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Spinfoam Formulation of Loop Quantum Gravity

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Recently there are a lot of progresses in developing the spinfoam formulation of loop quantum gravity. In this talk I give an overview of the subject. I introduce the formalism and the motivation of the theory, and I discuss the application of spinfoam formulation in black hole and cosmology. I also discuss the inclusion of the quantum matter fields and cosmological constant in the formalism. The inclusion of cosmological constant motivates a Chern-Simons formulation of LQG. Finally I discuss the semiclassical low-energy approximation of the spinfoam formulation, where Einstein gravity appears as the leading contribution.