Graduate Student Support for Summer School in Topos Theory

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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.