Symposium 33 – Tall Grass Prairie, 2009

SUMMER SYMPOSIUM IN REAL ANALYSIS XXXIII
"Tall Grass Prairie Symposium"

Southeastern Oklahoma State University
June 23-27, 2009

The Thirty-Third Summer Symposium in Real Analysis (The Tall Grass Prairie Symposium) was hosted by Southeastern Oklahoma State University, June 23--27, 2009. The Editorial Board of the EXCHANGE wishes to express its gratitude to Southeastern for its gracious hospitality and to the conference director, Patrick Reardon, for his outstanding leadership in organizing and conducting this symposium. We'd also like to give a special thank you to the students who did so much to make our stay enjoyable, Sarah Sprague (St. Olaf College) and Julie Aultman, Ryan Favors, Kevin Faulk and Cayce Roark (Southeastern). Furthermore, both Patrick and the Editorial Board sincerely thank The National Science Foundation which supported this conference under Grant No. 0909998. We also are warmly appreciative of the Gibson Fund and Southeastern for their financial and administrative support of Summer Symposium in Real Analysis XXXIII.

In addition to the formal mathematical program, time was set aside for research collaboration and a problem session. On Thursday afternoon, the symposium participants were treated to an informative and entertaining excursion to the nearby Headquarters and Museum of the Chickasaw Nation.

On Friday afternoon, the participants honored Jack Brown of Auburn University for his many contributions to the real analysis community. "Testimonials" were given by Udayan Darji and Patrick Reardon, two of Jack's Ph.D. students at Auburn University. A slideshow of action pictures of Jack and Jane at previous symposia and mini-conferences was shown and presented to Jack who was (reluctantly) in attendance.

At the traditional Friday evening banquet, Conference Director Reardon awarded the ``ANDY'' to Ondřej Zindulka who was overcome with irrational exuberance at the announcement. Congratulations, Ondřej!

The conference featured invited one-hour addresses by:

UDAYAN DARJI
University of Louisville

Udayan Darji received his Ph.D. from Auburn University in 1991 under the supervision of Jack Brown. After completing a two year Post-Doctoral Fellowship at North Carolina State University, he accepted an Assistant Professorship at the University of Louisville. He was promoted to Full Professor in 2004 and continues his work at the University of Louisville.

Professor Darji has had visiting positions at Vrije Universiteit, Amsterdam. February to July, 2008, Federico Secondo Universitá, Napoli, Italia. November to December, 2007, St. Andrews University, St. Andrews University, Scotland. September and October, 2007 and from November of 1999 to March of 2000 at the California Institute of Technology in Pasadena. From November of 2000 to May of 2001 Professor Darji was a resident Fulbright Research Scientist at Eötvös Loránd University, Budapest, Hungary.

His work has been recognized and grant supported by NWO (Nederland Science Foundations) to work on problems related to Erdöos space with Professor Jan Dijkstra of Vrije Universiteit, by a London Mathematical Society Scheme II grant to work with Dr. James Mitchell on transformation groups, by an Italian GNAMPA grant to teach a course on transformation groups to the PhD students and complete a project in dynamical systems in Naples, Italy and by a Research In Pairs Grant (joint with Marek Balcerzak), at the Oberwolfach Institute in Germany.

In addition, he has worked on numerous occasions for the Institute for Defense Analysis, Center for Communications Research (IDACCR) to work on communication problems for the Department of Defense.

Professor Darji has an extensive and wide ranging bibliography, publishing in set theory, topology, real analysis, dynamical systems, and algebraic structures.

MÁRTIN ELEKES
Rényi Institute of the Hungarian Academy of Sciences

Márton Elekes received his Ph.D. (with distinction) in 2002 at Eötvös Loránd University, Budapest under the supervision of Miklós Laczkovich. His thesis title was Set-Theoretical Methods in Real Analysis.

Since 2002 he has been a Research Fellow at the Rényi Institute of the Hungarian Academy of Sciences, except for two one-year visiting positions at the Fields Institute in Toronto. He also holds a position at the Mathematical Institute of Eötvös Loránd University.

His awards include a 2008 Young Researcher Award and a 2008-2011 Bolyai János Re- search Fel low both awarded by the Hungarian Academy of Sciences, and the 2006 Öveges Scholarship awarded by the Hungarian National Office for Research and Technology. Professor Elekes' recent invited lectures include the Logic and Mathematics 2008 conference in Urbana-Champaign, the 2008 Advances in Set-Theoretic Topology: Conference in Honour of Tsugunori Nogura on his 60th Birthday conference held in Erice, Sicily and the 2007 Logic Colloquium 2007 in Wroclaw, Poland. His work focuses on various branches of real analysis such as measure theory, geometric measure theory, real functions and descriptive set theory, and also on the connection between these fields and set theory.

More details may be found on:
http://www.renyi.hu/~emarci/

STEVE JACKSON
University of North Texas

Steve Jackson received his Ph.D. from the University of California, Los Angeles in 1983 under the supervision of Donald Martin. Upon graduation he was a Van Vleck Assistant Professor of Mathematics at the University of Wisconsin, Madison for three years, a two year IBM Research Fellow at the California Institute of Technology and then three years as a National Science Foundation Research Fellow at the California Institute of Technology . In 1984 he was awarded the Victoria Delfino Prize for his calculation of δ51. Presently he is Regents Professor of Mathematics at the University of North Texas.

Professor Jackson has had numerous grants from the National Science Foundation and other sources in support of his research program in descriptive set theory. He has given invited and supported addresses at a wide range of meetings including a three lecture tutorial at the European Summer Association of Symbolic Logic meeting in July, 2007 in Wroclaw, Poland, the Ninth International Workshop on Set Theory, Marseilles-Luminy in September of 2006, the International Conference in Set Theory in Oberwolfach, Germany during December of 2005 and was the plenary speaker at the 2004 annual meeting of the Association of Symbolic Logic held at Carnegie-Mellon.

His mathematical interests are wide ranging and deep with papers including work on partitions and Steinhaus type problems, countable Abelian group actions, classification of cardinals and ordinals, and Borel equivalences and selections.

More details may be found on:
http://www.math.unt.edu/~sjackson/

PARTICIPANTS

Linda Akpu, Yurij Andreev, Jack Brown, Jane Brown, Svetlana Butler, Bishweshwar Choudary, Emma D'Aniello, Udayan Darji, Mártin Elekes, Michael Evans, Jack Grahl, Paul, Humke, Steve Jackson, Ken Kellum, Samaila Kupongoh-Sylvanus, Veerabhadraiah Lokesha, Laurent Moonens, Paul Musial, Togo Nishiura, Lenka Obadalová, Innocent Opara, Dokubo Osuo-Siseken, Patrick Reardon, Jaroslav Smítal, Sarah Sprague, T.H. Steele, Václav Vlasák, Woodford Zachary, Ondřej Zindulka.

PICTURES of the TALL GRASS PRAIRIE SYMPOSIUM

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

Pat presents this years Andy to an astonished, yet deserving Ondřej Zindulka. Later Ondřej contemplates the aura of the Andy

Jack and Jane Brown at the Jack Celebration while Mike and Susan Evans, Emma D'Aniello and Sarah Sprague analyze the proceedings.

Additional pictures of the SUMMER SYMPOSIUM XXXIII can be found at http://mat.fsv.cvut.cz/Zindulka/galleries/durant/

PROGRAM of the TALL GRASS PRAIRIE SYMPOSIUM

WEDNESDAY Morning Session (Chair - Paul Humke)

OPENING CEREMONYWelcoming Remarks by Conference Director Patrick Reardon

9:00      U. Darji
            Applications of the Baire Category Theorem to three topics

10:10    L. Moonens
             Mean Value Theorems for tangential derivatives

10:35    K. Kellum
             Functions that separate XxR

11:10    M. Evans
            Analogs of Young's characterization of Baire one, Darboux functions

11:35    Y. Andreev
            Note about nondifferentiable extensions of real functions

WEDNESDAY Afternoon Session (Chair - Paul Musial)

13:10    T.H. Steele
             Adding machines and typical behavior of continuous self-maps of manifolds, Part I

13:35    E. D'Aniello
            Adding machines and typical behavior of continuous self-maps of manifolds, Part II

14:10   O. Zindulka
             Monotone spaces and nearly Lipschitz maps

14:35    W. Zachary
            Lebesgue measure on a version of R∞

THURSDAY Morning Session (Chair - Udayan Darji)

09:00    M. Elekes, The 2009 GIBSON Lecturer
            Hausdorff measures, Cantor sets, typical continuous functions and set theory

10:10    S. Butler
            Large deviations for martingales and derivatives

10:35   J. Grahl
            Convergence for the random Riemann integral

11:10  P. Musial
             New results for the Lr Henstock-Kurzweil integral

11:35    B. Choudhary
             Lacunary l-convergent sequences

FRIDAY Morning Session (Chair - Ondřej Zindulka)

09:00    S. Jackson       
            Countable Borel equivalence relations, markers and group colorings

10:10    V. Vlasak
             Classes of H1 and H2 sets have different polars

10:35   L. Obadalová
            Distributional chaos and irregular recurrence

11:10   J. Smítal
            Distributional chaos and topological entropy