Geometric Representation Theory and Low Dimensional Topology

《几何表示理论与低维拓扑学》会议将于2019年6月10日至14日在苏格兰爱丁堡国际数学科学中心举行。6月3日至7日将有一个暑期班，包括几个系列讲座，为参加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数学的两个领域之间的相互作用。“拓扑学”是研究允许拉伸和弯曲的形状的学科。例如，三角形和圆被认为是拓扑等价的，因为一个可以伸展到另一个中，同样，立方体和球体也被认为是拓扑等价的。“低维拓扑学”研究2维、3维和4维的形状或对象，例如三维空间中的曲面或结环。这在其他科学中可能很有用；例如，DNA可以打结，或者宇宙的形状可能具有不平凡的拓扑结构。“表示论”是对数学中的对称性的研究，在具体的层面上，这些对称性通常表现为方程系统的解，其中变量代表矩阵而不是数字。这个数学领域在其他科学中也有应用，例如物理学中基本粒子的对称性，或化学中分子的对称性。有一些复杂的数学技术可以用来求多项式方程的某些解空间并产生矩阵方程的解，最近，低维拓扑被用来寻找相同方程的解，使用完全不同的数学结构。这次会议的目标之一是用来自数学物理的想法来理解这一新现象。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，以便他们能够了解这些令人兴奋的新想法。有关会议的更多细节可在https://www.icms.org.uk/geometricrepresentation.php.This网站上获得，该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.