As a student I have grown a curiousity on Research Topics in Mathematics. Anyways I would like to know what are the current Research Topics in Mathematics for Phd students? I just want an idea of what they are researching on, to give me a focus in a particular area of study of the basics needed to understand such research. As well, another question I have. Can the Mathematics of General Relativity be considered a branch in Pure Mathematics? As to describe Geometrical Spaces leaving out the physics, or somewhat incorporating physics. Im interested particularly in Einstein Field Equations as a Pure Mathematics subject rather then a Theoretical Physics subject. Mainly I think my main problem in physics, is that my ideologies in Mathematics conflicts with Physics. I've always been somewhat of a Platonist believing in a Transcendental Mathematics of the Universe. Whereas I've tried rediculously to form understandings in Physics from Pure Mathematics with no applications of Physical Phenomenon which has led to my ultimate failure in understanding Physics. However I do understand that Einsteins General Theory of Relativity has a huge application of Riemann Geometry, is general relativity without the physics an understanding of Riemann Geometry? As for that, please list if you know of, the current research topics in Pure Mathematics for Phd students. I would be thankful for such.