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，在科学和社会中有着许多影响。自古希腊时代以来，这些学科就吸引了一些最优秀的数学人才，并继续对专业和业余数学家产生天然的吸引力。在整个数学历史上，这两个主题经常激发出重大的数学发展，这些发展对它们最初的应用产生了巨大的影响。数论的魅力可以从费马大定理的故事中得到体现。费马大定理的陈述写于1637年，它非常简单，任何熟悉高中数学的人都能理解。在怀尔斯著名的证明最终于1995年发表之前，经过了350多年的艰苦工作和数学领域的重大发展。怀尔斯的证明融合了数论和几何的思想，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。该中心需要教育下一代学术研究人员，以保持英国大学的卓越和竞争力，并提供训练有素的数学家，准备在金融和其他高科技行业占据一席之地。从英格兰银行、卫星应用弹射器、海尔布朗、苏格兰皇家银行和斯伦贝谢的支持信中可以看出，许多雇主都有远见，愿意投资训练有素的纯数学家。我们的合作伙伴都高度评价博士级别纯数学的分析和解决问题的能力。在该中心接受培训的学生将拥有更高的技能：培训计划的结构将鼓励独立性和领导力，并将专业发展和关键技能（如编程、沟通技巧和公共参与）与几何和数论领域的前沿研究结合起来。

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.