Awodey is requesting funding to send two Ph.D. students in Pure and Applied Logic at 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 Department of Mathematics of the University of Louvain-la-Neuve. In addition to the PI, several distinguished researchers are participating as instructors. The primary aim of the meeting is to provide students with an opportunity to 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, and realizability. The students have successfully completed M.S. studies in Carnegie Mellon's Logic and Computation program and are now doctoral students in Carnegie Mellon's PhD program in Pure and Applied Logic. They are judged to be promising logicians of outstanding ability, in a field that is under-represented in U.S. logic.
Topos theory occupies a unique position in mathematics, connecting logic, topology, and algebraic geometry. The notion of a topos originated in the Grothendieck school of algebraic geometry as a generalized notion of "space", but in logic it also subsumes Boolean-valued models, Cohen forcing, and Kripke semantics, as well as topological and sheaf models. It is also related to the logical notion of a deductive system of higher-order logic or type theory. The broader impacts of the proposed project include not only promoting graduate education, but also enhancing infrastructure for research and education through international partnerships; and the broad dissemination of results, enhancing scientific and technological understanding.
