PhD Studentship: Probabilistic Combinatorics

University of Birmingham; Birmingham; On-site; GBP 20,000 - 30,000; Full time

Job summary

The University of Birmingham invites applications for a graduate research project exploring probabilistic methods in combinatorics and computer science. You will study how random constructions can illuminate counting and probability, and how these ideas relate to models such as Erdős–Rényi graphs.

Under the supervision of Dr. Joshua Erde, you will develop understanding of these tools and apply techniques to open problems in the field, contributing to current research in discrete probability and

Qualifications

• First-class Master's degree in Mathematics or equivalent.
• Strong background in combinatorics and discrete probability.
• Good communication skills (oral and written).

Responsibilities

• Apply probabilistic methods to open research problems in combinatorics and computer science.

Skills

Combinatorics

Discrete probability

Communication skills

Education

Master's degree in Mathematics

Job description

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.

The project will be supervised Dr by Joshua Erde ([e-mail]).

Entry requirements:

We are looking for an enthusiastic and highly-motivated graduate with

• A first class degree in Mathematics at the Master’s level (or equivalent);
• A strong background in combinatorics and discrete probability, or related fields;
• Good communication skills (oral and written).