This project is concerned with two subjects, Mean-Field theory and Optimal transport in statistics and engineering.

Mean-Field theory is a powerful tool to efficiently approximate the behavior of a complex system involving infinitely many agents. In this approximation process, the mean-field replaces the agents' interactions; That is, the average collective effect of the agents becomes the basis of analysis. Mean-field theory finds applications in several fields and in recent years, it has gained popularity in game theory, artificial intelligence, and engineering. 

Furthermore, the theory of Optimal transport has deep connections with recent several research fields, e.g., efficient resource allocation in wireless communications and also domain adaptation in learning and trained algorithms. It stands as a powerful tool to study flows and analyze energy functionals on the space of probability measures. The theory has also attracted the attention of communication society to address the several problems that arise in wireless networks.

In this project, the goal is to analyze complex systems using the mean-field and transport theory in different settings, for example, when the agents have different types, or when the communication between the agents is constrained and limited. The theoretical results are then applied to optimize the ultra-dense wireless communication networks.