There is a rising use of ultrafilters in number theory,particularly additive number theory,as topological tools are being used to either simplify previous results or to develop new ones. Melvyn Nathanson recently gave a pair of as-yet-unpublished lectures describing Glazer's use of ultrafilters in giving a vastly simplified proof of Hindman's theorum. I plan to pursue this line of research this summer and I hope to make it the basis of my first published results by fall.Stay tuned.........

There is a rising use of ultrafilters in number theory,particularly additive number theory,as topological tools are being used to either simplify previous results or to develop new ones. Melvyn Nathanson recently gave a pair of as-yet-unpublished lectures describing Glazer's use of ultrafilters in giving a vastly simplified proof of Hindman's theorem. I plan to pursue this line of research this summer and I hope to make it the basis of my first published results by fall.Stay tuned.........