Carlo Rovelli delivers The Roger Penrose Lecture on the Quantum structure of Spacetime. In developing the mathematical description of quantum spacetime, Loop Quantum Gravity stumbled upon a curious mathematical structure: graphs labelled by spins. This turned out to be precisely the structure of quantum space suggested by Roger Penrose two decades earlier, just on the basis of his intuition. Today these graphs with spin, called "spin networks" have become a common tool to explore the quantum properties of gravity. In this talk Carlo will tell this beautiful story and illustrate the current role of spin networks in the efforts to understand quantum gravity. 
 Carlo Rovelli is a Professor in the Centre de Physique Théorique de Luminy of Aix-Marseille University where he works mainly in the field of quantum gravity and  is a founder of loop quantum gravity theory. His popular-science book 'Seven Brief Lesson on Physics' has been translated into 41 languages and has sold over a million copies worldwide. The Oxford Mathematics Public Lectures are generously supported by XTX Markets.