A Cayley object for a group G is a structure M on G such that the right regular action of G gives an automorphism group of M. (Thus a Cayley graph is a Cayley object which happens to be a graph.)

A relational structure is homogeneous if every isomorphism between finite substructures can be extended to an automorphism of M.

As part of a general investigation of homogeneous Cayley objects for countable groups, I conjectured in 2000 that the universal homogeneous n-tuple of total orders is a Cayley object for the free abelian group of rank m if and only if m > n. I have just succeeded in proving this conjecture, using a theorem of Kronecker on diophantine approximation.

The talk will be self-contained and all concepts will be explained.

# From homogeneous Cayley objects to Diophantine approximation

Speaker:

Peter Cameron (QMUL)

Date/Time:

Mon, 15/10/2012 - 17:30

Room:

M103

Seminar series: