EPSRC Centre for Doctoral Training in Geometry and Number Theory at the Interface

几何和数论是纯数学中的核心学科，在科学和社会中产生了许多影响。它们是自古希腊时代以来就吸引了一些最优秀的数学头脑的学科，并继续对专业和业余数学家产生自然的吸引力。纵观数学史，这两个主题经常启发了重大的数学发展，这些发展产生了巨大的影响，超出了它们最初的应用。数论的魅力以费马大定理的故事为例，它的陈述写于1637年，足够简单，任何熟悉高中数学的人都能理解。经过350多年的艰苦工作和数学上的重大发展，怀尔斯的著名证明终于在1995年出版。怀尔斯的证明涉及数论和几何的混合思想，这些主题之间的相互作用是当今纯数学研究中最活跃的领域之一。中心需要培养下一代学术研究人员，以保持英国大学的卓越和竞争力，并培养训练有素的数学家，准备在金融和其他高科技行业取而代之。正如我们从英格兰银行、卫星应用弹射器、海尔布隆、苏格兰皇家银行和斯伦贝谢发出的支持信所显示的那样，广泛的雇主都有投资于训练有素的纯数学家的愿景。我们的合作伙伴都高度评价受过博士级别培训的纯数学家的分析和解决问题的能力。在该中心培训的学生将拥有更高的技能：培训方案的结构将鼓励独立和领导能力，并将专业发展和关键技能，如编程、沟通技能和公众参与，以及从几何和数论中选择的专题的前沿研究。

Geometry and number theory are core disciplines within pure mathematics, with many repercussions across science and society. They are subjects that have attracted some of the best minds in mathematics since the time of the Ancient Greeks and continue to exert a natural fascination on professional and amateur mathematicians alike. Throughout the history of mathematics, both topics have very often inspired major mathematical developments which have had enormous impact beyond their original applications. The fascination of number theory is exemplified by the story of Fermat's last theorem, the statement of which was written down in 1637 and which is simple enough to be understood by anyone familiar with high school mathematics. It took more than 350 years of hard work and highly significant developments across mathematics before Wiles's celebrated proof was finally published in 1995. Wiles's proof involves a mixture of ideas from number theory and geometry, and the interplay between these topics is one of the most active areas of research in pure mathematics today.The Centre is needed to educate the next generation of academic researchers to maintain the excellence and competitiveness of the UK's universities and also to deliver highly trained mathematicians ready to take their place in financial and other high-tech industries. As shown by our letters of support from the Bank of England, the Satellite Applications Catapult, Heilbronn, Royal Bank of Scotland, and Schlumberger, a wide range of employers have the vision to invest in highly trained pure mathematicians. Our partners all speak highly of the analytical and problem-solving abilities of pure mathematicians trained to PhD level. The students trained in this Centre will be even more highly skilled: the structure of the training programme will encourage independence and leadership and will embed professional development and key skills such as programming, communication skills and public engagement alongside cutting-edge research in topics chosen from geometry and number theory.