Aspects of hyperbolicity in geometry, topology and dynamics

我们将在沃里克大学举办一个为期三天的研讨会，题目是“几何、拓扑和动力学中的双曲性”。我们已经收到了11位国际知名研究人员的承诺，并打算再邀请4位。研讨会时间将分为重点讨论小组和前沿主题的研究讲座。我们期望这种互动能够产生新的研究方向，并激发未来的研究建议。研讨会将包括海报会议，数学图像展览和庆祝活动（由华威数学研究所和参与者资助），以纪念卡洛琳系列教授的60岁生日。几何的历史可以追溯到几千年前。传统上，几何学家研究的是欧几里德几何或“平面”几何，其中任何三角形的内角和为180度。在现代，科学家和数学家对其他几何学产生了极大的兴趣。值得注意的是，在球面和双曲几何中，任何三角形的角之和分别大于或小于180度。在这些现代几何中，双曲是最丰富的，并且在许多不同的环境中自然出现。拓扑学是20世纪数学的伟大成就之一，它研究的是不考虑距离和角度的形状。从拓扑学的角度看，球体和立方体是相同的；从几何的观点来看，它们是不同的：球面具有更大的对称性。在过去的30年里，最伟大的见解之一是，对于大多数三维形状来说，最对称的几何是双曲几何。动力学研究系统如何随时间演化，一个经典的例子是行星的运动。特别是天体力学产生了难以处理的混沌系统。然而，由于直线的快速发散，双曲几何中产生了更容易处理的系统。

We will hold a three day workshop at the University of Warwickentitled ``Aspects of hyperbolicity in geometry, topology and dynamics''.We have received commitments from 11 internationally respected researchers, andintend to invite an additional 4. Workshop time will be divided between focuseddiscussion groups and research talks on cutting edge topics.We expect this interaction to generate new directions of research and inspirefuture research proposals. The workshop will include a poster session, an exhibition ofmathematical images and a celebration (funded by the Warwick Mathematics Instituteand participants) in honour of Professor Caroline Series' 60th birthday.Geometry has a history going back several millennia. Traditionally geometers studiedeuclidean or ``flat'' geometry where the angles of any triangle sum to 180 degrees.In modern times other geometries have become of great interest to scientistsand mathematicians. Notably, in spherical and hyperbolic geometry the angles ofany triangle sum to more than or less than 180 degrees respectively.Of these modern geometries, hyperbolic is the richest, and arises naturally inmany different contexts.Topology, one of the great triumphs of 20th century mathematics,is the study of shapes without regard to distance or angle.From the topological point of view, a sphere and cube are same;from the geometric point of view they are distinct: the spherehas much greater symmetry. One of the great insights of thelast 30 years has been that the geometry of greatest symmetryfor most 3-dimensional shapes is hyperbolic geometry.Dynamics studies how systems evolve with time, a classicalexample being the motion of the planets. Celestial mechanicsin particular gives rise to intractable chaotic systems.However there are much more tractable systems arising out ofhyperbolic geometry, due to the rapid divergence of straight lines.