Fredholm Theory and the Resolvent of the Laplacian near Zero Energy on Asymptotically Conic Spaces
Abstract
The speaker and his collaborators consider geometric generalizations of Euclidean low energy resolvent estimates, such as estimates for the resolvent of the Euclidean Laplacian plus a decaying potential, in a Fredholm framework. More precisely, the setting is that of perturbations $P(\sigma)$ of the spectral family of the Laplacian $\Delta_g-\sigma^2$ on asymptotically conic spaces $(X,g)$ of dimension at least $3$, and the main result is uniform estimates for $P(\sigma)^{-1}$ as $\sigma\to 0$ on microlocal variable order spaces under an assumption on the nullspace of $P(0)$ on the appropriate function space (which in the Euclidean case translates to $0$ not being an $L^2$-eigenvalue or having a half-bound state). These spaces capture the limiting absorption principle for $\sigma\neq 0$ in a lossless, in terms of decay, manner.
About the speaker
Prof. András Vasy received his PhD in Mathematics from the Massachusetts Institute of Technology (MIT) in 1997. He undertook postdoctoral research at the University of California at Berkeley before joining the faculty at MIT. He moved to Stanford University in 2006 and is now a Professor of Mathematics.
Prof. Vasy’s research interests include microlocal analysis, partial differential equations, many-body scattering, symmetric spaces and analysis on manifolds. He was awarded the Bôcher Prize of the American Mathematical Society (2017). He was a Clay Research Fellow (2004-2006) and a Alfred P Sloan Research Fellow (2002-2004).
About the program
For more information, please refer to the program website at http://iasprogram.ust.hk/inverseproblems.
