scnews: "Asia-Pacific Analysis and PDE Seminar: Nicola Garofalo -- A heat equation approach to some problems in conformal geometry" by Daniel Hauer

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 .

Abstract:

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 .

Best wishes,

Daniel

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Webinar Speaker

Nicola Garofalo

Professor @ University of Padova, Italy.

Nicola Garofalo is Professor of Mathematics at the University of Padova. He received his Ph.D. in Mathematics from the University of Minnesota in 1987 under the supervision of Eugene Fabes. He has held positions at the University of Bologna, Northwestern University and Purdue University. He has been invited visiting professor at the Institute H. Poincaré, Paris, invited visiting fellow at the I. Newton Institute for Mathematical Sciences, Cambridge, and invited visiting professor at the Mittag-Leffler Institute, Stockholm. He has also been Distinguished Visiting Professor of Mathematics at the Ohio State University, Visiting Professor of Mathematics at The Johns Hopkins University and Visiting Professor of Mathematics at the University of Maryland. He has received uninterrupted funding from the US National Science Foundation during the years 1989-2013, and was the recipient of the 2012 Ruth and Joel Spira Award for excellence in graduate teaching.