This is a momentous occasion for me. I want to thank Rector Harasimiuk, members of the University Senate, my friend and collaborator, Kazimierz Goebel, my friends and colleagues in the Mathematics Institute at UMCS, and the many others who initiated and supported the procedures that led to this award. This is without doubt the highest honor of my academic career. I thank you all.
I would also like to take this occasion to reflect briefly on my career and specifically on three of things about it that stand out: First, my graduate training at the University of Missouri; then a serendipitous research discovery I made in 1964; and finally my long association with UMCS, and especially my collaboration with Kazimierz Goebel.
Regarding my graduate training, I want to begin by paying tribute to the legacy that Polish mathematicians of the early 20th cen tury left the world. The accomplishments of many Polish mathematicians were familiar to me even when I was a student. I studied the topology of Kazimierz Kuratowski and Wacław Sierpiński, the functional analysis of Stefan Banach, and the set theory of Alfred Tarski. I also knew of other Polish mathematicians: Hugo Steinhaus, Juliusz Schauder, Samuel Eilenberg, Stanisław Mazur, Stanisław Ulam, Karol Borsuk, Władysław Orlicz, Antoni Zygmund - the list could go on. At the time I entered graduate school in 1958 some of these mathematicians had emigrated to the United States, some had already died, but many were still active in Poland. It would be impossible for me to overstate the impact their work had on mathematics worldwide, and certainly on my own training.
To begin with, I would like to recall two anecdotal stories about my graduate studies. The first involves a topology course I took in 1959 taught by Leonard Blumenthal, who later became my thesis adviser. At that time, university professors typically lectured from their own notes rather than from a formal text, and Blumenthal al ways followed this practice (except when he was lecturing from his own book). A student who could figure out the original source of the professor's notes had a distinct advantage. So I spent some time in the library, and I soon discovered that Blumenthal's topology lectures were obviously based on Sierpinski's book, General Topology. This book had been translated from Polish into English in 1952. I had my advantage, and to this day I still use Sierpiński's book as a primary resource.
Another story: As you know French was the lingua franca of science in much of Europe in the early part of the last century, and as a graduate student I was required to pass a reading examination in French. The examination, which I took in 1961, was administered by the French Department at Missouri. I was required to provide a mathematics book written in French with no English edition, from which the examiner would select a passage for translation. I chose the 3rd Edition of Kuratowski's Topologie, vol. 1, which had appeared in 1958. I had never studied French formally, but, as noted above, I had studied topology. I passed the examination easily, probably because I knew more topology than the examiner. (Fortunately, the examination did not have an oral component; otherwise failure would have been a certainty.)
The most critical stage in a mathematician's career probably comes in the years immediately after graduation. For me this was the period 1962-67 when I was at the University of California, Riverside. I attribute much of my early success to the excellent advice I received from two older faculty members at Riverside, Malcolm Smiley, who was the department chair at the time I was hired, and F. Burton Jones, a well-known topologist of that era. Although my Ph.D. dissertation was in the area of geometry, I became interested in functional analysis, and in 1964 I discovered a fixed point theorem that quickly attracted a lot of attention. That result paved the way for most of my future research, and it led to other opportunities as well. I won't go into the details here, but I owe a huge debt of gratitude to Burton Jones for recognizing the potential importance of my result and for taking specific action to insure that it was published quickly. (As an aside, in 1968 Burton Jones reviewed Jan Jaworowski's 1966 English translation of Kuratowski's Topologie for Mathematical Reviews, and in his review he remarked that Kuratowski's book was generally regarded as the set-theoretic topologist's "bible".)
I moved to the University of Iowa in 1967, and in 1971 a singular seminal event occurred that had a tremendous impact on my career. In the fall of that year Kazimierz Goebel arrived in Iowa City to spend the year at the University of Iowa under the aegis of a Kościuszko Foundation fellowship. The cultural differences between Poland and the United States were much greater then than now, and it undoubtedly took tremendous courage for him to embark on such a venture.
Kaz, as we almost immediately began to call him, thrived. He adjusted to our weather (probably easily, since I think it differs little from the climate in Lublin), he adjusted to our habits (surely more difficult); to our food; to our way of life; to our beer (easily, I think); to our bread (more difficult); and he made many friends. The year passed and, as planned, we collaborated on research projects. We had strikingly similar research interests, and we wrote four joint papers that year, two of which proved to be fundamental in the sense that they inspired much further research. In fact I have chosen to include those two in the small selective sample of my favorite papers.
So, my link to this university dates from 1971. Upon returning to Lublin, Kaz immediately began trying to arrange for me to visit UMCS. I am sure such arrangements were difficult at that time, but Kaz was successful, and I first came to Lublin in June, 1974. This was my first trip abroad, and I approached it with more than a little trepidation. Although this was a time when American scholars were visiting Poland, such visits were still unusual.
To my relief, the trip went exceedingly well. Kaz was a wonderful host. He met me when I arrived in Warsaw, and we drove to Lublin the next day. I remember meeting Kaz's professor, Adam Bielecki, and other members of the department. I gave a colloquium talk to the Mathematics Department that Kaz simultaneously translated into Polish. During the ensuing days we visited local sights in and around Lublin, and we drove to Krakow so I could give a talk at the Polish Academy there. On our return from Krakow we stopped for lunch in Kazimierz Dolny and found ourselves in the midst of a delightful folk festival. The music and costumes were unlike anything I had ever seen before and I took many photographs. I have other memories - for example, trying to get taxi in Warsaw while Poland was playing for the European football championship. The taxi drivers had all stopped to listen to the game so I had to wait at the taxi stand until the game was over. What I remember most about the trip, however, was how polite and friendly the people were, and the fact that they seemed especially pleased to learn that I was a visitor from America.
Kaz and I continued to keep in touch mathematically, but it was difficult to actually carry out joint research because the mail was so slow. The use of e-mail today makes things much easier, but for mathematicians there is still no substitute for direct verbal communication (and a blackboard) when exchanging ideas. (In a restaurant it helps to have paper napkins to scribble on.)
Fortunately Kaz and I both had opportunities to travel. In 1977 we attended a conference at Oberwolfache, Germany, after which we gave talks in Aachen, Germany. Then Kaz made a couple of short visits to Iowa City in the early eighties, and on one occasion we found time to write another joint paper which also has been frequently cited. Our paths continued to cross at mathematical conferences where at the same time I began meeting other mathematicians from UMCS. I met Tadeusz Kuczumow - I think it was in 1982 -when he made a brief visit to Iowa City. At that time he was at the University of Oklahoma where he was working with my former student, W. O. Ray. And, I first met Tadeusz Sękowski sometime in the mid-eighties when we were both in Milan, Italy.
Kaz arranged to spend another year at the University of Iowa in 1989. We felt that metric fixed point theory was solidly grounded, and we had discussed the need for a book summarizing its central themes. No such book existed and our objective was to write one. Kaz arrived in Iowa City with a plan for its structure already in mind. We worked hard that year, but because I was encumbered with my duties as department chair, Kaz had to do much more than his share of the work. The successful outcome of this visit was our book, Topics in Metric Fixed Point Theory, published by Cambridge University Press in 1990.
In May, 1992,1 was able to visit UMCS a second time. Compared with my visit in 1974, things had changed dramatically. I was particularly struck by the quality of research taking place in the areas of fixed point theory and Banach space geometry, and by the number of people involved. Also, Lublin was now an especially vibrant city.
I again came to Poland in 1997 in connection with a mathematics conference. Every two or three years, those of us who work in metric fixed point theory try to arrange a conference so that we can report on our most recent research and exchange ideas. There had been conferences in Marseille, France in 1989, in Halifax, Canada in 1991, and in Seville, Spain in 1995. Inspired by the fact that so many mathematicians from Poland, and especially UMCS, were participating in these conferences, it was the consensus of the participants in Seville that the time had come to actually have the conference in Poland. The mathematicians at UMCS responded magnificently. The organizing committee consisted of Kazimierz Goebel, Stanisław Prus, Tadeusz Sękowski, Adam Stachura, Krzysztof Bolibok, and Wiesława Kaczor. The conference was held in the beautiful village of Kazimierz Dolny in June, 1997. It was a tremendous success, both mathematically and socially. Over eighty people participated and many countries were represented. And I had the special pleasure of returning to the beautiful place I had first visited in 1974.
These fixed point conferences continue. The meeting was in Haifa, Israel in 2001 and in Valencia, Spain in 2003. The next meeting will be in 2005, perhaps in Guanajuato, Mexico. And perhaps we will have the opportunity to meet again in Poland as well.
A final comment: My research in fixed point theory and functional analysis would not exist were it not for the legacy Stefan Banach. Indeed, it is safe to say that he created this important branch of mathematics. The theories introduced in his classical treatise, Theorie des operations lineaires, published in 1932, endure to this day. They find wide application in mathematical physics and in other branches of mathematics. The very framework in which the modern theory of partial differential equations is couched was devised by Banach. The ideas of Banach and his closest collaborators and students were unknown to 19th-century mathematicians, but it would be impossible to overstate the impact they had on mathematics in the 20th century.
Therefore, one of the highlights of my career came during my most recent visit to Lublin, in June, 2001. At that time Kaz Goebel arranged for me, along with my Australian colleague, Brailey Sims to visit the historic city of Lwow (now Lviv, in Ukraine) where Stefan Banach spent most of his life. Yuri Kozitsky, a native of Lwow who is now on the faculty here, kindly served as our expert driver and guide. As everyone knows Banach died an untimely death in 1945. While in Lwow we had an opportunity to visit Banach's grave - a visit that was both somber and refreshing. Also Professor Yaroslav Prytula, Dean of Mathematics at Ivan Franko University - it was known as Jan Kazimierz University in Banach's time - graciously allowed us to examine Banach's personnel file and some of his papers. Brailey Sims has eloquently described this pilgrimage in an article he published in the December, 2001 issue of the Australian Mathematical Gazette. As Brailey states in his article, this was indeed the visit of a lifetime.
This is my fifth visit to Lublin, and I feel humbled by the occasion. This University is named after the renowned Noble Laureate Marie Curie-Skłodowska, who also, like Stefan Banach, died an untimely death, and also is an example of Poland's unique contribution to humanity. It is certainly an honor for me to be recognized by such a great university at this proud moment in its history. Again, I thank you for the privilege of being here and for the honor you have bestowed upon me.
William A. Kirk