23/Aug/2013, 13:30–15:00

Fields institute,Room 210

Speaker: Jack Wright

Title: Nonstandard Analysis and an Application to Combinatorial Number Theory

Abstract: Since nonstandard analysis was first formalized in the 60’s it has given mathematicians a framework in which to do rigorous analysis with infinitesimals rather than epsilons and deltas. More importantly, it has also allowed for the application of powerful techniques from logic and model theory to analysis (and other areas of mathematics). This brief presentation will outline some of those tools and discuss one particular application of them.

I will briefly state the key techniques: the transfer principle, the internal definition principle, and the overflow principle. I will then give an indication of the usefulness of these techniques by showing how they have been used to garner some technical results that might be able to help solve the Erd\H{o}s’ famous Conjecture on Arithmetic progressions.