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

会议的焦点是三维流形和纽结理论中的现代方法，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与例如规范理论、量子计算、非对易代数、表示理论以及几何和拓扑中其他相邻领域之间的关系。会议将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进行自我教育的机会。这次会议是对1989年至2000年在俄亥俄州立大学举行的年度几何和拓扑会议的另一种形式的延续。大部分资金用于支持博士生和新近毕业的博士生，他们正处于学术生涯的开端。会议向他们展示了三维拓扑中的各种新发展和相互关系，从中他们可以制定未来的研究方向和项目，并给他们一个机会向拓扑界介绍他们自己的工作。三维流形的拓扑学是研究三维空间中可能的形状。在两个维度上，这样的形状可以是圆盘、球体，也可以是甜甜圈和椒盐卷饼的表面。在1492年以前，当科学家和哲学家问地球的形状是什么时，他们显然是感兴趣的，也是科学家和哲学家们讨论的对象。值得注意的是，关于我们宇宙可能的三维形状的类似讨论现在正在现代天文学家和天体物理学家中发生。然而，三维形状更难描述和区分。相反，物理在很大程度上影响了三维拓扑。理论物理学家用来描述基本粒子的模型被证明是非常有洞察力的指导方针，以开发关于拓扑学中抽象的三维空间的新理论，从而最终形成了纯粹的数学学科--“量子拓扑学”和“规范理论”。此外，与拓扑学一起开发的代数工具和方法被证明具有更普遍的兴趣。例如，它们作为量子计算机的理论模型，如果建造起来，将能够破解所有已知的公共加密代码，例如用于军事和金融世界的那些代码。

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.