Warwick Symposium: Number Theory

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.

Number Theory is a core mathematical discipline in its own right with deep connections and relevance across mathematics. Number Theory has important applications to cryptography and coding theory, and emerging connections with physics. The primary beneficiaries of this symposium will be researchers working in number theory and in number-theoretic related cryptography. The symposium will impact the number theory community in the following ways:

1. Strengthening the knowledge base with number theory and related areas in the UK;
2. Bringing the best people worldwide to the UK in order to enhance its research basis;
3. Maintaining UK leadership at the cutting edge of research in this active and vibrant area.

In particular, this project will support UK universities' drive to be among the prime generators of top-quality research. This is not merely a matter of prestige; no country in the world can expect economic success without a strong scientific base and strong universities and, in particular, without strong mathematical foundation.

Expertise in number theory is sought after by a number of employers outside academia including government agencies. Our workshop NGC and the linked summer school will help raise awareness of such career opportunities among both mathematicians and computer scientists in the UK.

Within mathematics, number theory is a subject area that is much easier to popularize than many other areas. Many of the basic problems can be grasped by a GCSE mathematics student, even if the methods for resolving these demand many years of dedicated study. During the symposium year we plan to provide two talks aimed at the general public, by internationally renowned speakers, to raise public awareness and stimulate interest in this fascinating branch of science.