Analysis and PDE Seminar Homepage, Autumn-Winter-Spring 2016/2017
Time: Monday, 4pm.
Wednesday, August 24, 11am, Room 383N (unusual
Jan Derezinski (Warsaw)
``Almost homogeneous Schrödinger operators''
Abstract: First I will describe a certain natural holomorphic family of closed operators with interesting spectral properties. These operators can be fully analyzed using just trigonometric functions. I try to market them under the name "a toy model of renormalization group".
Then I will discuss 1-dimensional Schroedinger operators with a 1/x^2
potential with general boundary conditions, which I studied recently
with S.Richard. Even though their description involves Bessel and
Gamma functions, they turn out to be equivalent to the previous
Wednesday, August 31, 2pm, Room 383N (unusual
Frédéric Rochon (UQAM)
``QAC Calabi-Yau manifolds''
Abstract: We will explain how to construct new examples of quasi-asymptotically conical (QAC) Calabi-Yau manifolds that are not quasi-asymptotically locally Euclidean (QALE). Our strategy consists first in introducing a natural compactification of QAC-spaces by manifolds with fibred corners and to give a definition of QAC-metrics in terms of a natural Lie algebra of vector fields on this compactification. Using this and the Fredholm theory of Degeratu-Mazzeo for elliptic operators associated to QAC-metrics, we can in many instances obtain Kähler QAC-metrics having Ricci potential decaying sufficiently fast at infinity. We can then obtain QAC Calabi-Yau metrics in the Kähler classes of these metrics by solving a corresponding complex Monge-Ampère equation. This is a joint work with Ronan Conlon and Anda Degeratu.