Infinite derivative gravity:non-singular cosmology & blackhole solutions

Both Einstein's theory of General Relativity and Newton's theory of gravity possess a short dis- tance and small time scale catastrophe. The blackhole singularity and cosmological Big Bang singularity problems highlight that current theories of gravity are incomplete description at early times and small distances. I will discuss how one can potentially resolve these fundamental prob- lems at a classical level and quantum level. In particular, I will discuss infinite derivative theories of gravity , where gravitational interactions become weaker in the ultraviolet, and therefore re- solving some of the classical singularities, such as Big Bang and Schwarzschild singularity for compact non-singular objects with mass up to 10 25 grams. In this lecture, I will discuss quantum aspects of infinite derivative gravity and discuss few aspects which can make the theory asymp- totically free in the UV