Explore the intricacies of geodesically convex optimization and its potential implications for proving P!=NP in this nearly two-hour computer science and discrete mathematics seminar. Delve into topics such as perfect matching, symbolic matrices, and the matching problem as presented by Herbert H. Maass Professor Avi Wigderson from the Institute for Advanced Study's School of Mathematics. Gain insights into the alternate minimization algorithm, its analysis, and the real problem at hand. Examine the process of quantizing the problem and understand its meaning and invariants. Engage with this in-depth exploration of advanced mathematical concepts and their potential applications in computational complexity theory.