Dear friends and colleagues,
on Monday, 19 July 2021 at 6 PM, Professor Nicola Garofalo (University of Padova, Italy) is giving a talk in our Asia-Pacific Analysis and PDE Seminar on
A heat equation approach to some problems in conformal geometry .
The Heisenberg group plays an ubiquitous role in analysis, geometry and mathematical physics. Such Lie group is equipped with a natural second order pdo \(L\), the real part of the Kohn-Spencer sublaplacian, that is hypoelliptic (but fails to be elliptic at every point). It is of interest to study two different families of fractional powers of \(L\), \(L^s\) and \(L_s\), and their so-called extension problems. While the former has a purely analytical content, the pseudodifferential operators \(L_s\) play a critical role in conformal CR geometry. In this self-contained talk I plan to show that, notwithstanding their substantial differences, these two classes of nonlocal operators can be treated in a unified way by a systematic use of the heat equation and suitable modifications of the latter. Such approach leads to some intertwining formulas related to conformal geometry that are instrumental in inverting the relevant nonlocal operators, as well as in constructing explicit solutions of some nonlocal Yamabe problems.
The talk is based on joint works with G. Tralli
More information and how to attend this talk can be found at the seminar webpage .