This project investigates algebraic and geometric aspects of structures in quantum field theory and string theory, which will provide a theoretical framework for accounting for all fundamental interactions in particle physics. Particular attention is paid to the unification of quantum theory and general relativity, two cornerstones of 20th century physics. This unification, on one hand, seems to involve a beautiful mathematical structure hidden in its underlying theoretical framework. Understanding the underlying new hidden symmetries will enhance our understanding of how the fundamental physical laws are in action. On the other hand, it requires modifications of the geometry, that we have been familiar with in Einstein's theory of gravitation, at very small distances. We begin to attack the problems of how spacetime fabrics give rise to the observed Universe, of what is the origin of the mysterious dark energy that drives our Universe to an accelerated expansion etc. These modifications, if theoretically identified and observationally verified, will greatly change our world picture in a profound way. All these should help us to understand better the recent astrophysical and cosmological observations with high precision, that have begun to provide us detailed information about the origin of our Cosmos, its past, its present and its future as well.
