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要求资金发送两位博士学位。纯净和应用的Logicat Carnegie Mellon University的学生在Topos理论上为期一周的暑期学校。该学校将在比利时举行，并由Louvain-La-Neuve大学的数学系部分赞助。除了PI，几位杰出的研究人员正在作为讲师参加。会议的主要目的是为学生提供获得Topos理论的高级培训的机会。要涵盖的主题包括：一般的捆起来理论，对座椅的分类，血统理论和群体素体表示，座椅的同型和共同体学，代数集理论，andrealive andrealizity。学生已经成功地完成了M.S.在卡内基·梅隆（Carnegie Mellon）的智能和计算计划中的研究，现在是博士生的Incarnegie Mellon的博士学位纯和应用逻辑计划。在美国逻辑中占代表性的领域中，他们被认为是有前途的逻辑学家。 Topos的概念起源于Grothendieck代数几何学学院作为“空间”的广义概念，但在逻辑上，它还包含了布尔值模型，同伴和Kripke语义，以及Kripke语义，以及拓扑和拓扑模型。这与高阶逻辑类型理论的演绎系统的逻辑概念有关。拟议项目的更广泛影响不仅包括促进毕业生教育，还包括通过国际伙伴关系增强研究和教育的基础设施；以及结果的广泛传播，增强了科学和技术理解。