Conference: ``Borders in 3-Dim Topology''

摘要0400017会议的重点是三维流形和纽结理论的现代方法，以及它们与其他数学领域的相互作用。特别令人感兴趣的是量子拓扑学与规范理论、量子计算、非交换代数、表示论以及几何和拓扑学中其他相邻领域之间的关系。会议将同时概述三维拓扑学中现代代数和组合方法的现状，并为与会者提供一个沿着重叠研究领域的边界线自学的机会。这次会议是1989年至2000年在俄亥俄州举行的年度几何和拓扑会议的延续。大部分资金用于支持博士生和最近的博士生，他们正处于学术生涯的开端。该会议使他们接触到三维拓扑学的各种新发展和相互关系，从中他们可以发展他们未来的研究方向和项目，并给他们一个机会通过介绍自己的工作介绍自己到拓扑学社区。三维流形拓扑学是研究三维空间中可能的形状。在二维中，这样的形状可以是圆盘、球体或者也可以是甜甜圈和椒盐卷饼的表面。在1492年之前，当科学家和哲学家们问地球（的二维表面）的形状是什么时，他们对这些问题有着明显的兴趣和讨论。值得注意的是，现代天文学家和天体物理学家正在讨论我们宇宙可能的三维形状。然而，三维形状更难描述和区分。相反，物理学对三维拓扑学的影响很大。理论物理学家用来描述基本粒子的模型被证明是发展拓扑学中抽象三维空间的新理论的极具洞察力的指导方针，最终“量子拓扑学”和“规范理论”作为纯粹的数学学科出现。此外，代数工具和方法，正在开发沿着的拓扑证明是更普遍的利益。例如，它们作为量子计算机的理论模型，量子计算机-如果构建-将能够破解所有已知的公共加密代码，例如，在军队和金融界都有

Abstract0400017The focus of the conference is on the modern methods in 3-manifold and knot theory, and their interactions with other areas of mathematics. Of particular interest are the relations between quantum topology and, for example, gauge theory, quantum computing, non-commutative algebra, representation theory, and other adjacent areas in geometry and topology. The conference shall both give an overview over the current state of modern algebraic and combinatorial methods in 3-dimensional topology and provide an opportunity for participants to educate themselves along the borderlines of overlapping areas of research. The conference is continuing the annual geometry and topology conference that was held at Ohio State from 1989 to 2000 in a different format. Most of the funding is for the support of doctoral students and recent PhD's, who are at the beginnings of their academic careers. The conference exposes them to a variety of new developments and interrelations in 3-dim topology from which they can develop their future research directions and projects as well as gives them an opportunity to introduce themselves to the topology community with presentations of their own work.Topology of 3-manifolds is the study of the possible shapes in a 3-dimensional space. In two dimensions such shapes can be discs, spheres or also the surfaces of doughnuts and pretzels. They were of obvious interest and discussion among scientists and philosophers before 1492 when they asked what the shape of (the 2-dim surface of) the earth is. Remarkably, a similar discussion about the possible 3-dimensional shape of our cosmos is taking place right now among modern astronomers and astrophysicists. Yet, 3-dimensional shapes are much harder to describe and to distinguish. Conversely, physics heavily influenced 3-dimensional topology. The models that theoretical physicists use to describe elementary particles turned out to be highly insightful guidelines to develop new theories about the abstract 3-dimensional spaces in topology, from which eventually the areas of "quantum topology" and "gauge theory" emerged as purely mathematical disciplines. Furthermore, the algebraic tools and methods that are being developed along with the topology prove to be of much more universal interest. They serve, for example, as theoretical models for quantum computers, which - if constructed - would be able to break all known public encryption codes, such as those used, e.g., in the military and in the world of finance.