Title: Small ball estimates: what, how, and why

Abstract:  Small ball estimates are a quantitative measure of how a function can concentrate near zero, often reflecting singularities in the function. In this talk, we focus on such estimates for functions in high dimensions. We will present known results, outline common proof techniques, and discuss their limitations. These limitations will naturally lead to more recent advances as well as some open questions. Finally, we discuss potential applications in different fields such as Harmonic Analysis and Optimization.