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 2023 is the 46th and 12th 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.
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.
A week filled with mathematics, enthusiastic and talented young mathematicians, kind hospitality and beautiful surroundings: what more could we ask for ?
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.
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.
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 !
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.
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.
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.
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.
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).
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!
Jaroslav Lukeš
