Geometric Representation Theory and Low Dimensional Topology

几何表示理论和低维拓扑

• 批准号: 1856643
• 负责人: Peter Samuelson
• 金额: $ 2.95万
• 依托单位: University of California-Riverside
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-04-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1856643&HistoricalAwards=false
• 关键词: Geometric; Representation; Theory; Low; Dimensional

The conference "Geometric Representation Theory and Low Dimensional Topology" will take place at the International Centre for Mathematical Sciences in Edinburgh, Scotland, June 10-14, 2019. There will be a summer school June 3-7 with several lecture series to provide background material for early career participants in the conference. The overall goal of the conference is to study interactions between the two areas of mathematics in the title. "Topology" is the study of shapes that are allowed to stretch and bend. For example, a triangle and circle are considered to be topologically equivalent because one can be stretched into the other, and similarly a cube and sphere are considered topologically equivalent. "Low dimensional topology" studies shapes or objects in dimensions 2, 3, and 4, such as surfaces, or knotted loops in 3-dimensional space. This can be useful in other sciences; for example, DNA can be knotted, or the shape of the universe could have a nontrivial topology. "Representation theory" is the study of symmetries in mathematics, and at a concrete level, these symmetries often manifest themselves as solutions to systems of equations where the variables represent matrices instead of numbers. This mathematical area has also had applications in other sciences, such as symmetries of elementary particles in physics, or symmetries of molecules inchemistry. There are sophisticated mathematical techniques for taking certain spaces of solutions to polynomial equations and producing solutions to matrix equations, and recently low dimensional topology has been used to find solutions to the same equations, using completely different mathematical constructions. One of the goals of the conference is to understand this new phenomenon using ideas coming from mathematical physics. This award will fund participation of early career US scientists in this summer school and conference so they can learn about these exciting new ideas.More details about the conference are available at https://www.icms.org.uk/geometricrepresentation.php.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

“几何表示理论和低维拓扑”会议将于2019年6月10日至14日在苏格兰爱丁堡的国际数学科学中心举行。6月3日至7日将有一个暑期学校，有几个系列讲座，为会议的早期职业参与者提供背景材料。会议的总体目标是研究标题中两个数学领域之间的相互作用。“拓扑学”是对允许拉伸和弯曲的形状的研究。例如，三角形和圆被认为是拓扑等价的，因为一个可以拉伸到另一个中，类似地，立方体和球体被认为是拓扑等价的。“低维拓扑学”研究二维、三维和四维的形状或物体，如三维空间中的曲面或打结环。这在其他科学中也很有用，例如，DNA可以打结，或者宇宙的形状可以有一个非平凡的拓扑结构。“表示论”是对数学中对称性的研究，在具体的层面上，这些对称性通常表现为方程组的解，其中变量表示矩阵而不是数字。这一数学领域也在其他科学中得到应用，如物理学中基本粒子的对称性，或化学中分子的对称性。有复杂的数学技术采取某些空间的解决方案多项式方程和生产的解决方案矩阵方程，最近低维拓扑已被用来寻找解决方案，相同的方程，使用完全不同的数学结构。会议的目标之一是利用来自数学物理的想法来理解这种新现象。该奖项将资助美国早期职业科学家参加这个暑期学校和会议，使他们能够了解这些令人兴奋的新想法。有关会议的更多详细信息，请访问https://www.icms.org.uk/geometricrepresentation.php.This奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。