Symposium 32 – Wooster, 2010

SUMMER SYMPOSIUM IN REAL ANALYSIS XXXIV
"The Buckeye Symposium"

The College of Wooster
July 13-17, 2010

The Thirty-Fourth Summer Symposium in Real Analysis (The Buckeye Symposium) was hosted by The College of Wooster July 13-17, 2010. The Editorial Board of the EXCHANGE wishes to express its gratitude to The College of Wooster for its gracious hospitality and to the conference director, Pamela Pierce, for her outstanding leadership in organizing and conducting this symposium. Furthermore, both Pamela and the Editorial Board sincerely thank The National Science Foundation. The Buckeye Symposium was supported in part by grant DMS-1011888 from the National Science Foundation. We also are indebted to The College of Wooster for their financial and administrative support of this conference.

In addition to the formal mathematical program, time was set aside for research collaboration and a problem session. Wednesday evening found many of the participants enjoying the Ohio Light Opera's production of John Philip Sousa's {\em El Capitain}. On Thursday afternoon, the symposium participants were treated to a delightfully informative tour of the Amish region near Wooster. At the traditional Friday evening banquet, Conference Director Pierce awarded the {\it ANDY}' to {\bf Marianna Csornyei}. Congratulations, Marianna!

The conference featured invited one-hour addresses by:

STEVEN KRANTZ
Washington University, St. Louis

Professor Krantz was a student of E.~M.~Stein, graduating from Princeton in 1974. He served as Assistant and Associate Professor in the Departments of Mathematics at UCLA and Pennsylvania State University respectively before moving to Washington University in St. Louis as Professor of Mathematics in 1986. His distinguished career as a scientist of the highest caliber has included Visiting Professorships at Princeton, The Institute for Advanced Study, Uppsala University, Beijing University, the Mittag-Leffler Institute, and the Universite Paul Sabatier among several others. He has served as a principle speaker at dozens of national and international conferences on real analysis, complex analysis and functional analysis lecturing on his ground breaking work in each of these areas of research and has authored over one hundred and seventy research papers in these areas of analysis.

In addition, Professor Krantz has been honored with several awards for his teaching and his lecturing. His current research in real analysis includes a new look at convexity in real analysis and a norm approach to providing new perspectives (and simplified proofs) of how smoothness in each of several variables separately (or all directions) can provide joint smoothness.

MARIANNA CSORNYEI
University College, University of London

Professor Csörnyei received her Ph.D. degree from Eötvös Loránd University, Budapest in 1999 under the direction of György Petruska. She moved to University College, London University where she worked with David Preiss's research group in real analysis as a Research Fellow. In 2002 she received the Whitehead Prize from the London Mathematical Society for young mathematicians working in the United Kingdom. Later, also in 2002, she was awarded the prestigious Wolfson Research Merit Award carrying with it five years of full funding; the Wolfson Award was created to enable top universities in the United Kingdom to retain ``respected scientists of outstanding achievement and potential.'' In 2004, Professor Csörnyei was promoted to Full Professor of Mathematics at University College, London the youngest person so promoted in any discipline in the long history of that institution.

She has had long term visiting positions at the Isaac Newton Institute, Cambridge, the University of Jyvaskyla, Finland, the University of North Texas, Texas A\&M University, PIMS in Vancouver, B.C., and the University of Washington. Additionally, she has served year-long visiting research positions at the IAS in Princeton in 2003/2004 and at Yale University in 2009/2010.

Professor Csörnyei has been invited to give one of the invited hour addresses at next year's ICM in Hyderabad, India, August, 2010. Current among her research interests are:

  1. Investigating classes of exceptional sets in finite dimensional spaces that arise from the consideration of general regularity problems for partial differential equations.

  2. Building on the joint observation with J. Kolar that examples showing invalidity of Morse-Sard theorems beyond the classical Holder conditions on derivatives are incorrect and that we can indeed improve them.

as well as twenty-nine contributed talks. Following 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

James Aduci, Ali Alikhani, Pieter Allart, Chanchal Kumar Basu, Jack Brown, Jane Brown, Svetlana Butler, Marc Carnovale, Bishweshwar Choudary, Marianna Csörnyei, Udayan Darji, Geraldo de Souza, Gerald Edgar, Michael Evans, Márcia Federson, David Freund, Paul, Humke, Corey Jones, Robert Kantrowitz, Jun Kawabe, Kiko Kawamura, Steven Krantz, Eddy Armand Kwessi, Tamas Matrai, Mark Mc Clure, Paul Musial, Kirill Naralenkov, Lenka Obadalová, Pamela Pierce, Eric Samansky, Grzegorz Sitiniewski, Jaroslav Smital, Sarah Sprague, Tatiana Sworowska, Pietr Sworowski V\'aclav Vlas\'ak, Daniel Waterman, Martina Zähle, Ondrjěj Zindulka.

PICTURES of the BUCKEYE SYMPOSIUM

Pictured above are the participants of the Thirty-fourth Summer Symposium in Real Analysis.

Clockwise from the top: An astonished Marianna Csörnyei receives this year's "Andy" from an equally ebullient Pam Pierce. Eddy Kwessi finds plenty of mathematics to photograph in Wooster, while Ondrjěj Zindulka accompanies himself singing his own rendition of Edgar Allen Poe's The Raven.

PROGRAM of the TALL GRASS PRAIRIE SYMPOSIUM

WEDNESDAY Morning Session (Chair - Paul Humke)

9:00      P. Pierce and P. Humke
             Opening Remarks and Announcements

9:10      Carolyn Newton, Provost of The College of Wooster
             Welcome to Wooster!

9:25     S. Krantz
            Convexity in Real Analysis

10:45    M. McClure
            Finite Type Iterated Function Systems: a Computational Perspective

11:10    C. Jones
            The Golden Ana Set

11:35    E. Talvila
            Convolutions With the Continuous Primitive Integral

WEDNESDAY Afternoon Session 1 (Chair - Erik Talvila)

13:10    K. Naralenkov
             On Continuity and Compactness of Some Vector-Valued Integrals

13:55    L. Obadalova
            Irregular Recurrence in Compact Metric Spaces

14:20   G. Edgar
             Fractional Iteration of Series and Transseries

14:45    E. Samansky
            Probability Measures on Shrinking Neighborhoods

WEDNESDAY Afternoon Session 2 (Chair - Ali Alikhani)

15:30    M. Zähle
            Local and Global Curvatures of Self-Similar Sets

15:55   O. Zindulka
             Are Functions with a Monotone Graph Smooth?

16:20   R. Vallin
            Results for Slowly Oscillating Continuous Functions

16:20   P. Humke
             Transference of Density May be Possible

THURSDAY Morning Session 1 (Chair - Mark McClure)

9:00      R. Kantrowitz
            Banach Algebra Norms for Spaces of Functions of Generalized Bounded Variation

9:25      D. Waterman
           
Variations on Axer's Theorem

9:50     E. M. Bonotto
           
A Feynman-Kac Solution to a Random Impulsive Equation of Schrädinger Type

THURSDAY Morning Session 2 (Chair - Robert Vallin)

10:40    G. DeSouza
           
A New Characterization of the Lorentz Spaces L(p,1) for p>1 and Applications

11:05    E. A. Kwessi
            
Characterization of Lacunary Functions in Weighted Bergman Besov Lipschitz Spaces

11:30   J. Kawabe
            
New Smoothness Conditions on Riesz Spaces with Applications to Riesz Space-Valued Non-Additive Measures and Their Choquet Integrals

FRIDAY Morning Session 1 (Chair - Udayan Darji)

8:45     M. Csörnyei        
            Lipschitz Mappings

10:05   C. K. Basu
           
Uniformization Subtopology and a Sort of Converse of A. H. Stone's Theorem

10:35   P. Sworowski
         
On Baire One* Approximately Continuous Functions

10:55   P. Allart
           
Where does Takagi's Continuous, Nowhere Differentiable Function Have an Infinite Derivative?

11:20   K. Kawamura
           
The Derivative of Lebesgue's Singular Function

FRIDAY Afternoon Session 2 (Chair - Ondřej Zindulka)

13:30   B. Choudhary        
           
A Natural Extension of the Henstock-Kurzweil Integral

13:55   M. Federson
           
Linear FDEs in the Frame of Generalized ODEs: a Justification for Using Kurzweil Equations

14:20   U. Darji
           
Chaos Among Self-Maps of the Cantor Space

14:45   P. Musial
           
The $L^r$ Variational Integral

FRIDAY Afternoon Session 3 (Chair - Paul Musial)

15:30    J. Smital        
            
Distributional Chaos After 16 years

15:55    J. Adduci
           
Basis Properties of the Eigensystem of a Perturbed Harmonic Oscillator

16:20    T. Sworowska
           
On Recovery of a Function from its Trigonometric Integral

16:45   M. Evans
           
Baire one, Gibson and Weakly Gibson Real Functions of Several Real Variables