Toric degenerations of the algebra of conformal blocks and compactifications of character varieties
Abstract: The algebra of conformal blocks is a commutative ring built from the spaces of conformal blocks of the Wess-Zumino-Novikov-Witten model of conformal field theory attached to a smooth projective curve and a simple Lie algebra. For algebraic geometers, these rings emerge naturally as the total coordinate rings of the moduli of principal bundles on the curve.