Analysis for breakfast

At this meeting the four external committee members of the PhD committee of Emiel Lorist (defence 22 March at 10.00), will give 30 minute talks. For last minute updates see http://fa.its.tudelft.nl/

The talk of Pierre Portal will likely be pre-recorded, and the 30 minutes below reserved for discussion. In case of prerecording the link will be made available on http://fa.its.tudelft.nl/

Of course it is possible to watch this video during the discussion time slot as well.

 

The lecture will be given in Zoom and will not be recorded.

The Zoom link is: https://tudelft.zoom.us/j/93583145075

 

8.15-8.30:            welcome with cookies and tea (bring your own policy)

8.30-9.00:            Pierre Portal

9.00-9.30:            Ildoo Kim

9.30-9.45:            Break out session 1

9.45-10.15:         Andrei Lerner

10.15-10.30:       Break out session 2

9.45-10.30:         Tuomas Hytönen

 

Pierre Portal (Australia)

Title: Calderon-Zygmund and Littlewood-Paley theories in rough contexts

Abstract: In their classical form, Calderon-Zygmund and Littlewood-Paley theories are highly effective tools to establish linear estimates for PDE with sufficiently smooth coefficients.

In the 21st century, many mathematicians have extended these theories in order to treat problems that are rougher because they involve stochastic terms and/or non-smooth coefficients.

This includes major contributions by Emiel Lorist and Mark Veraar. In this talk, I’ll talk about these developments in general, with a bias towards those I have been involved in.

 

Ildoo Kim (South Korea)

Title: A sharp L^p regularity result for second-order stochastic partial differential equations with unbounded and fully degenerate leading coefficients

Abstract: In this talk, we give a short history of Lp-theories to stochastic

partial differential equations (SPDEs) and present existence, uniqueness,

and sharp regularity results of a solution to SPDEs with (time dependent)

unbounded and fully degenerate leading coefficients.

 

Andrei Lernel (Israel)

Title: On separated bumps for Calderon-Zygmund operators

Abstract: In this talk we discuss an improvement of the Rahm-Spencer bump condition for two-weight boundedness of Calderon-Zygmund operators.

 

Tuomas Hytönen (Finland)

Title: Extrapolation of compactness on weighted spaces

Abstract: The extrapolation theorem of Rubio de Francia is one of the most powerful tools in the theory of weighted norm inequalities: it allows one to deduce an inequality (often but not necessarily: the bounded of an operator) on all weighted L^p spaces with a range of p, by checking it just for one exponent p (but all relevant weights). My topic is an analogous method for extrapolation of compactness. In a relatively soft way, it recovers several recent results about compactness of operators on weighted spaces and also gives some new ones. I expect there to be many more applications to discover.