主 题: Introducing Dynamics in Elementary Geometry.
报告人: Prof.M.Berger ((法国科学院院士，IHES前所长))
时 间: 0000-00-00
地 点: 理科一号楼1114
We will consider three elementary geometric constructions. The first is the barycentric subdivision of a triangle, a tetrahedron, etc.The second is Pappus theorem, which starting with a pair of two sets of three points on a line in the plan, yields a third set of three points on a line. The third is , starting with a convex polygon (e.g. a pentagon), construct a new one by joining by lines the vertices from one to the next-next one.
Schwartz is studying what happens when one iterates up to infinity these constructions. In the case of barycentric subdivisions what are the possible shapes so obtained ? In Pappus theorem iteration how looks the figures made up by the infinite set of the so obtained pointed lines in the plane ? For polygons what are the shapes of the polygons so obtained ?
In the first case the answer is known for triangles and for tetrahedrons,but still open starting dimension four or higher. For Pappus configuration precise information is obtained by introducing an action of the modular group into the structure. For polygons, things are known completely for pentagons, partially for hexagons, and mostly open for polygons with seven or more vertices. But computer numerical experiments suggest some conjectures.