Dr John Talbot, PhD
Royal Society University Research Fellow

Pure Mathematics Graduate Tutor

Room 812a
Tel: ++44 (0)20 7679 4102
E-mail: talbotmath.ucl.ac.uk
Fax: 020-7383-5519

Research Interests
Combinatorics, Complexity Theory

My main research interests lie in extremal combinatorics.

I am particularly interested in Turan-type problems for hypergraphs. These are questions asking how large a family of sets can be, given that it does not contain a copy of some particular small subfamily.

For example, one of the oldest results in combinatorics determines the maximum number of edges in a triangle-free graph. I am currently looking at the natural generalisation of this problem to triple systems, which is a long standing open question in this field.

I am also interested in problems related to intersecting families of sets. Recent work in this area has included a characterisation of the intersection structure of such families. This answers questions of the form: "Given an intersecting family F, of r-sets from {1,2,...,n}, how many k-sets can occur as pairwise intersections of sets from F?"

Other recent work in this area includes Erdos-Ko-Rado theorems for various structures. A motivating conjecture in this area, due to Chvatal, asserts that in any hereditary family of sets no intersecting family is larger than the largest star.