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Geometric Construction Problems and Invariance - Prof. Pascal Schreck Geometric Construction Problems and InvarianceProf. Pascal SchreckUniversity of Strasbourg, France 报告时间:2015年1月29日下午15:00~17:00报告地点:北航数学与系统科学ag平台app下载主321学术交流厅报告摘要:Nowadays, geometric constructions are mainly considered in the domain of education whereas the professional occupations where they were traditionally used, like land surveyor or engineering draughtsman, take now advantage of the ability of computers to make complex calculations. Anyway, if we come back to these ancient days when tees, compass and drawing boards were the only instruments in use, construction problems coming from engineering were very similar to those considered in mathematics. All these problems share the same interesting feature: they are invariant under the action of direct isometries (also called rigid body motions). In this talk, I will first recall some basic facts about geometric constructions, and particularly straightedge and compass constructions, through some simple examples. I will also make a small detour through algebra via Wu's method and Galois theory. Then, I will expose the basic techniques used in CAD for decomposing construction problems. These techniques often mix elements of rigidity theory and counting of unknowns and equations on a so-called graph of constraints. I will show that not only the direct isometry group can be used but also translation group or similarity group. Finally, in the light of the previous points, I will discuss some relations between geometric constructions and proofs in geometry. 报告人概况:Pascal Schreck is professor of Computer Science at University of Strasbourg, France since 2002. He is the head of a research team specialized in geometric constructions in CAE (computer aided education), geometric constraint satisfaction in CAD, automated proofs in geometry and the use of proof assistant, like Coq, in geometry. He is a researcher at the Image Sciences Laboratory, Computer and Remote Sensing (LSIIT). He had been Director of Department of Computer Science of the Faculty of mathematics and Computer Science from 2008 to 2011 and published over 60 research papers since 1995. 北航数据与信息科学创新群体(NoDI)

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