对象来替换几何对象，比如结。在过去的二十年里，在规范理论、量子代数和数学物理的推动下，低维拓扑中出现了大量新的不变量。“华盛顿结会议”的目的是将该领域的研究人员聚集在一起，包括知名数学家、研究生和新近获得博士学位的人，讨论这一主题的核心状态。会议网页https://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.