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“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世界大型企业联合会的一部分。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。该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，可利用代数和拓扑等多个数学分支的理论思想来发现大型数据集中的重要特征。 本次会议包括由佛罗里达大学盖恩斯维尔分校的 Peter Bubenik 博士进行的一系列日常讲座。 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交互以及当前的应用程序和软件实现。 该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。还将举行两次结构化实验室会议，向参与者介绍可用于计算数据集上的各种 TDA 函数的软件。 讲座中涵盖的具体内容包括：回顾与 TDA 和 PT 相关的基本概念，例如单纯形和立方复形、同调、持久同调 (PH) 和 Vietoris-Rips 复形； TDA 和 PT 与理论代数概念（例如交换环、分级模和箭袋表示论）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，以及与深度学习和多层感知器等机器学习方法的相互作用；最后介绍了软件的实现以及TDA和PT的研究现状和进展。还将举行两次结构化实验室会议，向参与者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，请访问网站：https://www.cbmsweb.org 该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。