PhD in Mathematics

The probabilistic method is a powerful tool which has been especially influential in the fields of combinatorics and computer science. In the context of combinatorics, this method was pioneered by Erdős, who demonstrated that random constructions could often be effective in settings where explicit constructions are infeasible. These ideas, establishing a correspondence between counting and probability, allow for the application of tools from probability theory to combinatorial problems and motivate the study of the typical properties of various combinatorial models, such as the Erdős–Rényi random graph, and discrete random processes. The aim of this project is for the student to develop an understanding of these tools and to apply these techniques to open research problems in the field.