Combinatorics and graph theory
Project ID: 2228cd1406 (You will need this ID for your application)
Research Theme: Mathematical Sciences
UCL Lead department: Mathematics
Lead Supervisor: John Talbot
Project Summary:
Combinatorics is the branch of mathematics concerned with counting discrete structures of various types (permutations, graphs, lattice points, etc.). It has applications in computer science, statistical physics, molecular biology, and many other fields. In particular, the interface between theoretical computer science and combinatorics has been an extremely important catalyst in the subject’s modern development.
This research project will focus on some combination of the following three areas:
1) the interface of combinatorics with analysis and in particular the positivity of Taylor series of inverse powers of various combinatorially defined polynomials.
2) Discrete geometry including Tverberg-type theorems and problems concerning lattice points.
3) Extremal and probabilistic problems in graphs and hypergraphs.