Explore the challenges and techniques of fitting manifolds to data with significant noise in this 45-minute lecture by Hari Narayanan. Delve into advanced data science concepts as part of the "Data Science: Probabilistic and Optimization Methods" discussion meeting at the International Centre for Theoretical Sciences. Gain insights into cutting-edge approaches for handling noisy datasets and learn how manifold fitting techniques can be applied in the presence of large-scale disturbances. Discover the intersection of pure mathematics and practical data analysis, and understand how these methods contribute to the evolving landscape of data science and its applications across various fields.