Graduate Student Support for Summer School in Topos Theory

Awodey正在申请资金派遣两名博士。卡内基梅隆大学的纯逻辑和应用逻辑专业的学生参加了为期一周的拓扑理论暑期班。该暑期班将在比利时举行，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。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。课程内容包括：一般层理论、拓扑分类、下降理论和广群表示、拓扑的同伦和上同调、代数集合论和可实现性。在卡内基梅隆大学的逻辑和计算程序的研究，现在在卡内基梅隆大学的博士生在纯粹和应用逻辑课程。他们被认为是有前途的杰出能力的逻辑学家，在一个领域，是在美国代表逻辑。拓扑理论占据了独特的地位，在数学，连接逻辑，拓扑学和代数几何。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，但在逻辑中，它也包括布尔值模型、科恩强迫和克里普克语义，以及拓扑和层模型。它还与高阶逻辑或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;以及广泛传播成果，提高科学和技术理解。

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.