Warwick Symposium: Number Theory

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This is a proposal for a symposium to be held during the academic year 2012-2013 at the Mathematics Research Centre (MRC), University of Warwick. The overall theme of the symposium is number theory, a branch of mathematics that is thousands of years old, but also one that is thriving both internationally and in the UK. The prominence of number theory received a tremendous boost at the end of the 20th Century by the proof of Fermat's Last Theorem---a famous problem for over 350 years---by Sir Andrew Wiles. Much of cryptography makes heavy use of number theory, and thus number theory has found important applications to commerce, banking, information technology and national security.The symposium will facilitate a year-long sustained research activity across several strands of number theory. The general themes reflect a combination of some of the most important recent developments and the areas currently most active in number theory internationally.In practical terms the symposium will be structured around the following activities:1. A number of week-long workshops in various research areas of international significance pertaining to the general theme of the symposium. The various focus areas for the workshops provide a wide coverage of many aspects of modern number theory and foster interaction between researchers working in related by not necessarily overlapping areas.2. Research visits by internationally renowned experts who are encouraged to engage in discussions and collaborate with symposium participants and the UK number theory community. To maximize benefit to symposium participants and the UK number theory community, each of the visitors will be asked to give minicourse aimed at a broad number theory audience consisting of graduate students, postdocs and faculty members.3. A regular seminar that will be relayed to interested UK universities via the access grid system.The symposium will allow the UK and international research community to come together to exchange knowledge and ideas, explore new directions and deepen our understanding of this important and challenging subject.