Kiril Datchev (Purdue) and Charles Hadfield (UC Berkeley)

The Bay Area Microlocal Analysis Seminar will take place on Monday, September 25, in room 740, Evans Hall, with two talks, given by Kiril Datchev at 2:40 pm and Charles Hadfield at 4:10 pm.

Speaker: Kiril Datchev (2:40 pm)

Title: Semiclassical resolvent estimates away from trapping

Abstract: Semiclassical resolvent estimates relate dynamics of a particle scattering problem to regularity and decay of waves in a corresponding wave scattering problem. Roughly speaking, more trapping of particles corresponds to a larger resolvent near the trapping. If the trapping is mild, then propagation estimates imply that the larger norm occurs only there. However, in this talk I will show how the effects of heavy trapping can tunnel over long distances, implying that the resolvent can be very large far away as well. This is joint work with Long Jin.


Speaker: Charles Hadfield (4:10 pm)

Title: Resonances on asymptotically hyperbolic manifolds; the ambient metric approach

Abstract: On an asymptotically hyperbolic manifold, the Laplacian has essential spectrum. Since work of Mazzeo and Melrose, this essential spectrum has been studied via the theory of resonances; poles of the meromorphic continuation of the resolvent of the Laplacian (with modified spectral parameter). A recent technique of Vasy provides an alternative construction of this meromorphic continuation which dovetails the ambient metric approach to conformal geometry initiated by Fefferman and Graham. I will discuss the ambient geometry present in this construction, use it to define quantum resonances for the Laplacian acting on natural tensor bundles (forms, symmetric tensors), and mention an application showing a correspondence between Ruelle resonances and quantum resonances on convex cocompact hyperbolic manifolds.