Explore robust topological inference in this 54-minute lecture by Larry Wasserman. Delve into key concepts including persistence, target distribution, and distance to miss. Learn about effort results, self-confidence, and confidence bands. Examine bootstrap techniques and their comparison to bottleneck methods. Discover optimal tuning parameters and their application in real-world examples. Gain valuable insights into this complex topic, concluding with a Q&A session to reinforce understanding.