Symposium 39 – Northfield, 2015 — Real Analysis Exchange

SUMMER SYMPOSIUM IN REAL ANALYSIS XXXIX
"The Cows and Colleges Symposium"

St. Olaf College, Northfield, Minnesota
June 8-13, 2015

The Thirty-Ninth Summer Symposium in Real Analysis (The Cows and Colleges Symposium) was held at St. Olaf College in Northfield, MN from June 8 through June 13, 2015. The symposium's co-directors were Paul Humke and Bruce Hanson. We would like to thank St. Olaf College, particularly Patty Martinez for keeping everything running smoothly. For generous financial support thanks go to the NSF (DMS 1501013) and the Google Corporation, and specifically for the help of Jim Larson and Tilman Achberger. We were also thankful to have the gracious and tireless help of students Ben Bruce, Ben Hacker, Nick Rekuski, Jeremy Storvick, Cameron Wright, Alan Chang, Liyang Liu, and Jen Crawford.

In addition to the formal mathematical program, time was set aside for research collaboration. Then, on Thursday, participants travelled to Fort Snelling and toured (and shopped at) the Mall of America.

This year's "ANDY'' was awarded to a shocked, but grateful Andy Bruckner. Congratulations, Andy!

The conference featured invited one-hour plenary addresses by:

MARIANNA CSÖRNYEI
University of Chicago

Professor Csörnyei received her Ph.D. degree from Eotvos Lorand University, Budapest in 1999 under the direction of Gyorgy 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 Csornyei 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 moved the University of Chicago in 2013.

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 Csornyei presented one of the invited hour addresses at the ICM in Hyderabad, India, August, 2010. Current among her research interests are:

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

ALEXANDER OLEVSKII
University of Tel Aviv

Born: February 12, 1939, Moscow.

Ph.D. Moscow State University, 1963.
Doctor of Sciences, Moscow State University, 1966.

Selected Addresses :
Invited Speaker, ICM Berkeley, 1986;
Invited Speaker, International Conference "Kolmogorov and Contemporary Mathematics," Moscow, 2003;
Plenary speaker, Real Analysis Symposia: Santa Barbara, 1998; Oxford, 2007;
Invited Speaker, European Congress of Mathematics, Krakow, 2012;
Abel Symposium Lecture, Oslo, 2012;
Plenary Speaker, Function Spaces and Harmonic Analysis, Lumini, 2014.

Selected Visiting Positions:
IHES, Bur-Sur-Ivette,1995.
Institute of Advanced Study, Princeton, 1996;
University NSW, Sydney, 1997
Max-Planck-Institut fur Matematik, 1998.
University Paris-Sud, 2000.
University of Naples, 2008.
University of Minnesota, 2010.
Kent State University, 2014.

Additional Information:
Moscow Mathematical Society Prize,1966;
Barecha Fellowship of Israel Science Foundation, 1991;
Fellow of AMS, 2012.

Selected Publications

Fourier Series with Respect to General Orthogonal Systems. Ergebnisse der Mathematik and Ihrer Grenzgebiete , Band 86, Springer-Verlag, Berlin Heidelberg New York, 1975.
Homomorphisms of the circle and Fourier Series , Proceedings of ICM-86, Berkeley, vol.2 (1987) , 976-989.
with G.Kozma, Analytic representation of functions and a new quasi-analyticity threshold, Ann. of Math. 164 (2006), 1033-1064.
with A.Ulanovskii , Universal sampling and interpolation of band-limited signals, Geom.Funct. Analysis, 18 (2008), 1029-1052.
with N.Lev , Wiener's "closer of translates" problem and Pyatetskii- Shapiro uniqueness phenomenon. Ann. of Math.174 (2011), 519-541.
Sampling, Interpolation, Translates, Proc.of 6th ECM Krakow (2014), 489-502.

MIKLÓS LACZKOVICH
Eötvös Lorand University

A member of the Hungarian National Academy and a recipient of academic prizes and awards by The Hungarian Mathematics Society and the Hungarian Academy of Sciences, Laczkovich was awarded the Ostrowski Prize in 1993, sharing the prize that year with Marina Ratner (University of California--Berkeley). Laczkovich was an invited hour speaker at the First European Congress of Mathematics in Paris, 1992. He has served as a Visiting Professor at the University of Waterloo, the University of Naples and Michigan State University as well as the University of California--Santa Barbara. In 1986 he was a Fullbright Research Scholar at St. Olaf College in Minnesota. He currently holds joint appointments at Eotvos Lorand University, Budapest and University College, London University.

His main research interests cover much of combinatorial and set theoretic analysis. Some particular areas are as follows:

Problems in geometric measure theory; e.g. is it true that the ball in Rn is the Lipschitz image of every measurable set of positive Lebesgue measure?
Problems of equidecomposability: Is it true that two bounded measurable sets of the same positive measure and with rectifiable boundaries are always equidecomposable with finitely many measurable pieces? Is this true for the cube and the tetrahedron in R3? Is it true that if two measurable sets are equidecomposable under a commutative group of isometries then they are equidecomposable with measurable pieces?
Problems concerning the difference operator: can we characterise those topological groups where it is true that if the differences of a function are continuous then it is the sum of a continuous function and an additive function? Can we represent every Lp function on the circle with vanishing integral as the sum of finitely many differences of Lp functions?
Miscellaneous Problems: Does there exist an algorithm that decides, for every given polynomial with integer coefficients of the functions sin(xn) and cos(xn) whether or not it has a real root?

For more information, the link to Dr. Laczkovich's home page is provided below (in Hungarian).

https://laczk.web.elte.hu/

R. DANIEL MAULDIN
North Texas University

R. Daniel Mauldin received his Ph.D. from the University of Texas, Austin, in 1969 under the supervision of H.S. Wall. Dan has written extensively in the areas of set theory, logic, real analysis, dynamics and probability theory among others. His papers are known for their insight, depth and for providing penetrating clarity. He was a friend and frequent collaborator with Paul Erdős and gave one of the plenary lectures at the 2013 Erdős Centennial Conference in Budapest. He has served as Editor for several mathematical journals including the Proceedings of the AMS and Advances in Mathematics, as well as serving as a Contributing Editor for the Exchange for almost twenty years.

In 1982, Dan edited The Scottish Book: Mathematics from the Scottish Café and is currently preparing a new edition (This is good too, since new copies of the 1982 edition currently cost more than $2,500). In his lecture Dan will describe some of the unsolved analysis problems in the Scottish Book.

Dan’s Homepage

Z. BUCZOLICH
Eötvös Lorand University

https://buczo.web.elte.hu/

as well as twenty-seven 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

Yury Andreev, Jack Brown, Jane Brown, Ben Bruce, Andy Bruckner, Judy Bruckner, Zoltan Buczolich, Alan Chang, Krzysztof Chris Ciesielski, Barry Cipra, Don Cohn, Linda Cohn, Deborah Cool, Marianna Csörnyei, Emma D'Aniello, Mike Evans, Emmie Faure, Jim Foran, Chris Freiling, Ben Hacker, Bruce Hanson, Paul D. Humke, Pankaj Jain, Seung uk Jang, Max Jodeit, Jun Kawabe, Martin Koc, Eddy Kwessi, Miklós Laczkovich, Liyang Liu, María Guadalupe Morales Macías, Patty Martinez, Dan Mauldin, Harry I. Miller, Paul Musial, Kirill Naralenkov, Togo Nishiura, Eleanor Nishiura, Sasha Olevskii, Sophia Olevskii, Pamela Pierce, Patrick Reardon, Peter Rejto, Nick Rekuski, Trevor Richards, Alain Riviere, Jean Roelke, T H Steele, Jeremy Storvick, Tatiana Sworowska, Piotr Sworowski, Brian S Thomson, Julia Wodka, Cameron Wright, Ondrej Zindulka, Paul Zorn.