In Ramsey Theory, ultrafilters often play an instrumental role. By means of nonstandard models, one can reduce those third-order objects (ultrafilters are sets of sets of natural numbers) to simple points. In this talk we present a nonstandard technique that is grounded on the above observation, and show its use to prove new results in Ramsey Theory of Diophantine equations. In this field, one investigates whether a given equation is partition regular on N (that is, there exist monochromatic solutions in every finite coloring of N).
By Artem Chernikov
By Martin Bays
By Micha Sharir
By David Evans
By Pierre Simon
By Timothy Gowers
By Caroline Terry
By Saugata Basu
By Jan Hubička
By Gérard Ben Arous
By Giulio Biroli
By Giulio Biroli
By Gérard Ben Arous
By Gérard Ben Arous
