Asymmetric metric and coarse geometry
- June 20 (Thu) at 16:00 - 18:10, 2019 (JST)
- Dr. Hiroki Kodama (Visiting Scientist, iTHEMS / Assistant Professor, Advanced Institute for Materials Research (AIMR), Tohoku University)
Plan of the seminar: we separate each talk into two. In the first 60 minutes the speaker gives an introductory talk for non-mathematicians. After a short break, the second 60 minutes is spent for a bit more detailed talk for mathematicians (working in other areas). We welcome you joining both parts of the seminar or only the first/second half.
For most of mathematicians, metric is symmetric. However, we can define asymmetric metric without any difficulty. "Coarse" is a notion to describe some large scale viewpoint. For example, the set of real numbers is coarse equivalent to the set of integers (with respect to standard metric). I will discuss asymmetric metric space in "coarse" sense.
I will define metric space and asymmetric metric space.
I will also explain a notion of coarse equivalence.
I will discuss what kind of asymmetric metric space is
not coarse equivalent to (symmetric) metric space.
I also would like to give other generalizations of metric.