One of the most intriguing questions in physics is the fundamental structure of space and time at the smallest imaginable scale. In Einstein's general relativity space and time are united into space-time, and this theory describes the universe impeccably on large scales, from the solar system up to galaxies and the entire universe. On the smallest scale atoms and subatomic particles are described by quantum mechanics. The problem is that, so far, we cannot combine these theories into one description of reality. Such a combination of quantum theory and gravity is necessary, for example, to understand how the universe evolved during and immediately after the big bang and what happens inside black holes.
There are many attempts to find a theory of quantum gravity and I am interested in understanding all of them. So far I have worked mainly on Causal Dynamical Triangulations and Causal Set theory.
A new direction I have recently started to explore is how Monte Carlo Methods can be applied to Non-Commutative-Geometry.
But there are many new directions to explore and I hope to do so in future projects.