History of previous spring schools

The tradition of Spring Schools in Analysis, organized regularly by the Faculty of Mathematics and Physics of Charles University in Prague, was initiated by the late Professor Zdeněk Frolík. His idea was to gather a group of mathematical zealots, especially young ones, students or Ph.D. students, at some modest remote place and to concentrate on some problems from mathematical analysis. Since professor Frolík was also a sporting fan, he tried to organize schools in winter ski resorts in the mountains. The venues alternated among, for example, Štefanová (Slovakia), Strážné or Moravská bouda (Giant Mountains), and Srní (Bohemian Forest). At all these places, mathematics was combined with beautiful surroundings, skiing and tourism in perfect harmony.

The schools gradually grew, both in the number of participants, both from home and abroad, and in the number of topics. Currently there are organized schools in topology, geometry and functional analysis.

By the beginning of the 1980s, a separate section devoted to potential theory was an integral part of Frolík’s school. The participants included members of the so-called Prague Harmonic Group. Roughly at the same time there originated the idea of organizing one-week seminars outside Prague, which would be devoted to a particular topic in mathematics. These seminars consisted of series of lectures delivered by top specialists from around the world. They were intended mainly for students and young scientists. The students thus had an excellent opportunity to take part in informal discussions about problems of their interest (not only) from mathematics. Once again, the venues had changed each year: it all started in the modest conditions of Mariánská in the Ore Mountains; later the schools were organized, for example, near the Lipno Dam or in Teplýšovice.

The year 1989 was a year of big changes. A school devoted to Korovkin theorems had been scheduled for November; it should have been held in Alšovice. The main speaker, Professor Heinz Bauer from Erlangen, arrived just at the eve of our “Velvet Revolution”. As a result, rather than giving his series of lectures, he spent a week taking part in the revolution together with the students.

After 1989 there was no longer any problem in allowing mathematicians from abroad to participate, which naturally implied a further growth of the schools. At that time, Paseky nad Jizerou had been chosen as the school venue. Since everything went extremely well there, we have been organizing our schools in Paseky ever since.

The spring school in June 2019 is the 45th and 11th in the sequel of spring schools on function spaces. Hundreds of young mathematicians as well as well-known experts have found their way to the schools, traditionally organized under the logo “What am I if I will not participate”, quoted from a book by Antoine de Saint Exupéry. The speakers gave away their best knowledge for the benefit of participants. As can be clearly seen in the supplement, really the world topmost experts have been taking part; Friedrich Hirzebruch, Gustave Choquet, Carlos Kenig, Per Enflo or Joram Lindenstrauss, to name just few.

Finally, let us quote the inscriptions by some of the speakers; they should give the reader an idea of what the atmosphere of our schools is like.

The spring schools are definitely a good idea and I hope that they will be continued (for at least another 25 years !). I hope that the talks give even students at least a feeling for what happens in research in some directions of functional analysis.
Joram Lindenstrauss
I enjoyed enormously the week at Paseky. The place is surrounded by beautiful hills with full of wild flowers and our chalet is well-appointed. But the best of all, this is the place where 60 mathematicians, young and old, from different parts of the world gathered and talked mathematics informally anytime of the day. I appreciate the permutation of name cards at the meal-time very much. I learned a lot about other countries from the conversations I had with the people sitting at the same table.
Isaac I. Namioka
A week filled with mathematics, enthusiastic and talented young mathematicians, kind hospitality and beautiful surroundings: what more could we ask for ?
Joe Diestel
I could have closer contacts with students and refresh myself in their young enthusiasm. I never had previously such an opportunity to discuss with so diverse young or older mathematicians, coming from many countries.
Gustave Choquet
It will be impossible to forget this School. On a personal level, I greatly enjoyed the opportunity to become acquainted with so many students. Their contributions to my enjoyment varied from providing me with beer, kefir and buttermilk, to accompanying me on a 22 hike through hills, valleys, a railroad tunnel (!) and a brief step into Poland.
Bob Phelps
I let myself be persuaded by your good naturel enthusiasm to undertake the 25 km trek. My eyes and spirit were delighted, my feet and legs had a slightly different opinion... I would be so thoroughly and enjoyable reminded of Scottish and Irish songs that I had heard since my childhood. I am very enthusiastic about this meeting of cultures. May we all be to do it more !
Michael Cwikel
It is ten years since I was last in Paseky, and I feel that the area is even more delightful than I remember. The walks in the wood were a great pleasure, but also helped to keep me in trim after the abundant meals and plentiful supplies of beer. My fellow participants were excellent companions and it was a joy to socialize, as well as to discuss mathematics, with them.
W. Desmond Evans
I had some previous idea about Paseky schools from comments of colleagues but reality is much better than the picture I had. The nice and creative atmosphere, landscape, good music and the very interesting talks place Paseky Spring School among the best.
Fernando Cobos
I will never forget the Paseky Spring School. What a wonderful experience! Fine food, friendly students and, of course, the world–famous Czech beer, all helped to create a very pleasant atmosphere.
Grahame Bennett
It was a great pleasure to visit the Czech Republic and enjoy the warm hospitality of its people. My lectures on the boundary behavior of harmonic functions were very enthusiastically followed by a very friendly audience. It was a very nice experience to be in Paseky.
Carlos Kenig
For me it was a first opportunity to present some of the directions in this area that I believe are worth developing. It was also very special to spend a week in the mountains, away from all daily life duties, just concentrating on mathematics (except for a small amount of organ playing).
Per Enflo
Holding these “schools” is a very fine activity, and I am thankful for the opportunity to participate. Of course, I also enjoyed the beautiful countryside and especially the longtrip from Harrachov back to Paseky, followed by such good beer!
Terry Rockafellar

Jaroslav Lukeš

List of Spring Schools

J. Blietner : Potential Theory - A Probabilistic Approach
Ch. Berg : Harmonic Analysis and Potential Theory
P. Loeb : Nonstandard Analysis
M. Giaquinta, E. Giusti, G. Modica : Regularity of Weak Solutions of PDE's
F. Hirzebruch : A Development of Riemann-Roach and Atiyah-Singer Theorems
H. Bauer : Korovkin Theorems and Related Topics (Cancelled because of the Velvet Revolution)
T. Kilpelainen, O. Martio, Ju. Reshetnyak : Nonlinear Potential Theory and Quasiconformal Mapping
M. Roeckner : Dirichlet Forms
L.-I. Hedberg, J. Kral, L. Zajicek : Small and Exceptional Sets in Analysis and Potential Theory
R. Deville, G. Godefroy, V. Zizler : Recent Trends in Banach Spaces
M. Degiovanni, M. Kucera, A. Marino, P. Quittner, F. Schuricht : Variational Inequalities
R. Haydon : Recent Trends in Banach Spaces
J. Maly, W. Ziemer : Fine Regularity of Solutions of Elliptic PDE's
G. Choquet, M. Husek, S. Negrepontis, R. Phelps, V. Ptak, S. Troyanski, L. Tzafriri, V. Zizler : Banach Spaces, Related Areas and Applications
N. Tomczak-Jaegermann, B. Maurey, E. W. Odell, T. Schlumprecht : Recent Trends in Banach Spaces
C. Kenig : Harmonic Analysis Technique for PDE's in Lipschitz Domains
Y. Benyamini, P. Enflo, P. Mankiewicz, G. Schechtman : Recent Trends in Banach Spaces
Stefan Mueller : Mathematical models of microstructure
J. Diestel, H. Jarchow, R. Aron, G. Godefroy, V. Zizler : Recent Trends in Banach Spaces
1997 - April, June
F. Altomare, G. Choquet, S. Simons, V. Zizler : Boundaries and Convexity in Banach Spaces
V. Havin : Approximation and uniqueness properties of harmonic differential forms
1998 - April, June
J. Lindenstrauss, G. Godefroy, J. Orihuela, R. Paya : Recent Trends in Banach Spaces
S.J. Gardiner, P.J. Rippon : Harmonic Approximation and Complex Dynamics
1999 - April, June
I.I. Namioka, N. Kalton, V. Fonf, J.M.F. Castillo : Recent Trends in Banach Spaces
J. Appell, E. Pustylnik C. Perez: Function Spaces and Their Applications
2000 - April, June
Robert Deville, Alexander Ioffe, Philip Loewen, Terry Rockafellar: (Non)smooth Analysis in Banach Spaces
Victor Lomonosov, Sergei Treil , Alexander Volberg, Yurii Lyubarskii: Some Recent Techniques in Harmonic Analysis
2001 - April, June
Yoav Benyamini, Gilles Lancien, Joram Lindenstrauss, Gideon Schechtman: Analysis in Banach Spaces
Andrea Cianchi, Michael Cwikel, Mario Milman: Function Spaces and Interpolation
2003 - April, June
A. Ioffe, A. Lewis, B.S. Mordukhovich, J.-P. Penot: Variational Analysis
Lars-Inge Hedberg, Igor Verbitsky: Function Spaces and Applications
2004 - April
S. Argyros, W. Marciszewski, J. Orihuela, S. Todorcevic, S. Troyanski: Nonseparable Banach Spaces
2005 - June
W. Desmond Evans, Pavel Shvartsman: Function Spaces and Applications
2006 - April
R.T. Rockafellar, J. Borwein, J.V. Outrata, W. Roemisch, B.S. Mordukhovich: Variational Analysis and its Applications
2007 - June
Grahame Bennett, Mario Milman: Function Spaces, Inequalities and Interpolation
2009 - April
Frederic Bonnans, Aris Daniilidis, Assen L. Dontchev, Alexander Ioffe: Variational Analysis and its Applications
2009 - June
Anders Björn, Fernando Cobos, Thierry Coulhon, Peter A. Hästö: Function Spaces, Inequalities and Interpolation
2010 - May
Gerald B. Folland, Stéphane Jaffard, Thomas William Körner: Harmonic Analysis
2011 - June
Michael Lacey, Andrei K. Lerner: Function Spaces, Approximation, Inequalities and Lineability
2012 - April
René Henrion, Alexander Ioffe, Alejandro Jofré, Boris Mordukhovich: Variational Analysis and its Applications
2013 - June
Lars Diening, Javier Duoandikoetxea, Carlos Perez, Vladimir Stepanov: Function Spaces and Inequalities
2015 - April
Jonathan M. Borwein (lectures given by Matthew Tam), Marián Fabian, Alexander Ioffe, David Russell Luke: Variational Analysis and its Applications
2015 - June
Pekka Koskela, Luboš Pick, Juan B. Seoane-Sepúlveda: Function Spaces and Lineability IX
2017 - June
Andrea Cianchi, David Cruz-Uribe, Piotr Hajłasz: Embeddings and Extrapolation X