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.

该奖项为会议的“拓扑数据分析和持久理论”提供了资金，作为数学科学系列会议委员会的一部分。该活动将在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。该活动的主要目标是向更广泛的受众提供拓扑数据分析（TDA）和持久理论（PT）的介绍。 TDA和PT是相对较新的方法，可用于使用来自数学分支（包括代数和拓扑）的几个数学分支中的理论思想在大型数据集中发现重要特征。 这次会议由盖恩斯维尔大学佛罗里达大学的彼得·布布尼克（Peter Bubenik）博士进行的一系列每日讲座组成。 这些讲座的主题包括对与TDA和PT相关的基本数学概念的审查，与统计方法和机器学习的交互以及当前的应用程序和软件实现。 该讲座系列还将包括有关与TDA和PT相关的高级主题和当前研究的讨论。还将有两个结构化实验室会话，将参与者引入软件，可用于计算数据集的各种TDA功能。 讲座期间要涵盖的具体元素包括：对与TDA和PT相关的基本概念的回顾，例如简单和立方体复合物，同源性，持久性同源性（PH）和越野式 - 里普斯复合体； TDA和PT与理论代数概念的相互作用，例如交换环，分级模块和震颤的表示理论； TDA和PT与统计方法的相互作用，例如假设检验和排列测试，以及与机器学习（例如深度学习和多层感知）的方法的相互作用；最后，软件实施以及当前的趋势以及TDA和PT研究的进步。将会将参与者介绍给软件，用于计算数据集的pH和其他TDA功能，还将有两个结构化实验室会话。有关会议的更多信息将在网站上提供：https：//www.cbmsweb.orgthis Award反映了NSF的法定任务，并使用基金会的知识分子优点和更广泛的影响审查标准，认为值得通过评估来获得支持。