NSF/CBMS Regional Conference in the Mathematical Sciences: Tropical Geometry & Mirror Symmetry, December 13-17, 2008

这次会议的重点将放在热带几何学和镜面对称性之间的相互作用上。首席讲师将是加州大学圣地亚哥分校的马克·格罗斯。镜像对称性使得弦理论的不同模型之间具有等价性。这一现象涉及同调镜像对称性、Strominger-Yau-Zaslow对偶、Batyrev-Borisv对偶和Landau-Ginzburg模型等对偶现象。热带几何是一门相对较新的学科，已被证明非常有效地解决了计算机科学、数学生物学和统计物理中的问题。在过去的几年里，热带几何学也被应用于解决Gromov-Witten理论和最近的镜面对称性问题。会议将对热带几何学和镜面对称性之间的相互作用进行全面的解释性讨论。Mark Gross将围绕以下主题发表一系列演讲：热带曲线与仿射流形；Calabi-Yau退化与Amp；对数结构；以及热带Morse范畴。此外，还将举办入门迷你课程和由该领域领先专家主持的专题研讨会讲座。

The emphasis of this conference will be put on the interplay between tropical geometry and mirror symmetry. The principal lecturer will be Mark Gross from University of California, San Diego. Mirror symmetry poses the equivalence between different models of string theory. This phenomenon involves several dualities such as the Homological Mirror symmetry, the Strominger-Yau-Zaslow duality, the Batyrev-Borisov duality, and the Landau-Ginzburg model. Tropical geometry is a relatively new subject that has proved to be very effective solving problems in computer science, mathematical biology and statistical physics. In the past few years, tropical geometry has also been applied to solve problems in Gromov-Witten theory and, more recently, mirror symmetry.The conference will provide a comprehensive expository treatment of the interaction between tropical geometry and mirror symmetry. Mark Gross will deliver a series of lectures around subjects such as: tropical curves & affine manifolds; Calabi-Yau degenerations & logarithmic structures; and the tropical Morse category. In addition, there will be introductory mini-courses and special seminar lectures delivered by leading experts in the field.