Explore a 51-minute lecture by Thomas Sinclair from Purdue University on the concept of index for finite-dimensional operator systems. Delivered at the Fields Institute on August 28, 2023, this talk is part of the Workshop on Operator Algebras and Applications: Connections with Logic. Delve into the intricacies of operator systems and their indexing, gaining insights from Sinclair's expertise in the field. Note that some audio issues occur in the first 5 minutes of the presentation. For a more comprehensive understanding, access the abstract and additional information about the workshop and thematic program on Operator Algebras and Applications through the provided links.