Higher spin symmetry in quantum gravity, condensed matter and mathematics
A serious open issue is that there is no widely accepted solution to the Quantum Gravity Problem. This results in paradoxes and clouds the study of many problems from the cosmology of the early Universe to unified theories of fundamental interactions that should incorporate both the Standard Model of Elementary Particles and Gravity. This proposal aims at attacking the old problems from a new vantage point and to achieve long-awaited breakthroughs. 

The potential reward is enormous as the project aims to shed light on the wide range of problems by exploring a new avenue provided by the first working example of a Higher Spin Gravity (HiSGRA). It will (A) attack the Quantum Gravity Problem and give new consistent theories that should significantly extend our understanding; (B) the underlying higher spin symmetry should govern a number of condensed matter systems and we expect to prove the recently discovered remarkable dualities relating them; (C) these symmetries are also related to extensions of Deformation Quantization, which should lead to new developments in pure mathematics and consolidate A+B. HiSGRA's, as rather simple models, can give keys to the puzzles of the early Universe with potentially observable effects in the near future, to the old paradoxes of black hole physics and to real-world processes of black hole scattering, which together with B applies HiSGRA to physics. 

This project is timely and feasible thanks to the recent ground-breaking results obtained by me and collaborators: (1) the very first example of a quantum consistent HiSGRA has been constructed and shown not to suffer from the UV-divergences that are at the core of the Quantum Gravity Problem; (2) the same theory was instrumental in attacking the dualities in three-dimensional conformal field theories that govern the physics of many second-order phase transitions; (3) it made new verifiable predictions for correlation functions, which is the very first solid prediction from HiSGRA