A Geometrical Interpretation of Universally Quantified Inequalities and Its Applications to Mathematics

Explore a 37-minute conference talk by Raymond W. Yeung at ICBS2024 that delves into a geometrical interpretation of universally quantified inequalities and its wide-ranging applications across various mathematical disciplines. Discover how the study of Shannon entropy over the past two decades has led to groundbreaking insights, including the identification of non-Shannon-type inequalities and the establishment of connections between entropy and fields such as finite group theory, combinatorics, Kolmogorov complexity, probability, and matrix theory. Learn about a novel approach that extends this geometrical interpretation to any universally quantified inequality, with examples demonstrating its application to the Markov inequality in probability theory and the Cauchy-Schwarz inequality for inner product spaces. Gain insight into the potential of this methodology for uncovering new inequalities and constraints across different branches of mathematics.