Wenbo Sun

My research interest lies in using ergodic theory tools to solve problems in combinatorics and number theory, and vice versa. 

    In ergodic theory, my research interest is focused on structure theorems, which allows one to decompose a function or a system into two parts, the structural part and the random part. This theory has many applications in the convergence and recurrence results for multiple ergodic averages.

    In combinatorics, my research is focused on Ramsey type questions, i.e. questions on the existence of structural patterns in "large" sets. A typical result in this area is Szemeredi's theorem, which says that every subset of integers with positive density contains arbitrarily long arithmetic progressions.  

    In number theory, I am interested in the structure theorems for multiplicative functions and their applications. For example, I worked on the partition regularity problems, i.e. finding solutions to certain algebraic equations among large subsets of integers. I am also interested in Sarnak's conjecture, which claims that the Mobius function is orthogonal to any sequence arising from a dynamical system of zero entropy.