Information Center for Mathematical Science
한국과학기술원 수학과 김 인 강
This report is about the conference held at Paris during June, 1998.
The title of the conference was `Rigidity, representation and the ergodic theory'. As the title suggests, it was about the rigidity of some Riemannian space, specially the symmetric space of noncompact type.
People are interested in the local and global rigidity of such spaces. In terms of Lie group, it is about the rigidity of lattices such as arithmeticity, super-rigidity, deformation theory of lattices and ergodic theory on lattices. These kinds of work were opened up by Selberg, Mostow, Furstenberg and Margulis and many others. They developed the amazing techniques during the past century and proved the unexpected theorems. The influnce is everywhere in any fields of math. Most of the mathematicians are probably familiar with `Mostow rigidity, arithmetic lattices in higher rank symmetric space, Furstenberg boundary, Selberg lemma' and so on. The other side of this study is a Riemannian version using more hard analysis than just a Lie group theory and representation theory.
Recently more and more, people found the stability of symmetric space among other Riemannian manifolds. In many cases, some functionals on the space of Rimannian metrics attain the global mimia at the locally symmetric negatively curved metrics. Due to these reasons, these metrics became the special ones to which other metrics can be compared to.
In this vein, differential geometors launched their intensive study into the ocean of many curious properties of locally symmetic manifolds.
They study volume and topological entropy, geodesic conjugacy, ergodic theory of the geodesic flow, measures on the ideal boundary, minimal volumes and many other things.
To carry out this project, many different branches of mathematics should cooperate and many mathematicians of different fields and interests should get togather to dig into the mine of gold, hoping for finding the dazzling beauty of this jewel, and that someday they can completely understand these manifolds to characterize them as well as to characterize other manifolds as a byproduct.
This conference was the wonderful experience in this sense. I could meet many experts in this field such as Margulis, Katok, Goldman, Besson and many young promising mathematicians. Though, my country, Korea was defeated by 5 to nothing in the Coup du monde, the glaring sun of the Paris in the summer, the melancholy of the stree-cafes, the oddly-dressed gay and lesbien marching crowds around the jardin luxemburg and the simple-quick lunch over the chats with the fellow mathematicians and the curiosity of the new proofs and theorems succeeded by the aggresive queries...these were all great experiences to me, as a little mathematician who has not undersood many things, yet gasping for the thirst of untreaden path in this math-world to grow more in a near future.
- 마쯔야마 에히메 대학 방문