Bubble decomposition for the harmonic map heat flow in the equivariant case

I will discuss a joint work with Jacek Jendrej (CNRS, U. Sorbonne Paris Nord)  on the harmonic map heat flow for maps from the plane to the 2-sphere, under equivariant symmetry.  It is known that solutions can exhibit bubbling along a sequence of times -- the solution decouples into a superposition of harmonic maps concentrating at different scales and a body map that accounts for the rest of the energy.  We prove that this bubble decomposition is unique and occurs continuously in time. The main new ingredient is the notion of a collision interval from our proof of the soliton resolution conjecture for equivarant wave maps.