研究内容分为四个专题：I 几何与物理；II 代数与椭圆曲线码；III动理学理论的模型约简和数学理论；IV复杂数据的统计分析及其在生物中的应用。这些专题都有深厚的实际背景和广阔的应用前景，带来丰富而深刻的数学问题。北京大学数学学科在这几个方面具有长期的学术积累，取得了丰硕的科研成果，建立了强大的科研团队，具备科研合作的优良条件和多年传统。本项目以北大数学学科部分教师为核心，积极组织国内外专家开展形式多样的学术活动，促进实质性的合作研究，取得原创性科研成果，培养更多青年学术骨干，推动多学科多领域的交叉融合。经过3至5年的努力，使北大在这几个方向优势更加突出，成为有国际影响的研究基地。

This research project is consisted of four parts: geometry and physics; algebra and elliptic curve cryptography; model reduction and mathematical theory of kinetic theory; statistical analysis of complex data and applications in life sciences. With a strong practical background and broad prospects of application, these topics have rich and profound mathematical problems. With a long-term accumulation in research and a rich tradition of academic exchanges, the mathematics faculty at Peking University is very strong in these areas, has made ​​fruitful achievements, and possesses excellent conditions for research collaborations. With the core members from Peking University, this project will involve many experts in all parts of the world to make a coordinated effort in research in the areas mentioned above. In particular this project aims to attract and to nurture young talents. To this end, a subject will be designated in each semester to host visitors and to run workshops of various durations. Interdisciplinary cooperations in research among members, visitors and students are strongly encouraged and assisted. It is our hope that the leading edge of Peking University in these four areas will be more prominent after 3-5 years of efforts and an interdisciplinary platform for mathematics and frontiers of science will be constructed at Peking University with an international impact.