Explore advanced mathematical concepts in this 18-minute IEEE conference talk on accelerating polytope-related computations. Delve into the innovative "Ball Walk" algorithm, which offers sublinear implementation for faster polytope rounding, sampling, and volume computation. Learn about current bottlenecks in Markov chains, discover the key results, and understand why this approach works with high probability. Examine the faster implementation techniques, analyze running times and expected costs, and investigate the anti-concentration lemma. Conclude by exploring future directions in this cutting-edge area of computational geometry and probability theory.