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

该奖项为将于2019年6月17-28日在明尼苏达州明尼阿波利斯市的数学及其应用研究所举办的为期两周的“生物学、分析、几何、能量、链接”课程提供部分资金。这个项目的目标是双重的。一方面，它专注于跨学科，将不同的科学小组聚集在一起，他们的研究领域相邻，但将从更密切的合作中受益。另一方面，该计划旨在弥合科学发展的不同阶段之间的差距：即本科生学习、研究生工作和博士后研究。第一周是面向研究生和早期职业研究人员的暑期班。随后是一个研讨会，以前一周所涵盖的主题为基础，有来自数学物理、拓扑学、近似理论、分析和微生物学等广泛学科的演讲者参加。低维拓扑、几何和纽结理论是协作和培训的极好平台：它们高度跨学科，具有初学者可以访问的功能，同时连接到数学、生物和物理的最深和最高级领域。暑期班介绍了与曲线、曲面和高维类比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。课程包括：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、归类、接触几何、几何曲率能、几何流动离散化和离散微分几何。有关此次活动的更多信息，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。

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.