Explore an advanced cutting plane method for convex optimization and convex-concave games in this 24-minute conference talk presented at an Association for Computing Machinery (ACM) event. Delve into the setup of the cutting plane method, examine the speaker's results, and understand the role of separation oracles. Trace the historical development of cutting plane methods before diving into a simplified version of the Vaidya 89 algorithm. Analyze runtime bottlenecks and maintenance challenges, with a focus on leverage score maintenance. Discover a multi-layered data structure approach and its implications for the Matrix Multiplication Zoo. Investigate more general cutting plane methods and their practical applications. Conclude with a Q&A session to address any remaining questions on this sophisticated optimization technique.