Teichmueller dynamics and the birational geometry of moduli space

该项目旨在利用Teichmueller动力学领域最新的前沿进展来回答代数几何关于曲线模空间的长期悬而未决的问题，该对象与包括量子重力和理论物理在内的许多不同科学领域有着深刻的联系。该项目希望通过将这些观点联系起来的创新，以及揭示这些观点之间的新联系，在这两个领域产生新的理论和更多的理解。进一步的好处应该包括建立国际合作，以及这种多样化的观点对澳大利亚日益增长的代数几何界以及更广泛地对数学和相关科学领域的贡献。

The project aims to leverage recent cutting-edge advances in the area of Teichmueller dynamics to answer longstanding open questions from algebraic geometry on the moduli space of curves, an object with deep connections to many diverse areas of science including quantum gravity and theoretical physics. The project expects to generate new theories and increased understanding in both areas through the innovation of relating these perspectives, as well as uncovering new connections between the viewpoints. Further benefits should include building international collaborations and the contribution of this diverse perspective to the growing algebraic geometry community in Australia and to mathematics and related scientific fields more generally.