PARTICIPANT SUPPORT FOR ATTENDANTS TO THE CONFERENCE: TYPE THEORY, HOMOTOPY THEORY AND UNIVALENT FOUNDATIONS

与会者对与会者的支持：类型论、同伦论和统一基础

• 批准号: 1324746
• 负责人: Steven Awodey
• 金额: $ 2.1万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-04-15 至 2014-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1324746&HistoricalAwards=false
• 关键词: PARTICIPANT; SUPPORT; ATTENDANTS; CONFERENCE; TYPE

This grant is for participation in the conference "Type Theory,Homotopy Theory and Univalent Foundations", at the Centre deRecerca Matematica in Barcelona (Spain), September 23-27, 2013.The grant will enable selected mathematicians affiliated with U.S.institutions to participate in the conference. The allocationof funds will favor graduate students, postdocs, junior faculty,and faculty with no current NSF support.The topic of the conference are the recent connectionsdiscovered between type theory and homotopy theory based on theinterpretation of identity types as path spaces. Theseconnections provide a new topological intuition that facilitatesworking with type theories and allow for new computational toolsfor manipulating homotopy-theoretic structures. Furthermore,Voevodsky's Univalent Foundations program provides a solidlogical basis for the practice of identifying isomorphicstructures, common throughout mathematics even if it is notallowed by standard set-theoretic foundations.The topic of the conference has an unusually wide impact sinceit involves several areas: mathematical logic, theoreticalcomputer science, homotopy theory and category theory. Inparticular, the developments offer a new perspective oncomputer-assisted formalization of mathematical proofs andverification of their correctness, which promises to benefit allmathematical endeavor, and further influence on design ofprogramming languages.Conference web page: http://www.crm.cat/2013/ctype

这项赠款是为了参加2013年9月23日至27日，在巴塞罗那（西班牙）的中心Derecerca Matematica参加会议“类型理论，同义理论和单价基础”。该赠款将使授予的选定数学家与USIVESSINTICTIONS隶属于USIVESITTICT，以参加会议。 基金分配将偏爱研究生，博士后，初级教职员工和没有NSF支持的教师。会议的主题是类型理论与同型理论之间的最新联系，基于身份类型的解释为路径空间。 该连接提供了一种新的拓扑直觉，可促进类型理论的工作，并允许操纵同质理论结构的新计算工具。 此外，Voevodsky的单价基础计划为识别同构结构的实践提供了一个固体基础，即使在数学过程中也很常见，即使不是标准集合理论基础，会议的主题具有多种影响，自从涉及多个领域：Mathematical Intoric，Mathemotical Intoricational Computer Science，Hormotoppy Worys，类别和类别。 这些事态发展提供了一种新的观点，可以通过数学证明和对其正确性的数学证据进行形式化，这有望使Allmeshematical努力受益，并对编程语言的设计进一步影响。会议页面：http:/http：///wwwwwww.crm.crm.cat/2013/ctype-2013/ctype typepement。