Graduate Student Support for Summer School in Topos Theory

Awodey正在申请资金，将两名纯逻辑和应用逻辑卡内基梅隆大学的博士生送到Topos Theory为期一周的暑期学校。该学校将在比利时举行，部分资金由卢万大学数学系赞助。除了PI之外，还有几位杰出的研究人员作为讲师参加了会议。会议的主要目的是为学生提供一个获得拓朴理论高级培训的机会。课程包括：一般层理论，分类拓扑学，下降理论和群组表示，拓扑学的同伦和上同调，代数集合论，以及可实现性。学生已成功完成卡内基梅隆大学逻辑和计算程序的硕士学位学习，现为卡内基梅隆大学纯粹逻辑和应用逻辑博士课程的博士生。他们被认为是有前途的杰出的逻辑学家，在一个在美国逻辑中没有得到充分代表的领域。拓扑论在数学、连接逻辑、拓扑学和代数几何中占有独特的地位。拓扑点的概念起源于代数几何的格罗森迪克学派，是“空间”的广义概念，但在逻辑上，它也包括布尔值模型、Cohenforcing和克里普克语义学，以及拓扑学和束模型。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，增进对科学技术的理解。

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.