On the Complexity of the Problem of Equivalence

Lead Student Presenter(s)

Yoojung Kwon

Abstract or Description

The problem of equivalence, which dates back to Gauss and Cartan, has been a subject of study for centuries. The problem asks for simple, necessary and sufficient conditions for deciding when two Riemannian metrics represent the same geometry, albeit in a different coordinate system. This research project aims to employ modern methods from descriptive set theory to identify the intrinsic complexity of the problem of equivalence in the special case of dimension 2. Through this approach, we hope to gain insights as to which invariants can and cannot be used in solving the problem of equivalence.

Mentor

Aristotelis Panagiotopoulos