Title: Pseudofinite structures

Abstract: We say that a structure is pseudofinite if it is infinite, but every first 
order sentence which it satisfies has a finite model. A rather rich theory of 
pseudofinite stuctures emerges, with the random graph, smoothly 
approximable structures, and pseudofinite fields as motivating examples.
There are connections with the model theory of pseudofinite structures (e.g. 
stability/simplicity of its theory) and asymptotic conditions on definable sets 
in finite structures. Interesting connections with finite simple groups have 
emerged. I will survey this topic, describing joint work with Steinhorn, 
some key results of Hrushovski and his coauthors, and work here of Elwes, 
Ryten, Tomasic, and Marshall.