CBMS Conference on Topological Data Analysis and Persistence Theory

CBMS拓扑数据分析与持久性理论会议

• 批准号: 2132497
• 负责人: Jose Velez
• 金额: $ 3.5万
• 依托单位: Valdosta State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-07-01 至 2023-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2132497&HistoricalAwards=false
• 关键词: CBMS; Conference; Topological; Data; Analysis

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.

该奖项为会议提供资金“拓扑数据分析和持久性理论”作为数学科学系列会议委员会的一部分组织。该活动将于2022年8月8日至12日在格鲁吉亚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，用于使用数学的几个分支（包括代数和拓扑学）的理论思想来发现大型数据集中的重要特征。 本次会议由盖恩斯维尔市佛罗里达大学的彼得·布贝尼克博士提供的一系列日常讲座组成。 这些讲座的主题包括与TDA和PT相关的基本数学概念的回顾，与统计方法和机器学习的交互以及当前的应用和软件实现。 本系列讲座还将包括与TDA和PT相关的高级主题和当前研究的讨论。还将有两个结构化的实验室会议，参与者将被介绍给软件，可用于计算数据集上的各种TDA函数。 具体内容将涵盖在讲座期间包括：有关的基本概念，如单纯和立方复形，同源性，持久性同源性（PH），和Vietoris-Rips复合物的TDA和PT的审查与理论代数概念，如交换环，分次模和表示理论的箭图的相互作用; TDA和PT与统计方法（如假设检验和排列检验）的交互，以及与机器学习方法（如深度学习和多层感知器）的交互;最后介绍了TDA和PT的软件实现和研究现状。还有两个结构化的实验室会议，参与者将被介绍给软件，可用于计算PH和其他TDA功能的数据集。有关会议的进一步信息将在网站上提供：https://www.cbmsweb.orgThis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。