The Long Path to √d Monotonicity Testers - Lecture 1

Explore the theoretical foundations of monotonicity testing algorithms in this lecture delivered by C. Seshadhri at the International Centre for Theoretical Sciences. Delve into the mathematical journey toward achieving √d monotonicity testers, examining the algorithmic challenges and geometric insights that have shaped this field of research. Learn about the intersection of combinatorial optimization, probability theory, and geometric approaches that contribute to understanding monotonicity testing problems. Discover how spectral methods, convex programming techniques, and random walk approaches apply to this specific area of theoretical computer science. Examine the connections between high-dimensional expanders, isoperimetry, and sampling algorithms as they relate to monotonicity testing. Understand the progression of research that has led to current √d complexity bounds and the mathematical techniques required to achieve these results. This lecture forms part of a comprehensive discussion meeting on Geometry, Probability, and Algorithms, bringing together cutting-edge research at the intersection of these three fundamental areas of theoretical computer science.