Graduate Student Support for Summer School in Topos Theory

拓扑理论暑期学校研究生支持

• 批准号: 0501035
• 负责人: Steven Awodey
• 金额: $ 0.54万
• 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: 2005
• 资助国家: 美国
• 起止时间: 2005-05-15 至 2006-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0501035&HistoricalAwards=false
• 关键词: Graduate; Student; Support; Summer; Topos

Awodey is requesting funding to send two Ph.D. students in Pure and Applied Logicat Carnegie Mellon University to a week-long summer school in topos theory.The school will be held in Belgium, and is partially sponsored by the Departmentof Mathematics of the University of Louvain-la-Neuve. In additionto the PI, several distinguished researchers are participating as instructors.The primary aim of the meeting is to provide students with an opportunityto acquire advanced training in topos theory. Topics to be covered include:general sheaf theory, classifying toposes, descent theory and groupoid representations,homotopy and cohomology of toposes, algebraic set theory, andrealizability.The students have successfully completed M.S. studies in Carnegie Mellon'sLogic and Computation program and are now doctoral students inCarnegie Mellon's PhD program in Pure and Applied Logic. They arejudged to be promising logicians of outstanding ability, in a field that isunder-represented in U.S. logic.Topos theory occupies a unique position in mathematics, connectinglogic, topology, and algebraic geometry. The notion of a topos originatedin the Grothendieck school of algebraic geometry as a generalized notionof "space", but in logic it also subsumes Boolean-valued models, Cohenforcing, and Kripke semantics, as well as topological and sheaf models. It isalso related to the logical notion of a deductive system of higher-order logicor type theory.The broader impacts of the proposed project include not only promotinggraduate education, but also enhancing infrastructure for research andeducation through international partnerships; and the broad disseminationof results, enhancing scientific and technological understanding.

Awodey正在申请资助，将卡内基梅隆大学纯逻辑与应用逻辑专业的两名博士生送到为期一周的拓扑理论暑期学校。这所学校将在比利时举办，部分由新鲁汶大学数学系赞助。除了PI之外，还有几位杰出的研究人员作为讲师参加。会议的主要目的是为学生提供一个获得拓扑理论高级培训的机会。涵盖的主题包括：一般束理论，分类拓扑，下降理论和群样表示，拓扑的同伦和上同调，代数集合理论和可实现性。这些学生已经成功完成了卡内基梅隆大学逻辑与计算专业的硕士课程，现在是卡内基梅隆大学纯粹与应用逻辑博士课程的博士生。他们被认为是有前途的逻辑学家，具有杰出的能力，在美国逻辑学中代表性不足。拓扑理论在数学、连接逻辑、拓扑和代数几何中占有独特的地位。拓扑的概念起源于代数几何的格罗滕迪克学派，作为“空间”的广义概念，但在逻辑上它也包括布尔值模型，科恩强迫和克里普克语义，以及拓扑和束模型。它还与高阶逻辑或类型论的演绎系统的逻辑概念有关。建议项目的广泛影响不仅包括促进研究生教育，还包括通过国际伙伴关系加强研究和教育的基础设施；并广泛传播成果，增进科学技术认识。