The Third Ahlfors-Bers Colloquium; May 19-22, 2005; Ann Arbor, MI

Ahlfors-Bers学术讨论会是为了纪念Lars Ahlfors和Lipman Bers的数学遗产。这一遗产的核心在于几何函数论、泰希穆勒理论、双曲流形和偏微分方程等领域。然而，他们的工作影响并创造了许多其他领域的互动，如代数几何、数学物理、动力学、几何群论、数论和拓扑学。过去几年是该领域紧张活动和进步的时期。最近的进展包括瑟斯顿终止层合猜想、Bers-Sullivan-瑟斯顿密度猜想和Marden‘s Tamness猜想的解，球面Bloch常数的确定，渗流共形不变性的证明，映射班组准等距刚性的证明，以及Weil-Petersson几何和Witten-Kontsevich猜想之间关系的发现。学术讨论会将作为传播这些结果和考虑该领域未来方向的场所。12个全会将由该领域的领导者进行。较小的研讨会将为年轻的数学家们提供一个传播他们的工作和与其他年轻数学家互动的极好机会以及该领域的知名研究人员。

The Ahlfors-Bers Colloquium commemorates the mathematical legacy ofLars Ahlfors and Lipman Bers. The core of this legacy lies in thefields of geometric function theory, Teichmuller theory, hyperbolicmanifolds, and partial differential equations. However, their workhas impacted and created interactions with many other fields, such as algebraicgeometry, mathematical physics, dynamics, geometric group theory,number theory and topology. The last several years have been aperiod of intense activity and progress in the field. Recentprogress includes the solutions of Thurston's Ending LaminationConjecture, the Bers-Sullivan-Thurston Density Conjecture, and Marden'sTameness Conjecture, the determination of the spherical Bloch constant,a proof of the conformal invariance of percolation, a proof of thequasi-isometric rigidity of mapping class groups and the discovery ofthe relationship between Weil-Petersson Geometry and the Witten-KontsevichconjectureThe Colloquium will serve as a venue for the dissemination of theseresults and the consideration of future directions in the field.Twelve plenary lectures will be given by leaders in the field.Smaller workshops will provide an excellent opportunity for youngmathematicians to disseminate their work and to interact with otheryoung mathematicians, as well as the established researchers in the field.