Abstract:
I'll discuss recent progress on the existence theory for harmonic maps on higher-dimensional manifolds, giving harmonic maps of optimal regularity from manifolds of dimension n>2 to every non-aspherical closed manifold containing no stable minimal two-spheres. As an application, we'll see that every manifold carries a canonical family of sphere-valued harmonic maps, which (for n<6) stabilize at a solution of a spectral isoperimetric problem generalizing the conformal maximization of Laplace eigenvalues on surfaces. Based on joint work with Mikhail Karpukhin.
Speaker:
Daniel Stern is currently a Dickson Instructor at the University of Chicago. He received his PhD in 2019 at Princeton University under the supervision of Fernando Coda Marques, and from 2019-2020 was a postdoctoral fellow at the University of Toronto. His research addresses geometric and analytic problems arising in the study of harmonic maps, minimal submanifolds, and other geometric PDEs.
Zoom:
Link: https://us06web.zoom.us/j/82706232690?pwd=ZldLSURHcUZXczFYZUdwcTgrYUVldz09
ID: 827 0623 2690
Passcode: 332559
