Correlations of the Riemann zeta function

Abstract: Shifted moments of the Riemann zeta function, introduced by Chandee, are natural generalizations of the moments of zeta. While the moments of zeta capture large values of zeta, the shifted moments also capture how the values of zeta are correlated along the half line. I will describe recent work giving sharp bounds for shifted moments assuming the Riemann hypothesis, improving previous work of Chandee and Ng, Shen, and Wong. I will also discuss some unconditional results about shifted moments with small exponents.