This talk will give an easy introduction to non-commutative L_p spaces associated with a tracial von Neumann algebra. Then I will focus on non-commutative L_p spaces associated to locally compact groups and talk about some interesting completely bounded multipliers on them.

This talk will introduce some of the basic notions and results in the theory of C_0-semigroups, including generation theorems, growth and spectral bounds. If time permits, I will also try to discuss one or two classical results in the asymptotic theory of C_0-semigroups.