Differential Schemes and Differential Cohomology (12w2151)
Richard Churchill (Hunter College, City University of New York (CUNY), Graduate Center, CUNY, and University of Calgary)
Yang Zhang (The University of Manitoba)
There are two main objectives. The first is to introduce very recent work on the ``modernization'' of differential algebra to algebraic geometers/number theorists having little or no acquaintance with the field.
The basic properties of the differential spectrum (``DiffSpec'') of a differential ring have now been established in a manner which workers in those areas can quickly grasp, but those ideas need a proper venue for communication. The informal nature of BIRS' workshops, which are familiar to both applicants, would be ideal.
The second objective is to illustrate how algebraic problems which can be solved ''locally'' in terms of differential equations may admit global solutions in terms of differential cohomology. Specifically, very recent work by Ray Hoobler enables one to understand Kolchin's constrained cohomology in terms of the $,Delta$-flat topology, and that should offer new methods to algebraic geometers and number theorists. And of course the interaction of people in those areas with differential algebraists should result is new methods for use by the latter group.