Brennan's conjecture for semigroups of holomorphic functions

J. E. Brennan in 1978 conjectured that the p-integral means of the derivative of a univalent function in the unit disk are finite whenever p is between -2 and 2/3. Brennan's conjecture is one of the most famous remaining open problems in the field of geometric function theory. It is known that the conjecture holds for the values between -1.752 and 2/3. This talk aims to give a short and elementary proof of the conjecture in the special case where the univalent function can be embedded into a non-elliptic continuous semigroup of holomorphic functions in the unit disk. This is joint work with Alexandru Aleman.