A Finite Dimensional Proof of the Verlinde Formula

Explore a groundbreaking algebraic-geometric proof of the Verlinde formula in this advanced mathematics lecture. Delve into the historical context of the formula, which predicts dimensions for spaces of generalized theta functions on moduli spaces of parabolic bundles on curves. Learn about the transition from infinite-dimensional proofs using conformal blocks to finite-dimensional approaches. Examine the speaker's novel unconditional proof, based on two key recurrence relations: one for the genus of curves and another for the number of parabolic points. Gain insights into this collaborative work that advances our understanding of complex mathematical structures and their applications in theoretical physics.