Abstract:
We resolve the problem for the optimal hypercontractive constant $r_{p,q}(\mathbb{Z}_3)$ of the cyclic group $\mathbb{Z}_3$ for all $1 < p < q < \infty$, by characterizing them via an explicit system of equations. As a consequence of our main result, for rational $p, q\in \mathbb{Q}$, the constants $r_{p,q}(\mathbb{Z}_3)$ are algebraic numbers which generally admit no radical expressions, since their often rather complicated minimal polynomials may have non‑solvable Galois groups. Our formalism relies on a key observation of the existence of nontrivial critical extremizers. This formalism can also be adapted to yield a resolution of the long-standing open problem of determining all optimal $(p,q)$-hypercontractive constants for biased Bernoulli random variables. The talk is based on a recent joint work with Jie Cao, Yong Han, Shilei Fan and Zipeng Wang.
Biography:
Yanqi Qiu is a Professor at the Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences. In 2007, he was admitted to École Normale Supérieure (Paris) after graduating from Tsinghua University. He obtained his Master's degree in Mathematics from Université Paris VI in 2010 and his Ph.D. in Mathematics from the same university in 2013. From 2013 to 2015, he conducted postdoctoral research at Aix-Marseille University. In 2015, he became a tenured researcher (Chargé de Recherche) at CNRS. In 2017, he became an Associate Professor at the Institute of Mathematics, Chinese Academy of Sciences, and was promoted to Professor in 2019. From 2021 to 2023, he also served as a Professor at the School of Mathematics and Statistics, Wuhan University. In 2023, he transferred from the Institute of Mathematics, Chinese Academy of Sciences, to his current position as a Professor at the Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences. His research spans multiple areas of analysis, including functional analysis, random analysis, and harmonic analysis.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.