Biology, Analysis, Geometry, Energies, Links: A Program on Low-dimensional Topology, Geometry, and Applications

该奖项为为期两周的“生物学，分析，几何，能源，链接”项目提供部分资金，该项目将于2019年6月17日至28日在明尼苏达州明尼阿波利斯的数学及其应用研究所举行。该方案的目标是双重的。一方面，它侧重于跨学科，将不同的科学团体聚集在一起，其研究领域相邻，但将受益于更密切的合作。另一方面，该计划旨在弥合科学发展不同阶段之间的差距：即本科学习，研究生工作和博士后研究。第一周是针对研究生和早期职业研究人员的暑期学校。接下来是一个研讨会，该研讨会以前一周所涵盖的主题为基础，演讲者来自广泛的学科，如数学物理，拓扑学，近似理论，分析和微生物学。低维拓扑学，几何学和纽结理论是合作和培训的绝佳平台：它们是高度跨学科的，具有初学者可以访问的功能，同时连接到数学，生物学和物理学的最深和最先进的领域。暑期学校介绍了与曲线，曲面和高维类似物有关的几个数学领域的最先进的介绍。研讨会将介绍暑期学校及以后讨论的领域的最新发展。要探讨的主题包括非线性力学，拓扑流体动力学，低维拓扑，量子不变量，同调理论，分类，接触几何，几何曲率能量，几何流的离散化，和离散微分几何。有关该活动的更多信息请访问：https://www.ima.umn.edu/2018-2019/SW6.17-28.19This奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估来支持。

This award provides partial funding for a two-week program "Biology, Analysis, Geometry, Energies, Links" that will take place during June 17 - 28, 2019 at the Institute of Mathematics and its Applications in Minneapolis, MN. The goals of this program are twofold. On the one hand, it is focused on interdisciplinarity, bringing different scientific groups together whose research areas are adjacent but would benefit from closer collaborations. On the other hand, this program aims at bridging gaps between different stages of scientific development: namely undergraduate study, graduate work, and postdoctoral research. The first week is a summer school targeted at graduate students and early career researchers. This is followed by a workshop that builds on the topics covered in the prior week and features speakers from a broad set of disciplines such as mathematical physics, topology, approximation theory, analysis, and microbiology.Low-dimensional topology, geometry and knot theory are excellent platforms for collaboration and training: they are highly interdisciplinary, and have features that are accessible to a beginner, while at the same time connecting to the deepest and most advanced realms of mathematics, biology, and physics. The summer school presents a state-of-the-art introduction to several mathematical fields concerned with curves, surfaces, and higher-dimensional analogs. The workshop will present the latest developments in the fields discussed at the summer school and beyond. Topics to be explored include nonlinear mechanics, topological fluid dynamics, low-dimensional topology, quantum invariants, homology theory, categorification, contact geometry, geometric curvature energies, discretization of geometric flows, and discrete differential geometry. More information about the event is at : https://www.ima.umn.edu/2018-2019/SW6.17-28.19This 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.