Sampling, Privacy, and Spectral Geometry - Insights from Low-Rank Approximation

Explore the intersection of sampling techniques, privacy considerations, and spectral geometry through the lens of low-rank approximation methods in this conference talk. Delve into how geometric, probabilistic, and algorithmic approaches converge to address complex theoretical computer science problems. Examine the connections between spectral methods in combinatorial optimization, the role of expanders and high-dimensional expanders, and random walk-based sampling and counting techniques. Discover insights into isoperimetry and its geometric implications while understanding how low-rank approximation serves as a unifying framework for these diverse mathematical concepts. Learn about cutting-edge research directions that emerge from the interplay between geometry, probability, and algorithms, with particular emphasis on how these theoretical foundations apply to practical sampling problems and privacy-preserving computations.