Noncommutative Functional Inequalities and Applications to the Quantum KKL-conjecture

In this seminar talk, explore noncommutative functional inequalities and their applications to the quantum KKL-conjecture with speaker Sijie Luo from Central South University. The presentation begins with an overview of functional inequalities background and motivations, covering well-known results like Poincaré inequality, log-Sobolev inequality, and Talagrand inequality. Learn about recent advancements in noncommutative functional inequalities, including the noncommutative Eldan-Gross inequality and p-log-Sobolev inequality for general noncommutative hypercontractive semigroups. Discover how these results provide an alternative answer to the quantum KKL conjecture. The talk is part of the BIMSA-Tsinghua Quantum Symmetry Seminar series and is based on joint work with J. Yong, D. Zanin, and D. J. Zhou.