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We consider the energy critical four dimensional semi linear heat equation\partial tu-\Deltau-u3 = 0. We show the existence of type II finite time blowup solutions and give a sharp description of the corresponding singularityformation. These solutions concentrate a universal bubble of energy in thecritical topology u(t,r)-1/{\lambda} Q(r/{\lambda})\rightarrow u* in$\dot{H}^1$ where the blow up profile is given by the Talenti Aubin solitonQ(r)= 1/(1 +r^2/8) and with speed {\lambda}(t) ~(T-t)/|log(T - t)|^2 ast\rightarrowT. Our approach uses a robust energy method approach developped forthe study of geometrical dispersive problems, and lies in the continuation ofthe study of the energy critical harmonic heat flow and the energy criticalfour dimensional wave equation.

Type II Blow Up for the Four Dimensional Energy Critical Semi Linear Heat Equation