School of Mathematical Sciences

Partition regular equations menu

Partition regular equations

Imre Leader (Cambridge)
Mon, 26/11/2012 - 16:30
Seminar series: 

A finite or infinite matrix M is called `partition regular' if whenever the
natural numbers are finitely coloured there exists a monochromatic vector
x with Mx=0. Many of the classical results of Ramsey theory, such as 
van der Waerden's theorem or Schur's theorem, may be naturally rephrased
as assertions that certain matrices are partition regular,

While the structure of finite partition regular matrices is well understood, 
little is known in the infinite case. In this talk we will review some
known results and then proceed to some recent developments.