Polytopes and the Standard Model
We present new developments in the project which aims to understand interesting features of the Electroweak interaction which are observed but unexplained, such as the weak mixing angle, from embeddings of subalgebras into larger groups. This talk will explore historical examples of recognizing deeper structure from observed symmetries and draw analogies to what is being attemped now to describe new symmetries which seem to underly the Electroweak quantum numbers. The talk will introduce relevant concepts from group theory and representation theory and how they relate to all areas of physics, including gravity and cosmology. We speculate on insights this proposed symmetry may give to the problem of quantum gravity and unifying the spacetime symmetries and internal symmetries.
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