Local-to-global in random topology

Wednesday, May 23, 2018 - 10:30am - 11:30am
Lind 305
Omer Bobrowski (Technion-Israel Institute of Technology)
In this talk I will review some recent progress in the study of the homology and persistent homology of random simplicial complexes. In the spirit of sheaf theory, I will focus on situations where global conclusions are drawn from local arguments. Since proving global probabilistic statements about random structures (e.g. about homology) is quite hard, often we find a local calculation that is doable, and then apply some topological machinery to integrate the local information into the global statement we seek.
The results discussed do not have a direct connection to sheaf theory at the moment, but hopefully such a connection could be found.