Structure-Randomness and The Green-Tao Theorem

Mr. Kushlam Srivastava
PhD Student
University of Wisconsin – Milwaukee

In this talk we will give a brief introduction of the dichotomy between structure and randomness in the context of Szemeredi’s Theorem and the celebrated Green-Tao theorem. We will look at the definition of a positive upper density set and look at a few examples exploring the dichotomy between structure and randomness. We will then look at a sketch proof of one case of Szemeredi’s Theorem and touch upon the techniques used to expand this result to the Green-Tao Theorem.