Combinatorics is concerned with counting discrete structures of various types, it has applications in computer science, statistical physics, molecular biology, and many other fields.

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.

There is a long and distinguished history of combinatorics at UCL, indeed the first recorded use of the term "graph" in the sense of a network is found in a Nature article from 1878 by the former UCL student J.J.Sylvester.

Recent research at UCL into combinatorics centres on three main 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.

Our regular Combinatorics and Discrete Geometry Seminar is on Tuesdays at 5pm during Autumn and Spring term.

#### Group members

Prof Imre Barany

Prof Alan Sokal

Dr John Talbot