Year:    2013

CAM-Net Digest, Vol. 10 (2013), Iss. 19 : p. 2

Abstract

为了庆祝北京大学数学科学的现代教育体系创建100周年，我们邀请了世界顶级的数学家们在北京国际数学研究中心（BICMR）开展系列专题报告。
【系列报告之一】
演讲人：Jean-Michel Bismut (法国 巴黎第十一大学 数学教授，法国科学院院士)
时间：2013年10月10日，晚17:00—18:00
地点：北京大学镜春园82号甲乙丙楼二楼报告厅
报告主题：An introduction to the hypoelliptic Laplacian
摘要：
If X is a Riemannian manifold, the Laplacian is a second order elliptic operator on X.The hypoelliptic Laplacian Lb is an operator acting on the total space X of the tangen bundle of X, that is supposed to interpolate between the elliptic Laplacian  when b → 0)and the geodesic flow (when b → +∞). Up to lower order terms, Lb is a weighted sum of the harmonic oscillator along the fibre TX and of the of the geodesic flow. One expects that, in the deformation, there are conserved quantities.
In the talk, I will describe three applications of the hypoelliptic Laplacian:The case of the circle. Selberg's trace formula and the evaluation of orbital integrals.A Riemann-Roch-Grothendieck theorem in Bott-Chern cohomology
【系列报告之二】
演讲人：John Ball (牛津大学 数学教授，英国皇家学会会员)
时间：2013年10月11日，下午14:30—15:30
地点：北京大学镜春园82号甲乙丙楼二楼报告厅
报告主题：Defects in materials and their mathematical description
摘要：
Cracks, cavities, dislocations, phase boundaries and disclinations are all examples of material defects. In some mathematical models they may be described by singularities in solutions, whereas in others they may be represented differently. The lecture will describe some examples in which the understanding of such defects raises interesting mathematical, scientific and philosophical issues.
【系列报告之三】
演讲人：Phillip A. Griffiths (普林斯顿大学 数学系教授，美国科学院院士，沃尔夫奖得主)
时间：2013年10月11日，晚16:30—17:30
地点：北京大学镜春园82号甲乙丙楼二楼报告厅
报告主题：A Class of Differential Equations Arising from Representation Theory
摘要：
This talk will discuss how the Harish-Chandra modules arising from the discrete series representations, and their limits, of a real semi-simple Lie group satisfy a canonical linear PDE system. In case the Harish-Chandra parameter is very regular, this PDE system is the initial term in the classical Spencer sequence. In the general case the PDE system appears to be of a new type and its structure is not yet understood. The connection between representation theory and PDE’s will be established using complex geometry. The talk is intended for a general audience and all of the major concepts will be defined and illustrated in low dimensional examples.
【系列报告之四】
演讲人：Andrei Okounkov (哥伦比亚大学 数学系教授，菲尔兹奖得主)
时间：2013年10月12日，晚16:30—17:30
地点：北京大学镜春园82号甲乙丙楼二楼报告厅
报告主题：待定
摘要：待定
【系列报告之五】
演讲人：Martin Groetschel (柏林工业大学 教授，Zuse研究所主席，国际数学联盟秘书长，爱因斯坦基金会主席)
时间：2013年10月12日，晚18:00—19:00
地点：北京大学镜春园82号甲乙丙楼二楼报告厅
报告主题：Fewer Walls, More Bridges
摘要：
On the occasion of a 100th anniversary of a mathematical institute one may dare to very briefly review the history of mathematics in the past century and to speculate about its future development.
This is what I will attempt to do in my lecture.
It is my firm belief that mathematics will become the most important scientific endeavor of the 21st century. The reason for this conviction is twofold. Mathematics is strongly entering into every scientific and technological area now, e.g., every technology needs or will need the support of mathematics via a combination of mathematical modeling, simulation, and optimization. The (meanwhile generally accepted)necessity to treat the world’s resources with care, to produce everything efficiently, and to develop a sustainable lifestyle will change the goals of our nations and societies and the focus of most human activities,and it will force more rationality into political and economic decision making. Mathematics will be an indispensable part of all these processes.
The development I hope for will not proceed automatically. To go in the right direction, cooperation and collaboration are necessary; nothing will be achieved without new insights and significant efforts on all sides.Mathematics has to change as well, of course. We have to be more open to society needs, we have to support
other sciences in their attempts to understand their aspects of the world, and we have to contribute to the well-being of the world by developing the mathematical tools needed and by applying them. This means that we have to build more bridges within the various mathematical disciplines and, more importantly, towards all those who seek for our support (and may not even know that yet). This, moreover, means that the walls within mathematics that have been erected in the last century need to be torn down as well as the walls which mathematics built to separate itself from the real world.
I am aware that the statements above may be viewed as quite pretentious. In my lecture I will make an effort to substantiate some of my claims. I will call for a rethinking of our goals concerning mathematical education and research as well as our attitude towards applications and collaboration with others.