The HADES seminar on Tuesday, September 24th will be given by  Mohandas Pillai in Evans 740 from 3:40 to 5 pm.

Speaker: Mohandas Pillai, Berkeley

Abstract: This talk will be about the wave maps problem with domain $\mathbb{R}^{2+1}$ and target $\mathbb{S}^{2}$ in the 1-equivariant, topological degree one setting. In this setting, we recall that the soliton is a harmonic map from $\mathbb{R}^{2}$ to $\mathbb{S}^{2}$, with polar angle equal to $Q_{1}(r) = 2 \arctan(r)$. By applying the scaling symmetry of the equation, $Q_{\lambda}(r) = Q_{1}(r \lambda)$ is also a harmonic map, and the family of all such $Q_{\lambda}$ are the unique minimizers of the harmonic map energy among finite energy, 1-equivariant, topological degree one maps.

In this talk, I will discuss how to construct a collection of infinite time blowup solutions along the $Q_{\lambda}$ family, with a symbol class of possible asymptotic behaviors of $\lambda$.