Random groups and largescale geometry
Introductory Workshop: Geometric Group Theory August 22, 2016  August 26, 2016
Location: SLMath: Eisenbud Auditorium
geometric group theory
hyperbolic group
random graphs
expander graph
asymptotic results
random groups
generators and relations
word problem
Kazhdan's property T
20Jxx  Connections of group theory with homological algebra and category theory
00A35  Methodology of mathematics {For mathematics education, see 97XX}
0604  Software, source code, etc. for problems pertaining to ordered structures
14599
Probabilistic methods have been used highly successfully in graph theory over the past 70 years, with two different flavors of approach. First, such methods are used to show the existence of graphs with some pathological properties that are hard to explicitly construct. Second, random or typical graphs are studied in their own right as interesting and important objects.
In Gromov's 1987 paper on hyperbolic groups, he described how many typical finitely presented groups are hyperbolic. Since then a variety of authors have studied random groups, again with the two approaches above: building exotic counterexamples (notably Gromov's construction of a finitely presented group that does not coarsely embed into Hilbert space), and the study of properties of typical finitely presented groups in a variety of models (notably Gromov's density model).
In this talk we'll survey this history and discuss some work, in part joint with Cornelia Drutu, which takes steps towards distinguishing the quasiisometry types of random groups
Mackay Notes

Download 
14599
H.264 Video 
14599.mp4

Download 
Please report video problems to itsupport@slmath.org.
See more of our Streaming videos on our main VMath Videos page.