Explore a 55-minute lecture on combinatorial topological quantum field theories and their geometrical implications. Delve into the elegant expressions for partition functions on closed higher genus Riemann surfaces in lattice gauge theory with finite gauge group G. Examine finite algorithms that derive irreducible representation dimensions from group multiplications. Investigate integrality properties of character table partial sums for surfaces with boundaries. Compare G-Flat-TQFTs and G-Fusion-TQFTs to uncover row-column duality in character table integrality properties. Gain insights from recent research by Robert de Mello Koch et al. and Adrian Padellaro et al. on combinatoric topological strings and row-column duality in combinatorial topological strings.