The 35th Summer Conference on Topology and its Applications

该奖项支持参加2020年7月13日至17日在俄亥俄州扬斯敦的扬斯敦州立大学举行的第35届拓扑及其应用夏季会议(SUMTOPO 2020)。拓扑学是19世纪末从分析和几何学发展而来的一门抽象数学学科。自那以后，它已成为数学的基础学科之一，奠定了许多数学及其在科学中的应用的基础。拓扑学的现代应用包括逻辑、计算机科学、数据处理、生命科学、博弈论和丰富的范畴理论。与之前的会议一致，SUMTOPO 2020将是一项反映不断扩大的拓扑学及其应用世界的重要国际活动，会议将致力于自然科学和社会科学、范畴理论、计算拓扑学(包括区块链和数据科学)、代数和几何、一般和集合论拓扑学、动力学和连续体理论、不对称性和多值性，以及丰富的范畴和拓扑学。SUMTOPO 2020将有助于更好地理解大数据固有的拓扑结构，并巩固作为数据科学基础的拓扑学，从而有助于实现利用数据革命的NSF目标。SUMTOPO 2020将为最近的博士获得者和较小机构的教职员工举办特别会议，帮助他们制定可持续的研究计划，并概述招收女性和少数族裔数学专业的战略。参与者将包括一群不同的资深研究人员、初级研究人员、研究生和退休人员，特别强调从国际上和代表性不足的人群中招募演讲者和参与者。SUMPTOPO 2020以代数和几何、一般和集论拓扑学、动力学和连续体理论以及不对称性为特色，同时开始和/或扩展自然科学和社会科学数据科学中的拓扑学、范畴理论、计算拓扑学、多值性和丰富的类别和拓扑学的会议。在每一次会议中，“拓扑”，无论是否明确说明，都是会议的基础。在自然科学和社会科学中，科学家和数学家发现，有一些自然现象和现象可以用拓扑学来解释或更好地理解，而且一些解释提出了新的拓扑学问题。数据科学在SUMTOPO 2020的两个会议上特别令人感兴趣。数据科学本身不仅是一个快速发展的领域，它也是许多学科重要和持续发展的推动力，包括大多数自然科学和社会科学。拓扑学正在被证明是数据科学及其应用发展的一个不可或缺的部分。关于范畴理论，我们想要探索范畴理论过去影响拓扑学的方式，以及范畴理论在未来继续影响拓扑学的方式。由于(大数据)的本质意味着涉及数据科学的应用程序必须是计算性的，所以计算拓扑学是一个关键的关注领域。计算拓扑学也产生了新的拓扑学问题和研究领域。非对称拓扑是指其相关的专门化前序是非对称的拓扑；而多值拓扑是开集的集合，每个开集都是从空间的载体集到指定的“真值”完备格的映射。近年来，人们发现这两个拓扑学领域相互关联，并与计算拓扑学有关，特别是与经常与编程语义相关的空间和拓扑系统。会议网页是https://ysu.edu/sumtopo.This奖，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 supports participation in the 35th Summer Conference on Topology and Its Applications (SUMTOPO 2020) taking place 13–17 July 2020 at Youngstown State University in Youngstown, Ohio. Topology is an area of abstract mathematics that emerged from analysis and geometry as its own discipline in the late 19th century. It has since become one of the foundational disciplines of mathematics, underlying much of mathematics and its applications to the sciences. Modern applications of topology include logic, computer science, data processing, life sciences, game theory, and enriched category theory. In keeping with its predecessor conferences, SUMTOPO 2020 will be an important international event that reflects the ever-expanding world of topology and its applications, with sessions dedicated to natural and social sciences, category theory, computational topology (including block chains and data science), algebra and geometry, general and set-theoretic topology, dynamics and continuum theory, asymmetry and many-valuedness, and enriched categories and topology. SUMTOPO 2020 will contribute to better understanding the topological structures inherent in big data, as well as solidifying topology as a foundation of data science, thus contributing to the NSF goal of Harnessing the Data Revolution. SUMTOPO 2020 will have special sessions for recent doctoral recipients and faculty at smaller institutions to help them develop sustainable research programs, as well as outlining strategies for recruiting women and minorities to mathematics. Participants will comprise a diverse group of established researchers, junior researchers, graduate students, and retirees, with special emphasis on recruiting speakers and participants both internationally and from underrepresented populations. SUMPTOPO 2020 features sessions on Algebra and Geometry, General and Set-Theoretic Topology, Dynamics and Continuum Theory, and Asymmetry, while beginning and/or expanding sessions on Topology in Data Science for Natural and Social Sciences, Category Theory, Computational Topology, Many-Valuedness, and Enriched Categories and Topology. In each session, “topology,” whether explicitly stated or not, is a basis of the session. In the natural and social sciences, scientists and mathematicians are discovering that there are natural occurrences and phenomena that can be explained or better understood using topology and that some of the explanations raise new topological questions. Data science is of special interest in two of the sessions in SUMTOPO 2020. Data science is not only a rapidly developing area in its own right, it is also a driving force in important and on-going developments in many disciplines including most if not all the natural and social sciences. Topology is proving to be an integral part of the development of data science and its applications. Regarding category theory, we want to explore the ways in which category theory has influenced topology in the past and the ways that category theory will continue to influence topology in the future. Since the very nature of (big) data means that applications involving data science must be computational, computational topology is a critical area of focus. Computational topology also gives rise to new topological questions and areas of research. An asymmetric topology is one for which the associated specialization preorder is non-symmetric; while a many-valued topology is a collection of open sets, each of which is a mapping from the carrier set of a space to a designated complete lattice of “truth values.” In recent years it has been discovered that these two areas of topology are linked to each other and to computational topology, particularly to spaces and topological systems often associated with programming semantics.The conference web page is https://ysu.edu/sumtopo.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.