Explore the intricacies of continuous maximum entropy distributions and their applications in this 24-minute conference talk presented at the Association for Computing Machinery (ACM). Delve into the dual program and key questions surrounding the topic, examining motivating examples from quantum entropy and interior point methods. Uncover the main results of the research, including an application to SDP rounding. Learn about the overall algorithm, bounding box, and counting oracle for projections of fixed rank. Conclude by considering future directions in this field of computational mathematics and its potential impact on various applications.