Recently powerful techniques have emerged for performing multi-loop computations of scattering amplitudes in quantum gravity and  supergravity.  These techniques include generalized unitarity and the double-copy property, related to color-kinematics duality in gauge theory.  Using these  techniques, the ultraviolet divergence structure of N=8 supergravity, and more recently pure N=4 supergravity, have been assessed, not only in four space-time dimensions but also in higher dimensions.

Causal dynamical triangulations (CDT) define a nonperturbative path integral for quantum gravity as a sum over triangulations. Causality is enforced on the kinematical level by means of a preferred
foliation.

By way of presenting some classic and many new results, my talk will indulge shamelessly in
advertising "Causal Dynamical Triangulations (CDT)" as a hands-on approach to nonperturbative quantum gravity that reaches where other approaches currently don't. After summarizing the rationale and basic ingredients of CDT quantum gravity and some of its key findings (like the emergence of a classical de Sitter space), I will focus on some very recent results: how we uncovered the presence of a second-order phase transition (so far unique in 4D quantum

Causal set quantum gravity is based on the marriage between the concept of causality as an organising principle more basic even than space or time and fundamental atomicity. Causal sets suggest novel possibilities for "dynamical laws" in which spacetime grows by the accumulation of new spacetime atoms, potentially realising within physics C.D. Broad's concept of a growing block universe

Our understanding of the physical world at the most fundamental level is based on two theories: quantum theory and general relativity. They are impressively successful when each is considered on its own, but in situations where both play a role, we are reduced to puzzles and absurdity. To the great frustration of researchers, candidate theories of quantum gravity produce more puzzles than answers. We shall tour of some of the problems, focusing on the role of spacetime and causality.

Effective field
theory techniques allow reliable quantum calculations in general relativity at
low energy. After a review of these techniques, I will discuss the attempts to
define the gravitational corrections to running gauge couplings and to the
couplings of gravity itself. I will also describe an attempt to understand the
relation between the effective field theory and Asymptotic Safety in the region
where they overlap.

In this talk, I will discuss about the notion of quantum renormalization group, and explain how (D+1)-dimensional gravitational theories naturally emerge as dual descriptions for D-dimensional quantum field theories. It will be argued that the dynamical gravitational field in the bulk encodes the entanglement between low energy modes and high energy modes of the corresponding quantum field theory.

The existence of three generations of neutrinos and their mass mixing is a deep mystery of our universe. On the other hand, Majorana's elegant work on the real solution of Dirac equation predicted the existence of Majorana particles in our nature, unfortunately, these Majorana particles have never been observed. In this talk, I will begin with a simple 1D condensed matter model which realizes a T^2=-1 time reversal symmetry protected superconductors and then discuss the physical property of its boundary Majorana zero modes.