Department of Mathematics

Title: A degenerate one-phase free boundary problem arising from the Alt-Phillips equation for negative exponents Abstract: We study viscosity solutions for a degenerate one-phase free boundary problem of the form $Delta w = frac{h( abla w)}{w}$. We assume the existence of a star-shaped domain $D$ such that $h < 0$ in $D$, $h = 0$ on […]

Title: Periods and skeletonsAbstract:  Given a degeneration X of a complex algebraic variety over the punctured unit disk, one can associate to X,  a non-archimedean analytic space called its analytification X^an.  The analytification retains all the original information about X but in general can be very complicated. A beautiful aspect of the theory is that X^an contains a […]

Title: Profinite transfers in K(n)-local homotopy theoryAbstract: After K(1)-localization, the classical J-homomorphism can be interpreted as a profinite transfer map. More precisely, it is a transfer map Sigma^{-1}KO^wedge_2 to mathbb{S}_{K(1)} from the C_2-homotopy fixed points (with a twist) to the mathbb{Z}_2^times-homotopy fixed points of the 2-complete complex topological K-theory. In joint work in progress with […]

Title: A conformally invariant energy for the Paneitz operator on cornered Riemannian manifolds Abstract: We construct conformally invariant boundary and corner operators associated to the Paneitz operator on a cornered Riemannian manifold. These operators give rise to a conformally invariant energy for the Paneitz operator on a cornered Riemannian manifold, and hence to formulations of […]