14/12/2012 Sexta-feira, 14 de Dezembro de 2012, 16:00, IIIUL - Sala B1-01
Peter Cameron (Queen Mary, University of London, UK)
Instituto para a Investigação Interdisciplinar da Universidade de Lisboa
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.