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Combinatorial Construction

Objective

Combinatorial Construction is a mathematical challenge with many applications. Examples include the construction of networks that are very sparse but highly connected, or codes that can correct many transmission errors with little overhead in communication costs. For a general class of combinatorial objects, and some desirable property, the fundamental question in Combinatorial Construction is to demonstrate the existence of an object with the property, preferably via an explicit algorithmic construction. Thus it is ubiquitous in Computer Science, including applications to expanders, sorting networks, distributed communication, data storage, codes, cryptography and derandomisation. In popular culture it appears as the unsolved `lottery problem' of determining the minimum number of tickets that guarantee a prize. In a recent preprint I prove the Existence Conjecture for combinatorial designs, via a new method of Randomised Algebraic Constructions; this result has already attracted considerable attention in the mathematical community. The significance is not only in the solution of a problem posed by Steiner in 1852, but also in the discovery of a powerful new method, that promises to have many further applications in Combinatorics, and more widely in Mathematics and Theoretical Computer Science. I am now poised to resolve many other problems of combinatorial construction.

Host institution

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
Net EU contribution
€ 1 706 729,00
Address
Wellington Square University Offices
OX1 2JD Oxford
United Kingdom

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Region
South East (England) Berkshire, Buckinghamshire and Oxfordshire Oxfordshire
Activity type
Higher or Secondary Education Establishments
Non-EU contribution
€ 0,00

Beneficiaries (1)

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
United Kingdom
Net EU contribution
€ 1 706 729,00
Address
Wellington Square University Offices
OX1 2JD Oxford

See on map

Region
South East (England) Berkshire, Buckinghamshire and Oxfordshire Oxfordshire
Activity type
Higher or Secondary Education Establishments
Non-EU contribution
€ 0,00