Explore the intricacies of two-dimensional topological field theories and their connection to partial fractions in this comprehensive lecture. Delve into joint research conducted with M. Khovanov and Y. Kononov, focusing on the evaluation of topological field theories on surfaces of varying genera. Investigate the resulting sequences and analyze how they are influenced by the assumptions made about the target category. Gain insights into the mathematical foundations of this complex topic and its implications for the field of topology.