Date/Time:

Monday, January 22, 2018 - 12:00 to 13:00

Location:

Stag 110

Guest Speaker:

Andrey Blinov

Abstract:

What is the difference between an empty glass and an open

empty bottle? Topologically there is none: they both are homeomorphic

to a disc. Geometrically, however, there is a difference: the glass is

flat (i.e. has zero Gaussian curvature everywhere), but the surface of

the bottle has points of positive, negative, and zero curvature.

Interestingly enough, it is possible to find this difference using

topological invariants: if we filter points by their curvature, and

then take the corresponding sublevel sets, some of them will be

topologically different: for example, the set of points of Gaussian

curvature not greater than zero is connected for the glass, but

disconnected for the bottle. This observation lies at the basis of

the idea of persistence in topological data analysis. I will

discuss this idea in more detail, and show other examples when this

approach gives us something reasonable.