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和镜面对称之间的相互作用。首席讲师将是来自加州大学圣地亚哥分校的马克·格罗斯。镜像对称使得弦理论的不同模型之间具有等价性。这种现象涉及到几个对偶性，如同调镜像对称、斯特罗明格-尤-扎斯洛对偶、巴特列夫-鲍里索夫对偶和朗道-金兹堡模型。热带几何是一门相对较新的学科，已被证明是非常有效地解决计算机科学、数学生物学和统计物理学中的问题。在过去的几年里，热带几何也被应用于解决Gromov-Witten理论中的问题，以及最近的镜像对称问题。会议将对热带几何和镜像对称之间的相互作用进行全面的阐述。Mark Gross将会做一系列的讲座主题包括：热带曲线&仿射流形；Calabi-Yau退化及对数结构；以及热带摩尔斯电离层。此外，还将有由该领域的主要专家提供的介绍性迷你课程和特别研讨会讲座。

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.