Theory and application of exact and approximate enumeration

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Enumeration is the branch of mathematics that examines questions of the form "How many..."; it is perhaps the apparent simplicity and yet universal nature of these questions that explains their ubiquity. They arise in many different areas of mathematics and in problems at the interface between mathematics and physics, chemistry and computer science. The primary aim of this program is develop and apply different types of approximation techniques which will help to answer problems in combinatorics, group theory, statistical physics, coding theory, and the mathematics of random knotting and linking.