Aspects of hyperbolicity in geometry, topology and dynamics

我们将在华威大学举办一场为期三天的研讨会，题为《几何、拓扑学和动力学中的双曲性视角》。我们已收到11名国际知名研究人员的承诺，并打算再邀请4名。研讨会时间将分成聚焦讨论小组和关于前沿话题的研究讲座。我们希望这种互动将产生新的研究方向，并启发未来的研究建议。工作坊将包括海报展示、数学图像展览和庆祝Caroline Series教授60岁生日的庆祝活动(由华威数学研究所和参与者资助)。几何的历史可以追溯到几千年前。传统上，几何学家研究的是平面几何，即任何三角形的角度之和为180度。在现代，科学家和数学家对其他几何已产生了极大的兴趣。值得注意的是，在球面和双曲几何中，任何三角形的角度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，并自然地出现在许多不同的环境中。拓扑学是20世纪数学的伟大成就之一，研究形状而不考虑距离或角度。从拓扑学的观点来看，球体和立方体是相同的；从几何学的角度来看，它们是不同的：空间具有更大的对称性。过去30年的最大洞察之一是，对于大多数三维形状来说，对称性最大的几何是双曲几何。动力学研究系统如何随时间演变，经典的例子是行星的运动。特别是天体力学，会产生难以处理的混沌系统。然而，由于直线的快速发散，从双曲几何中产生的易处理系统要多得多。

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.