Delve into the advanced realm of BPS spectra and quantum invariants in this comprehensive lecture, the third installment of a series. Explore complex mathematical concepts and their applications in theoretical physics as presented by renowned expert Sergei Gukov. Over the course of 1 hour and 45 minutes, gain insights into cutting-edge research and developments in this specialized field. Engage with challenging ideas and expand your understanding of quantum mechanics and its intersection with mathematical theory. Suitable for advanced students and researchers in physics and mathematics, this lecture offers a deep dive into the intricacies of BPS spectra and their role in quantum invariants.