On Monday, July 3rd, 2017, there will be a special event called the Banach spaces day. This will consists of special courses that will be to introduce younger participants (graduates, PhD students and junior researches) into current topics in functional analysis, and help them participate fruitfully in the ensuing conference.

On Friday, June 30th, 2017, professor Michael Cwikel will give a course on interpolation theory.

Schedule of courses

 Friday, June 30th, 2017
10:00−11:30Michael Cwikel An introduction to interpolation of operators and interpolation spaces
11:30−12:00coffe break
12:00−13:15Michael Cwikel An introduction to interpolation of operators and interpolation spaces
 Monday, July 3rd, 2017
09:00−09:30registration
09:30−11:00Natan Kruglyak Real interpolation and applied mathematics
11:00−11:30coffe break
11:30−12:15Natan Kruglyak Real interpolation and applied mathematics
12:30−14:00Loukas Grafakos Fourier Analysis: an introduction, applications, and multilinear aspects
14:00−15:30lunch
15:30−17:00Loukas Grafakos Fourier Analysis: an introduction, applications, and multilinear aspects

Summary of courses

An introduction to interpolation of operators and interpolation spaces

Michael Cwikel

This brief course is intended for graduate students who are familiar with the basic results of functional analysis and real and complex analysis, but have not yet studied interpolation theory. We will briefly sketch the historical origins of this theory, describe some of the basic methods for constructing interpolation spaces, and indicate some of their applications to various fields of analysis. If time permits we will discuss some more exotic topics, such as the descriptions ofall interpolation spaces, which can be achieved in some settings, and/or some other more recent developments.

The course will consist of three 45 minute lectures. If there is interest in additional material, we may schedule an additional lecture and/or some time assigned to informal discussions.

To get into the mood for this course you might care to glance at, for example,

J. Bergh and J. Löfström, Interpolation spaces. An Introduction, Grundlehren der mathematische Wissenschaften 223, Springer, Berlin-Heidelberg-New York 1976.

and/or

A. P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 113−190. http://matwbn.icm.edu.pl/ksiazki/sm/sm24/sm24110.pdf

Of course we will only be able to cover some very small part of the wealth of material that appears in these items and in many other very fine books and papers on this topic.


Real interpolation and applied mathematics

Natan Kruglyak

I plan to discuss connections between real interpolation with some problems in image processing and communication theory.


Fourier Analysis: an introduction, applications, and multilinear aspects

Loukas Grafakos

I plan to give a short introduction, some applications to other fields, and discuss aspects of the multilinear theory, presenting open problems.