Continuous Time Bubbling for the Harmonic Map Heat Flow in Two Dimensions

Explore recent research on harmonic maps of finite energy from the plane to the two-sphere in this 59-minute lecture by Wilhelm Schlag from the Institut des Hautes Etudes Scientifiques (IHES). Delve into the collaborative work with Jacek Jendrej (CNRS, Paris Nord) and Andrew Lawrie (MIT), which extends the understanding of bubbling phenomena in harmonic map heat flow. Learn how the team demonstrates that bubbling occurs continuously in time, building upon the elliptic Palais-Smale mechanism known since the 1990s. Discover the crucial concept of "minimal collision energy" and its role in the soliton resolution result for critical equivariant wave maps. Gain insights into this advanced topic in mathematical physics without assuming any symmetry conditions.