Title: Uniform distribution of generalized polynomials and applications
Speaker: Younghwan Son (POSTECH, South Korea)
Abstract: Generalized polynomials are real-valued functions which are obtained from conventional polynomials by the use of the operations of addition, multiplication, and taking the integer part. They form a natural extension of conventional polynomials, and appear, under different names, in a variety of mathematical contexts, from dynamics on nilmanifolds to number theory and mathematical games. Unlike the conventional polynomials, generalized polynomials may have quite intricate distributional properties. In this talk we will present recent results on uniform distribution of a large class of generalized polynomials and discuss some ergodic-theoretical applications. This is a joint work with Vitaly Bergelson and Inger Håland Knutson.