Metaphors in Systolic Geometry
| MEMBERS SEMINAR | |
| Topic: | Metaphors in Systolic Geometry |
| Speaker: | Larry Guth |
| Affiliation: | University of Toronto; Member, School of Mathematics |
| Date: | Monday, October 18 |
| Time/Room: | 2:00pm - 3:00pm/S-101 |
The systolic inequality says that if we take any metric on an n-dimensional torus with volume 1, then we can find a non-contractible curve in the torus with length at most C(n). A remarkable feature of the inequality is how general it is: it holds for all metrics.
Although the statement of the inequality is short, the proofs are difficult. The general idea of each known proof comes from a metaphor connecting the systolic problem to another area of geometry/topology. I will introduce three useful metaphors, connecting the systolic problem to geometric measure theory, topological dimension theory, and scalar curvature.