Join us for these events hosted by the Department of Mathematics, including colloquia, seminars, graduate student defenses and outreach, or of interest to Mathematicians hosted by other groups on campus.

### The Method of Moving Spheres on Hyperbolic Space and Classification of Solutions to a Class of PDEs

**Speaker:** Jianxiong Wang

The classification of solutions for semilinear partial differential equations, as well as the classification ofcritical points of the corresponding functionals, have wide applications in the study of partial differential equationsand differential geometry. The classical moving plane method and the moving sphere method on $\mathbb{R}^n$ provide aneffective approach to capturing the symmetry of solutions. In this talk, we focus on the equation\begin{equation*} P_k u = f(u)\end{equation*}on hyperbolic spaces $\mathbb{H}^n$, where $P_k$ denotes the GJMS operators and $f : \mathbb{R} \to \mathbb{R}$ satisfies certain growth conditions. I will introduce a moving sphere approach on $\mathbb{H}^n$, to obtain the symmetry property as well as the classification result towards positive solutions. Our methods also rely on Helgason-Fourier analysis and Hardy-Littlewood-Sobolev inequalities on hyperbolic spaces together with a newly introduced Kelvin-type transform on $\mathbb{H}^n$. Read more.