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

NSF/CBMS 数学科学区域会议：热带几何

• 批准号: 0735319
• 负责人: Ricardo Castano-Bernard
• 金额: $ 3.3万
• 依托单位: Kansas State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-02-01 至 2010-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0735319&HistoricalAwards=false
• 关键词: NSF; CBMS; Regional; Conference; Mathematical

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.

本次会议的重点将放在热带几何学和镜像对称之间的相互作用。首席讲师是来自加州大学圣地亚哥分校的马克·格罗斯(Mark Gross)。镜像对称提出了弦理论不同模型之间的等价性。这种现象涉及多种对偶性，例如同调镜像对称性、Strominger-Yau-Zaslow 对偶性、Batyrev-Borisov 对偶性和 Landau-Ginzburg 模型。热带几何是一门相对较新的学科，已被证明可以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。在过去的几年中，热带几何也被应用于解决格罗莫夫-维滕理论以及最近的镜像对称问题。本次会议将对热带几何与镜像对称之间的相互作用进行全面的阐述。马克·格罗斯（Mark Gross）将围绕热带曲线和仿射流形等主题发表一系列讲座；卡拉比-丘变性和对数结构； 和热带莫尔斯电码类别。此外，还将提供由该领域领先专家主讲的入门迷你课程和专题研讨会讲座。