Thu, 15 Oct 2015

16:00 - 17:00
L5

Sums of seven cubes

Samir Siksek
(University of Warwick)
Abstract

In 1851, Carl Jacobi made the experimental observation that all integers are sums of seven non-negative cubes, with precisely 17 exceptions, the largest of which is 454. Building on previous work by Maillet, Landau, Dickson, Linnik, Watson, Bombieri, Ramaré, Elkies and many others, we complete the proof of Jacobi's observation.

How do networks shape the spread of disease and gossip?

A new approach to exploring the spread of contagious diseases or the latest celebrity gossip has been tested using London’s street and underground networks. Results from the new approach could help to predict when a contagion will spread through space as a simple wave (as in the Black Death) and when long-range connections, such as air travel, enable it to seemingly jump over long distances and emerge in locations far from an initial outbreak.

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