Speaker
Description
This talk will provide an introduction to Loop Quantum Gravity and Spin Foam models. Loop Quantum Gravity is founded on a gauge-theoretic approach to the quantization of gravity. This approach leverages the huge diffeomorphism invariance of General Relativity to make the Wilson loops of gauge theory into practical probes of spacetime curvature and centers focus on the metrical areas of surfaces, rather than the usual lengths of curves. The simplest example of a loop quantization of geometry is the quantum tetrahedron. I will report on advances connecting classical and quantum tetrahedra to elliptic curves. In addition to the compelling connections with the quantization of geometry and gauge theories, recent years have seen substantial developments in the discrete geometry path integrals known as Spin Foam models. I will overview recent advances in the numerical treatment of these path integrals. This work is demonstrating how these path integrals can be used to address dynamical questions. I will emphasize the multifaceted approach of Loop Gravity, its connections to other approaches to quantum gravity, and some open questions.
