Homological Mirror Symmetry MIAMI, Jan 27- Feb 1, 2014

同调镜像对称迈阿密，2014 年 1 月 27 日至 2 月 1 日

• 批准号: 1404779
• 负责人: Ludmil Katzarkov
• 金额: $ 3.5万
• 依托单位: University of Miami
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-01-15 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1404779&HistoricalAwards=false
• 关键词: Homological; Mirror; Symmetry; MIAMI; Jan

The main goals of the Conference on Homological Mirror Symmetry, to be held on January 27-February 1, 2014 at the University of Miami, will be dissemination of results and encouragement a wave of young, early career researchers to join these projects. The wide range of topics appearing in HMS research necessitates venues for the open exchanges of ideas in order for graduate students and early career researchers to stay afloat on current topics. The subject has developed extremely rapidly in recent years, and this conference will really help engage young researchers.Over the last several years, a variety of new categorical structures have been discovered by physicists. Furthermore, it has become transparently evident that the higher categorical language is beautifully suited to describing cornerstone concepts in modern theoretical physics. As we head into the second decade of the 21st century, modern geometry and theoretical physics are more intertwined than ever before. The convergence of ideas from mathematics and physics is accelerating at the same time as elementary particle physics is on the cusp of a profound revolution to be brought about by the new experimental results coming out of the Large Hadron Collider (LHC). These will serve to identify among the multitude of theoretical possibilities currently open, which ones best address quantum field theory at the high energy scale. At the same time, a lot of mathematical work remains to be done to provide a suitable framework for the new physical theories that are being proposed. The geometric objects which we investigate today are the foundations for such a framework: homological mirror symmetry is the mathematical realization of dualities among super-symmetric theories, and higher categories are the mathematical foundation for quantum field theories. These new flavors of geometry, in which categorical structures play a primordial role, will certainly continue to play a fundamental role in 21st century theoretical physics.The conference website: http://math.berkeley.edu/~auroux/miami2014.html

同调镜像对称会议将于 2014 年 1 月 27 日至 2 月 1 日在迈阿密大学举行，其主要目标是传播成果并鼓励年轻的早期职业研究人员加入这些项目。 HMS 研究中出现的广泛主题需要开放的思想交流场所，以便研究生和早期职业研究人员能够关注当前的主题。近年来，这个学科发展极其迅速，这次会议将真正有助于吸引年轻的研究人员。在过去的几年里，物理学家发现了各种新的分类结构。此外，显而易见的是，高级分类语言非常适合描述现代理论物理学中的基石概念。当我们进入 21 世纪的第二个十年时，现代几何学和理论物理学比以往任何时候都更加紧密地交织在一起。数学和物理思想的融合正在加速，同时基本粒子物理学正处于大型强子对撞机（LHC）新实验结果所带来的深刻革命的风口浪尖。这些将有助于在目前开放的众多理论可能性中确定哪些最能解决高能尺度的量子场论。与此同时，仍有大量数学工作要做，以便为正在提出的新物理理论提供合适的框架。我们今天研究的几何对象是这样一个框架的基础：同调镜像对称是超对称理论中对偶性的数学实现，而更高范畴是量子场论的数学基础。这些新的几何风格，其中分类结构发挥着原始作用，必将继续在 21 世纪理论物理学中发挥基础性作用。会议网站：http://math.berkeley.edu/~auroux/miami2014.html