Extreme values of the Riemann zeta function and its argument

It is of central importance in the theory of the Riemann zeta function $\zeta(s)$ to have as precise information as possible about the size of $\zeta(1/2+it)$ and its argument. I will present lower estimates for the growth of these two functions, giving the first improvement of the order magnitude since 1977. The talk is based on joint work with Andriy Bondarenko.