Probability at the interface of computation, combinatorics, and statistical physics

Birmingham has a vibrant research group in combinatorics, broadly defined. Research interests of group members include discrete probability, algorithms and computational complexity, extremal combinatorics, graph theory, and combinatorial number theory.

This project is based in probability theory and in particular in how randomness and computation interact and in probabilistic models of physical systems. Some of the important questions we look to understand include: 1) Can hard computational problems be generated efficiently from a probability distribution? 2) Does randomization allow for stronger algorithms? 3) Is there a purely geometric explanation for the liquid solid phase transition in physics?

Some topics the project could involve include Markov chains, random graphs, independent sets in graphs, spectral algorithms, and geometric probability.

To learn more about the combinatorics group at Birmingham, please visit: http://www.birmingham.ac.uk/research/activity/mathematics/pure-maths/combinatorics.aspx

To find out more about studying for a PhD at the University of Birmingham, including full details of the research undertaken in each school, the funding opportunities for each subject, and guidance on making your application, you can now order your copy of the new Doctoral Research Prospectus, at: www.birmingham.ac.uk/students/drp.aspx