Chandra Nair (CUHK)June 19, 2025 Title and AbstractInformation Inequalities on Additive Structures This talk will consist of two parts. In the first part, we will present formal equivalences between inequalities in additive combinatorics and inequalities involving information measures. Analogies between these two families of inequalities were previously observed and established by Tao and Ruzsa, with Ruzsa having proven formal equivalences between some of these families. Building on Ruzsa’s work, we extend these equivalences to larger families of inequalities. In the second part, we will establish a finite Abelian group analogue of a family of inequalities that unify the Entropy Power Inequalities and the Brascamp-Lieb inequalities. We demonstrate that Haar distributions (in a manner similar to Gaussians in continuous spaces) are the maximizers of these families in discrete spaces. This work is done jointly with my doctoral student Chin Wa (Ken) Lau. BioChandra Nair is a professor in the Department of Information Engineering at The Chinese University of Hong Kong. His research primarily focuses on developing innovative ideas, tools, and techniques to tackle combinatorial and non-convex optimization problems within information sciences. His recent work explores the optimality of inner and outer bounds of capacity regions in multiuser information theory, closely linked to the sub-additivity properties of information functionals. This research extends to the study of information inequalities at the intersection of functional analysis and additive combinatorics. He (co)-received the 2016 Information Theory Society Paper Award for a novel approach to establishing the optimality of Gaussian distributions in a class of non-convex optimization problems in multiuser information theory. His doctoral dissertation included a proof of the Parisi and Coppersmith-Sorkin conjectures related to the Random Assignment Problem. During his postdoctoral research, he resolved several conjectures concerning the Random Energy Model approximation of the Number Partition Problem. He earned his Bachelor of Technology in Electrical Engineering from the Indian Institute of Technology Madras, where he was given the Philips (India) and Siemens (India) awards for academic excellence. He continued his graduate studies at Stanford University as a Stanford Graduate Fellow (2000–2004) and Microsoft Graduate Fellow (2004–2005). He subsequently worked as a postdoctoral researcher with the Theory Group at Microsoft Research in Redmond (2005–2007). Since joining The Chinese University of Hong Kong in 2007, he has served as an Associate Editor for the IEEE Transactions on Information Theory (2014–2016) and as a Distinguished Lecturer for the IEEE Information Theory Society (2017–2018). He is a Fellow of the IEEE and currently serves as the Programme Director for the undergraduate program in Mathematics and Information Engineering |