# Like a burning torch

**Adam Jakubowski**

Translated by Paweł Schreiber

I have had the pleasure of observing, and sometimes stimulating, dr Tomasz Schreiber’s development since he began his studies at the Faculty of Mathematics and Computer Science, Nicholas Copernicus University, i.e. the year 1994. Without any hesitation I can say that Dr. Tomasz Schreiber is the most talented young mathematician I have ever had the opportunity to cooperate with. He is an extraordinary combination of a keen and original intellect with an exceptionally active personality.

I have had the pleasure of observing, and sometimes stimulating, dr Tomasz Schreiber’s development since he began his studies at the Faculty of Mathematics and Computer Science, Nicholas Copernicus University, i.e. the year 1994. Without any hesitation I can say that Dr. Tomasz Schreiber is the most talented young mathematician I have ever had the opportunity to cooperate with. He is an extraordinary combination of a keen and original intellect with an exceptionally active personality.

He arrived at the University already famous after winning the gold medal at the International Mathematical Olympiad of 1994. Especially for him, as well as several other very good students we have had the luck to accept in 1994, we prepared a customised curriculum, allowing these exceptional people to cover a large part of the doctoral studies syllabus and begin their own research still before they got their MA degrees.

He arrived at the University already famous after winning the gold medal at the International Mathematical Olympiad of 1994. Especially for him, as well as several other very good students we have had the luck to accept in 1994, we prepared a customised curriculum, allowing these exceptional people to cover a large part of the doctoral studies syllabus and begin their own research still before they got their MA degrees.

Dr Schreiber’s achievements have been noticed numerous times. In the years 1995-1999 he received the Ministry of Education scholarship three times. In 1998 he was named the best student at the University. In the same year, he spent 3 months at Oxford University, having won a Stefan Batory Trust contest. His MA thesis, “Estimation for the support of a multidimensional uniform distribution by the maximal likelihood method” won the first prize in a contest organised by the Polish Mathematical Society branch in Wrocław as the best work in the field of probability theory and applied mathematics. In 2000, he got the prestigious S. Saks Scholarship, awarded by the Wrocław mathematical milieu to the most promising young mathematicians.

Dr Schreiber’s achievements have been noticed numerous times. In the years 1995-1999 he received the Ministry of Education scholarship three times. In 1998 he was named the best student at the University. In the same year, he spent 3 months at Oxford University, having won a Stefan Batory Trust contest. His MA thesis, “Estimation for the support of a multidimensional uniform distribution by the maximal likelihood method” won the first prize in a contest organised by the Polish Mathematical Society branch in Wrocław as the best work in the field of probability theory and applied mathematics. In 2000, he got the prestigious S. Saks Scholarship, awarded by the Wrocław mathematical milieu to the most promising young mathematicians.

*is a record of broad research, whose common denominator is constituted by the asymptotic distributional properties of random geometric structures. It contains a variety of subjects, motivations and examples, fully showing the author’s erudition and technical perfectionism.*

I also emphasized the fact that

*Whether presenting the state of research on a given subject or his own results, mgr Schreiber always retains a high level of knowledge as well as great clarity and precision of discourse, thus proving his maturity as a mathematician.*

Throughout last year I have observed Dr. Tomasz Schreiber's activities, and I can say that he has not in the slightest slowed down the speed of his development as a scientist. He has become a much more mature mathematician and a more interesting person.

Throughout last year I have observed Dr. Tomasz Schreiber's activities, and I can say that he has not in the slightest slowed down the speed of his development as a scientist. He has become a much more mature mathematician and a more interesting person.

In the initial stages of his development, Dr. Schreiber's research interests necessarily coincided with those of his supervisor, Prof. A. V. Nagaev. However, already in his doctoral thesis one could see a strong tendency towards the possible physical applications of the models he examined. This tendency successfully continued in the past year, and I think it will lead to the formation of Dr. Tomasz Schreiber's fully mature research profile.

In the initial stages of his development, Dr. Schreiber's research interests necessarily coincided with those of his supervisor, Prof. A. V. Nagaev. However, already in his doctoral thesis one could see a strong tendency towards the possible physical applications of the models he examined. This tendency successfully continued in the past year, and I think it will lead to the formation of Dr. Tomasz Schreiber's fully mature research profile.

While benefiting from the Foundation for Polish Science scholarship, Dr. Schreiber visited, among other places, the United States, invited by the famous mathematicians D. Mason and J. Yukich. Co-operation with Yukich, a well-established authority representing a similar field and style of mathematics, can play an especially important role in Dr. Schreiber's development. It is also worth noticing that Dr. Schreiber started a joint project with P. Calka, from Paris V University. The fact that they are preparing joint publications proves that Dr. Schreiber has learned to co-operate with other mathematicians, which had so far been, in a way, his weaker point (out of the total of 17 papers only 3 have co-authors, despite numerous foreign contacts).

While benefiting from the Foundation for Polish Science scholarship, Dr. Schreiber visited, among other places, the United States, invited by the famous mathematicians D. Mason and J. Yukich. Co-operation with Yukich, a well-established authority representing a similar field and style of mathematics, can play an especially important role in Dr. Schreiber's development. It is also worth noticing that Dr. Schreiber started a joint project with P. Calka, from Paris V University. The fact that they are preparing joint publications proves that Dr. Schreiber has learned to co-operate with other mathematicians, which had so far been, in a way, his weaker point (out of the total of 17 papers only 3 have co-authors, despite numerous foreign contacts).

The matter of dr Schreiber's research is very difficult and concerns mostly problems from the space between mathematics and mathematical as well as statistical physics, which requires broad knowledge and a high level of mathematical culture. I am happy to say that nevertheless he remains a probabilist in spirit, which can be seen in last year's very interesting results of research devoted to polygonal Markov fields in the plane (…)

The matter of dr Schreiber's research is very difficult and concerns mostly problems from the space between mathematics and mathematical as well as statistical physics, which requires broad knowledge and a high level of mathematical culture. I am happy to say that nevertheless he remains a probabilist in spirit, which can be seen in last year's very interesting results of research devoted to polygonal Markov fields in the plane (…)

It is very much worth emphasising that in spite of his great involvement in research, Dr. Schreiber is also a well-liked and active member of the Faculty staff, and his reputation is impeccable. The Faculty authorities have been giving him more and more sensitive didactic tasks (e. g. the Introduction to Probability Theory lecture), and students gave him high grades in the anonymous evaluation questionnaire. At the same time, for the last two years Dr. Schreiber has led the group of young staff members and students preparing and taking care of the booth representing the Faculty during the yearly event promoting the University among secondary school graduates. Dr. Schreiber has also become the main organiser of the National Children's Fund mathematical workshops, regularly taking place in Toruń. All of this shows a harmoniously developing personality of a young researcher and teacher.

It is very much worth emphasising that in spite of his great involvement in research, Dr. Schreiber is also a well-liked and active member of the Faculty staff, and his reputation is impeccable. The Faculty authorities have been giving him more and more sensitive didactic tasks (e. g. the Introduction to Probability Theory lecture), and students gave him high grades in the anonymous evaluation questionnaire. At the same time, for the last two years Dr. Schreiber has led the group of young staff members and students preparing and taking care of the booth representing the Faculty during the yearly event promoting the University among secondary school graduates. Dr. Schreiber has also become the main organiser of the National Children's Fund mathematical workshops, regularly taking place in Toruń. All of this shows a harmoniously developing personality of a young researcher and teacher.

- Boolean models and Widom-Rowlinson gas;
- models of random sequential packing;
- polygonal Markov fields.

The results for boolean models allow to draw known conclusions, concerning, for example, asymptotics of a volume generated by points of a point process in a ball, but this is not where their importance lies. It turns out that on the level of generality adopted by Dr. Schreiber, many important issues connected, among others, with Voronoi cells, can be easily reduced to Boolean models with the use of suitable geometrical manipulations, freely performed by the author. For random sequential packing the dissertation gives large deviations for empirical distributions built on centers of balls used in the process of packing. The results achieved here are based on another spectrum of very advanced techniques connected i.a. with the so-called stabilising functionals.

The results for boolean models allow to draw known conclusions, concerning, for example, asymptotics of a volume generated by points of a point process in a ball, but this is not where their importance lies. It turns out that on the level of generality adopted by Dr. Schreiber, many important issues connected, among others, with Voronoi cells, can be easily reduced to Boolean models with the use of suitable geometrical manipulations, freely performed by the author. For random sequential packing the dissertation gives large deviations for empirical distributions built on centers of balls used in the process of packing. The results achieved here are based on another spectrum of very advanced techniques connected i.a. with the so-called stabilising functionals.

The third class of models examined in the dissertation – polygonal Markov fields – is derived from Arak’s work from the mid-eighties. The theory of such fields was developed by Arak, Surgailis, Clifford and others, and has always had the reputation of being very difficult.

The third class of models examined in the dissertation – polygonal Markov fields – is derived from Arak’s work from the mid-eighties. The theory of such fields was developed by Arak, Surgailis, Clifford and others, and has always had the reputation of being very difficult.

Polygonal Markov fields are families of random polygonal contours in the plane, with interactions excluding contour- and self-intersections. Binary colouring (e.g black-white) of contours and interpretation of a monochromatic contour as an area representing identical magnetisation exhibits graphical similarity of a typical realisation of the random Markov field to pictures obtained for the Ising model on the two-dimensional lattice. However, contrary to the Ising model, polygonal Markov fields have a continuous (non-lattice) nature and are isometrically invariant. The main result of the thesis referring to polygonal Markov fields is a complex theorem on phase separation (a Dobrushin-Kotecký-Shlosman-type theorem), characterising the geometry of interphase curves in microcanoninical ensembles imposing a domination of a chosen phase. It is then observed an aggregation of dominated phase and formation of so-called “Wulff’s body”, whose geometry has also been described).

Polygonal Markov fields are families of random polygonal contours in the plane, with interactions excluding contour- and self-intersections. Binary colouring (e.g black-white) of contours and interpretation of a monochromatic contour as an area representing identical magnetisation exhibits graphical similarity of a typical realisation of the random Markov field to pictures obtained for the Ising model on the two-dimensional lattice. However, contrary to the Ising model, polygonal Markov fields have a continuous (non-lattice) nature and are isometrically invariant. The main result of the thesis referring to polygonal Markov fields is a complex theorem on phase separation (a Dobrushin-Kotecký-Shlosman-type theorem), characterising the geometry of interphase curves in microcanoninical ensembles imposing a domination of a chosen phase. It is then observed an aggregation of dominated phase and formation of so-called “Wulff’s body”, whose geometry has also been described).

In conclusion, Dr. Tomasz Schreiber’s habilitation dissertation yields very rich results and could easily form a basis for at least two separate dissertations of this kind. The state-of-the-art, original subjects, the depth of the research, and the author’s skill in using a broad spectrum of advanced, new techniques from the field of stochastic geometry, limit theorems of probability theory and statistical physics, and the ease and intuition with which the author notices links between apparently distant issues make this dissertation an exceptional one.[…]

In conclusion, Dr. Tomasz Schreiber’s habilitation dissertation yields very rich results and could easily form a basis for at least two separate dissertations of this kind. The state-of-the-art, original subjects, the depth of the research, and the author’s skill in using a broad spectrum of advanced, new techniques from the field of stochastic geometry, limit theorems of probability theory and statistical physics, and the ease and intuition with which the author notices links between apparently distant issues make this dissertation an exceptional one.[…]

Dr. Tomasz Schreiber is, beyond any doubt, an exceptionally talented, dynamic mathematician with broad interests and impressive technical skills, who, in spite of his youth, has already achieved much in the field of mathematics and will definitely be even more successful in the future.

Dr. Tomasz Schreiber is, beyond any doubt, an exceptionally talented, dynamic mathematician with broad interests and impressive technical skills, who, in spite of his youth, has already achieved much in the field of mathematics and will definitely be even more successful in the future.

Those were not empty compliments. At the moment, Tomasz Schreiber’s results concerning stabilising functionals of stochastic geometry have been universally accepted as a breakthrough. His achievements in the field of stochastic geometry have been honoured by making him responsible for the chapter „Limit Theorems in Stochastic Geometry" in the monograph „New Perspectives in Stochastic Geometry", published in 2010 by Oxford University Press. The book, edited by Wilfrid S. Kendall (the president of the Bernoulli Society for Mathematical Statistics and Probability) and Ilya Molchanov, will determine the trends of development in stochastic geometry in the near future. The results concerning polygonal Markov fields became the subject of a prestigious lecture at the 28th European Meeting of Statisticians 2010 in Pireus, Greece, where Tomasz Schreiber acted as a special invited speaker.

Prof. Stanisław Kwapień from the University of Warsaw, a member of the Polish Academy of Science, wrote: *Dear Adam, I want you to receive our condolences to the Chair of Theory of Probability and all the friends at Toruń University on Tomek’s death. It has made us all very sad. We remember the papers he presented at our seminar, his enthusiasm and his great abilities. It was clear he was facing a great future in science and he would become one of the pillars of Polish studies on probability theory. Apparently, God needed him more.*

Prof. Joseph Yukich from the prestigious Legigh University (Bethlehem, USA) wrote: *It was a great privilege and honor to collaborate with Tomasz. He was a source of great mathematical inspiration and I learned an enormous amount from him, thanks to his patience and immense kindness. As much as I feel privileged to have known Tomasz on a mathematical level, I feel even more blessed to have known him as very good friend. As much as anything else, Tomasz taught me 'til the very last a lot about life, including love, honor, and, courage. His optimism and spiritual strength shall live on ... they shall live on in Bethlehem, in the department of mathematics at Lehigh University, and in my home and heart.*

During the funeral service at the church in Grębocin, on December 4th 2010, I had to say goodbye to Tomek Schreiber, my pride and my successor. *When in the mid-nineties Tomek decided to join our team, my life was unexpectedly fulfilled. Not only because of the appearance of a great scientific leader, who would take over from us, the older generation, but also because all of my activities at that time, the renovations, buying equipment, struggling for funds, all the bustle, suddenly gained a new meaning: I was here in order to create better working conditions and help somebody greater than myself. Tomek was great in repaying the trust he was given. He moved through mathematics, computer science and physics like a burning torch, dropping sparks of brilliant ideas, bringing light to regions of helpless ignorance. And, like a torch, he was suddenly extinguished.
However, his cheerfulness, his helpful nature, his modesty and courage with which he fought his illness for so many years, will always remain in our hearts and minds. We will remember:
*

[1] Article published in no 3 (2011) of “Głos Uczelni. Pismo Uniwersytetu Mikołaja Kopernika”

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