Our RiT project concerns both geometry and general relativity. The intersection of those fields has been the subject of intense studies in recent years, with steadily growing interest in the mathematical community in the problems involved. We wish to develope gluing methods as a very general tool to construct interesting initial data for (nonlinear) geometric field equations of mathematical physics, such as those arising from the k-Yamabe models, the Lovelock theories of gravity, or extended theories of gravity. As a result of this, we will not only construct of new classes of physically significant field configurations but also identify and exhaustively describe the obstructions to gluings, and thus obtain a better understanding of the mathematical invariant structure of those field models.

Research Team:

Piotr T. Chruściel (U Vienna), Luc Nguyen (Oxford U)