School of Mathematical Sciences

From homogeneous Cayley objects to Diophantine approximation menu

From homogeneous Cayley objects to Diophantine approximation

Speaker: 
Peter Cameron (QMUL)
Date/Time: 
Mon, 15/10/2012 - 17:30
Room: 
M103
Seminar series: 

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.