East Midlands Branch

THE INSTITUTE OF MATHEMATICS

AND ITS APPLICATIONS

The Random Graph

a talk by

Peter Cameron

Queen Mary College

London University

Thursday 21st February, 2002

starting at 7.30 pm

The Nottingham Trent University

Clifton Site, Main Building, Room CM004

No charge is made to attend meetings, non-IMA members are welcome

Abstract

According to Leibnitz, the best of all possible worlds is also the most probable. In striking agreement with this principle, Erdos and Renyi showed that there is a countably infinite graph R with the property that, if a countable graph is chosen at random (by selecting edges independently with probability ½), then it is almost surely isomorphic to R. Moreover, R has many interesting properties such as universality and a high degree of symmetry, and arises in contexts as different as axiomatic set theory and quadratic reciprocity.

For further details of this event or other East Midlands Branch activities consult the Web Site http://science.ntu.ac.uk/msor/ccb/ima.html or by contacting the Branch General Secretary:

Dr Stephen Hibberd, Division of Theoretical Mechanics, School of Mathematical Sciences, University of Nottingham, Tel. (0115) 9513841 or email: Stephen.Hibberd@nottingham.ac.uk