# Algebra Seminar talk

2020-01-24

Clemens **Schindler***Reconstruction from Automorphism Groups - Rubin's approach*

Abstract:

Given a relational structure, how much does its automorphism group know
about the structure? In other words, if two structures have automorphism
groups which are isomorphic (as abstract groups), how much are the two
structures resembling each other?
In general, the automorphism group contains very little information, but
under suitable hypotheses, some remarkable results are known. Using his
notion of so-called forall-exists-interpretations of structures, M.Rubin
proved a particularly strong theorem: He gave conditions for the two
structures from above to be "interdefinable", i.e. if viewed over a
canonical expansion of the signatures, the structures are isomorphic.
Examples for this kind of reconstruction include the rationals as well
as the random graph.
In my talk, I will give an overview of some conditions which are
necessary for this kind of reconstruction to happen, define Rubin's
notion of interpretation and motivate his theorem as well as provide the
proof strategy. If time permits, I will also describe a possible method
to show that a structure is within the realm of Rubin's theorem.