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Wednesday, September 28, 2016

4:20 PM - 5:30 PM (ET)

Exley Science Center Tower ESC 638

Event Type

Seminar/Colloquium

Contact

Canalia, Caryn

2182

Link

https://eaglet.wesleyan.edu/MasterCalendar/EventDetails.aspx?EventDetailId=72044

Dave Constantine, Wes: "Hausdorff
dimension and the CAT(K) condition for *surfaces"*

** Abstract: **A geodesic metric
space satisfies the CAT(K) condition if its geodesic triangles are all
`thinner' than triangles with the same side lengths in the model space of
constant Riemannian curvature K. This condition allows one to extend many
arguments relying on an upper curvature bound from Riemannian geometry to the
metric space setting.

How `strange' can
a metric be while still satisfying the CAT(K) property? One way to measure this
is with the difference between the topological dimension of the space and its
Hausdorff dimension with respect to the metric. In this talk I'll show that, at
least for surfaces, a CAT(K) metric is tame in the sense that it yields
Hausdorff dimension 2. I'll also provide some motivation for this question by
showing how results like this allow one to extend volume entropy rigidity
statements to the CAT(-1) setting.* *