|Topic:||Metaphors in Systolic Geometry|
|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.