CBMS Conference on Topological Data Analysis and Persistence Theory

该奖项为“拓扑数据分析和持久性理论”会议提供资金，该会议是数学科学系列会议委员会的一部分。该活动将于2022年8月8日至12日在佐治亚州瓦尔多斯塔的瓦尔多斯塔州立大学举行。本次活动的主要目标是向更广泛的受众介绍拓扑数据分析（TDA）和持久性理论（PT）。TDA和PT是相对较新的方法，用于发现大型数据集中的重要特征，这些方法使用的理论思想来自数学的几个分支，包括代数和拓扑。这次会议由佛罗里达大学盖恩斯维尔分校的Peter Bubenik博士每天的一系列讲座组成。这些讲座的主题包括回顾与TDA和PT相关的基本数学概念，与统计方法和机器学习的相互作用以及当前的应用和软件实现。本系列讲座还将讨论与TDA和PT相关的高级主题和当前研究。此外，还将有两个结构化的实验课程，向参与者介绍可用于计算数据集上各种TDA函数的软件。具体内容包括：回顾与TDA和PT相关的基本概念，如简单和立方配合物、同源性、持久性同源性（PH）和Vietoris-Rips配合物；TDA和PT与交换环、梯度模和颤振表示理论等代数概念的相互作用；TDA和PT与假设检验和排列检验等统计方法的相互作用，以及与机器学习方法（如深度学习和多层感知器）的相互作用；最后，软件实现以及TDA和PT研究的当前趋势和进展。还有两个结构化的实验室会议，参与者将被介绍可用于计算数据集上的PH和其他TDA函数的软件。有关会议的更多信息可在网站上获得：https://www.cbmsweb.orgThis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知识价值和更广泛的影响审查标准进行评估，认为值得支持。

This award provides funding for the conference "Topological Data Analysis and Persistence Theory" organised as part of the Conference Board of the Mathematical Sciences series. The event will take place at Valdosta State University in Valdosta, Georgia during August 8-12, 2022. The main goal of this event is to provide an introduction to topological data analysis (TDA) and persistence theory (PT) to a broader audience. TDA and PT are relatively recent methods useful for discovering important features in large data sets using theoretical ideas from several branches of mathematics including algebra and topology. This conference consists of a series of daily lectures given by Dr. Peter Bubenik of the University of Florida, Gainesville. The topics of these lectures include a review of the basic mathematical concepts related to TDA and PT, interactions with statistical methods and machine learning as well as current applications and software implementations. This lecture series will also include a discussion of advanced topics and current research related to TDA and PT. There will be also be two structured Lab Sessions where the participants will be introduced to software that can be used to compute various TDA functions on data sets. Specific elements to be covered during the lectures include: a review of basic concepts related to TDA and PT such as simplicial and cubical complexes, homology, persistence homology (PH), and Vietoris-Rips complexes; interactions of TDA and PT with theoretical algebraic concepts such as commutative rings, graded modules and representation theory of quivers; interactions of TDA and PT with statistical methods such as hypothesis testing and permutation tests as well as interactions with methods from machine learning such as deep learning and multilayer perceptrons; and finally, software implementation and current trends and advances in the research on TDA and PT. There will be also two structured Lab Sessions were the participants will be introduced to software that can be used to compute PH and other TDA functions on data sets. Further information about the conference will be available at the website: https://www.cbmsweb.orgThis 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.