REAL ANALYSIS
EXCHANGE

Summer Symposium in Real Analysis XLII
"The Saint-Petersburg - The White Nights' Symposium"


REPORT ON THE SUMMER SYMPOSIUM IN REAL ANALYSIS XLII
Steklov Institute of Mathematics and Herzen University, Saint-Petersburg, Russia
June 9-14, 2018

The 42nd Summer Symposium in Real Analysis (The Saint- - The White Nights' Symposium) was held at the Steklov Institute of Mathematics and Herzen University, Saint-Petersburg, Russia from June 9 through June 14, 2018.

A note from Paul Humke, Editor-in-Chief of the Real Analysis Exchange:

The success of our conferences depends on a great deal of leadership and work by many people and it is wholly appropriate that I thank them and acknowledge their efforts on our behalf.

This year Yuri Andreev has provided the energy and leadership to enable this conference to be held in Russia, and I owe him a great personal debt for all his effort. Without the help of co-organizers, Sergei Kislyakov, the Director of the Steklov Institute of the Russian Academy of Sciences and Victor Budaev, the Head of Mathematics Faculty of Herzen University this conference would simply not have been possible. Too, I'm grateful to Alexander Olevskii, Valentin Skvortsov, and Maria Skopina for their essential local support, and the plenary speakers.


In addition to the formal mathematical program, time was set aside for research collaboration.

This year's "ANDY'' was awarded to Sergei Konyagin.

Congratulations, Sergei!

Four Small "ANDY"s were also awarded.

Generally speaking, this is award for the international scientific and cultural collaboration. This year it was given to those of participants who had essential difficulties "on the way" to the conference (preparations, travel and so on) but finally came.

Slobodan Tričković -- As a new face, Slobodan had been out of company and he always had been lost. And even from the beginning, he had a problems to reach a site from the airport.

Bernd Kirchheim -- Bernd moves around the world, and there is a question: how and where apply for a Visa. It was not clear at all. Finally, he did it!

Trevor Richards -- Trevor did his first overseas! (with two stops and changes during flight) Moreover, he had been out of US by the first time. Great experience!

Paul Humke -- All flights from the departure airport had been cancelled just two day before conference because of the runway damage. But finally he came exactly at the first day of the conference.

The conference featured invited one-hour plenary addresses by:

Sergei Konyagin
Vladimir Bogachov
Natalia Kholshchevnikova
Bernd Kirchheim
Evgeny Semenov
and one-hour special sessions by:
Chris Ciesielski

as well as 33 contributed talks. Following is the participant list is the program of the Symposium, and then the summaries of the talks. The editorial board of the EXCHANGE wishes to thank the speakers for preparing these summaries.

PARTICIPANTS

Saint-Petersburg

Victor Budaev (Herzen University), Dmitry Pavlov (Herzen University), Aleksandr Florinskiy (Saint-Petersburg State University), Oleg Reinov (Saint-Petersburg State University), Serguei Kisliakov (Mathematical Institute of RAS /PDMI/), Elena Riss (Herzen University), Aleksandr Krivoshein (Saint-Petersburg State University), Serguei Rukshin (Herzen University), Elena Lebedeva (Saint-Petersburg State University), and Maria Skopina (Saint-Petersburg State University).

Russia and former Soviet Republics

Vladimir Bogachov (Moscow State University and HSE Moscow), Julia Plotnikova (Vologda State Academy of Milk Industry), Natalia Kholshchevnikova (Moscow State University of Technology), Artyom Radomskii (Mathematical Institute of RAS, Moscow), Sergei Konyagin (Mathematical Institute of RAS, Moscow) , Evgeny Semenov (Voronezh State University), Yuri Malykhin (Mathematical Institute of RAS, Moscow), Selena Sharonova (Tolyatti), Vazgen Mikayelyan (Yerevan State University, Armenia), Valentin Skvortsov (Moscow State University), Mikhail Plotnikov (Vologda State University), and Sergei Voronov (University of Chemical Technology of Russia, Moscow).

North America

Ali A. Alikhani-Koopaei (Pennsylvania State University, PA), Paul Humke (St.Olaf College, MN), Svetlana Butler (University of California, Santa Barbara, CA), Fabio Milner (Arizona State University, AZ), Chris Ciesielski (West Virginia University, WV), Boris Mityagin (Ohio State University, OH), Don Cohn (Suffolk University, MA), and Trevor Richards (Monmouth College, IL).

Asia and Africa

Pratulananda Das (Jadavpur University, India), Shamim Shariat (Islamic Azad University, Science and Research Branch, Iran), Pranav Sharma (Lovely Professional University, India), Jun Kawabe (Shinshu University, Japan), Palani Shunmugaraj (Indian Institute of Technology, Kanpur, India), Daniyal Israfilov (Balikesir University, Turkey), and Soroosh Farsani (Koosha College of Applied Science and Technology, Iran).

Europe

Damir Ferizovic (Technical University of Graz, Austria), Jacek Hejduk (Łódź University, Poland), Martin Doleźal (Institute of Mathematics AS CR, Czech Republic), Graźyna Horbaczewska (Łódź University, Poland), Martin Koc (RSJ, Czech Republic), Małgorzata Filipczak (Łódź University, Poland), Martin Rmoutil (Charles University, Czech Republic), Anna Loranty (Łódź University, Poland), Janusz Morawiec (Institute of Mathematics, University of Silesia, Poland), Bernd Kirchheim (Leipzig University, Germany), Piotr Sworowski (Casimirus the Great University, Poland), Nikolaos Macheras (University of Piraeus, Greece), Tatiana Sworowska (Poland), Francesco Maiale (University of Pisa, Italy), Tričković (University of Nis, Serbia), and Emanuel Chetcuti (University of Malta, Malta).

PICTURES of the THE SAINT-PETERSBURG - THE WHITE NIGHTS' SYMPOSIUM

Pictured above are the participants of the 42nd Summer Symposium in Real Analysis.


Sergei Konyagin is awarded the 2018 "Andy."


The Small "Andy" Awards were awarded to (from left to rogjt) Paul Humke, Trevor Richards, Bernd Kirchheim, and Slobodan Tričković,


Participants having a great time in St. Petersburg!


PROGRAM of the THE SAINT-PETERSBURG - THE WHITE NIGHTS' SYMPOSIUM


SUNDAY, June 10 Mathematical Institute, Marble Hall

9:00                    Breakfast

9:50-10:20         Opening

CHAIRPERSON: Valentin Skvortsov

10:20-11:20       Sergei Konyagin
                  Convergence to zero of exponential sums with positive integer coefficients and approximation by sums of shifts of a single function on the line

11:30-11:50       Maria Skopina
                  Approximation by multivariate quasi-projection operators

CHAIRPERSON: Maria Skopina

12:00-12:20       Aleksandr Krivoshein
                  Multivariate sampling-type expansions

12:30-12:50       Elena Lebedeva
                  Unconditional convergence for wavelet frame expansions

13:00-13:20       Artyom Radomskii
                  On some trigonometric polynomials with extremally small uniform norm

13:20-15:00       Lunch

CHAIRPERSON: Evgeny Semenov

15:00-15:20       Pranav Sharma
                  Sequences valued in convergence groups

15:30-15:50       Martin Dolezal
                  On convergence of graphons

16:00-16:20       Svetlana Butler
                  Quasi-linear functionals on locally compact spaces

16:20-17:00       Coffee Break

17:00-18:00       Chris Ciesielski
                  Differentiability versus continuity: Restriction and extension theorems and monstrous examples

19:00                  Dinner

MONDAY, June 11 Mathematical Institute, Marble Hall

9:00                    Breakfast

9:50-10:00         Opening

CHAIRPERSON: Chris Ciesielski

10:00-11:00       Vladimir Bogachev
                  Distributions of polynomials in many variables and Nikolskii-Besov spaces

11:15-12:15       Collaboration Time

11:15-12:15       Coffee Break

12:30-12:50       Jun Kawabe
                  The Vitali convergence theorem for distribution-based nonlinear integrals

13:00-13:20       Nicolaos Macheras
                  Marginals and the product strong lifting problem

13:20-14:50       Lunch

CHAIRPERSON: Vladimir Bogachev

14:50-15:50       Bernd Kirchheim
                  Derivatives and their geometry

16:00-16:20       Emmanuel Chetcuti
                  Equilateral weights on subsets of R^n

16:30-16:50       Martin Rmoutil
                  c-Removable sets: Old and new results

17:00-18:00       Chris Ciesielski
                  Higher level differentiability: Generalized Ulam-Zahorski problem and small coverings by smooth maps

18:00-19:40       Dinner

CHAIRPERSON: Paul Humke

18:00-19:40       Problem Session

TUESDAY, June 12 Russia Day

9:00                    Breakfast

10:45                  Tour to Peterhof

19:50                  Problem Session

WEDNESDAY, June 13 Herzen University, Auditorium 237

9:00                    Breakfast

9:50-10:00         Opening

CHAIRPERSON: Jun Kawabe

10:00-11:00       Natalia Kholshchevnikova
                  The union problem and the category problem of sets of uniqueness in the theory of orthogonal series

11:10-11:30       Valentin Skvortsov
                  Some problems in harmonic analysis on compact zero-dimensional groups (non-abelian case)

11:30-12:00       Coffee Break

Split into two auditoriums:

Auditorium 237:

CHAIRPERSON: Natalia Kholshchevnikova

12:00-12:20       Mikhail Plotnikov
                  U- and V-sets for multiple Vilenkin series

12:30-12:50       Julia Plotnikova
                  On rearranged multiple Haar series

13:00-13:20       Sergei Voronov
                  Convergence of Fourier series by Vilenkin system in the case of unlimited p(k)

Auditorium 214:

CHAIRPERSON: Svetlana Butler;

12:00-12:20       Slobodan Tričković
                  On the generalized binomial transform

12:30-12:50       Slobodan Tričković
                  On applications of the generalized binomial transform

13:00-13:20       Fabio Milner
                  Structured population model with diffusion in structure space)

13:20-15:00       Lunch

Auditorium 237:

CHAIRPERSON: Mikhail Plotnikov

15:00-15:20       Piotr Sworowski
                  On variational and Riemann approach to some Lusin-type integrals

15:30-15:50       Vazgen Mikayelyan
                  Monotonically boundedly completeness of the Franklin system in C[0,1] and L^1[0,1]

Auditorium 214:

CHAIRPERSON: Victor Budaev

15:00-15:20       Yuri Malykhin
                  On some lower bounds for Kolmogorov widths

15:30-15:50       Aliasghar Alikhani-Koopaei
                  On the sets of fixed points, periodic functions points, recurrent points and chain recurrent points of bounded Baire one functions

15:50-16:10       Coffee Break

16:10-16:30       Anna Loranty
                  On dynamical systems, entropy and certain classes of real functions

16:10-16:30       Janusz Morawiec
                  Means of iterates

16:10-16:30       Aleksandr Florinskiy
                  Some dynamical and order properties of maps related to the real line

17:30-18:45       Break

18:45-23:00       Excursion, Banquet & Andy Award

THURSDAY, June 14 Herzen University, Auditorium 237

9:00                    Breakfast

9:50-10:00         Opening

CHAIRPERSON: Jacek Hejduk

10:00-11:00       Evgeny Semenov
                  On strictly singular operators

11:10-11:30       Oleg Reinov
                  On products of nuclear operators

11:30-12:00       Coffee Break

CHAIRPERSON: Grazyna Horbaczewska

12:00-12:20       Palani Shunmugaraj
                  Some geometric properties in Banach spaces

12:30-12:50       Trevor Richards
                  Luzin type properties, and the difference quotient set

13:00-13:20       Pratulananda Das
                  On generalized statistical and ideal convergence of metric-valued sequences

13:30-13:50       Artyom Radomskii
                  On the inequality of Sidon

13:50-15:00       Lunch

CHAIRPERSON: Piotr Sworowski

15:00-15:20       Grazyna Horbaczewska
                  On sets which can be moved away from sets of a certain family

15:30-15:50       Malgorzata Filipczak
                  Homeomorphisms of Hashimoto topologies

16:00-16:20       Jacek Hejduk
                  On a strong generalized topology with respect to the outer Lebesgue measure

16:45                  Tour to Catherine Palace

FRIDAY, June 15

9:00                    Breakfast

Symposium Closing