Mgr. Jan Volec, Ph.D.

2023 - 2027

This project will create novel mathematical methods that facilitate a better understanding of the properties of massive networks. Such networks appear in many real-life situations including links between Internet routers, user connections on social networks, or protein-to-protein interactions inside a molecule. Large networks are, however, also fundamental to many open problems in pure mathematics. In particular, they are a central object in extremal combinatorics. One of the key elements of this project focuses on providing new techniques of using a computer in order to find mathematical proofs. Another important aspect of the project revolves around randomness, which turns out to be extremely effective in various mathematical and computer science scenarios. In fact, for many problems involving decisions that were solved in this randomized way, we currently do not know anything that would perform even nearly as good as random choices do. In this project, we will study so-called pseudorandomness - a systematic way that aims at catching up with the randomness by being smart.