M3 Math Majors Matter ----------------------------------


       Anatolii (Tolya) Puhalskii

Tolya Puhalskii received his Ph.D. in Mathematics and Operations Research from the Moscow Institute of Physics and Technology in 1984. He was a Senior Researcher at the Institute for Problems in Information Transmission of the Russian Academy of Science from 1990-97. He visited CU-Denver during the '94-'95 academic year, and was hired as an Associate Professor at UCD in 1997. His research area is in Applied Probability, more specifically, Large Deviation Theory and applications in queuing and statistics.
"My research focuses on studying asymptotic properties of stochastic processes, in particular, their large deviation asymptotics. Asymptotics are often an only way of gaining insight into the behaviour of complex stochastic dynamical systems. Limit theorems for the associated stochastic processes are function space extensions of the classical limit theorems of probability theory. Large deviation asymptotics can be expressed in the form of large deviation convergence to idempotent processes. Applications include queueing networks, statistics, and random graphs."
In 2001 Chapman & Hall/CRC published Tolya's book, Large Deviation and Idempotent Probability.

More information on Tolya's research can be found on his webpage.

We asked Tolya to write something about himself in 1998, and he responded with this article.

Hockey craze

by Tolya Puhalskii

My life for about a decade from early seventies to early eighties rotated very much around ice-hockey. Ice hockey and football used to be the two major sports in the U.S.S.R. I think, football was more popular, actually, because to play hockey you need equipment:skates, hockey sticks, protecting gear; you also need to be able to skate (though not necessarily). Football is much more democratic: just a ball, that's what it takes. But somehow I was more successful in hockey.

So, like a lot of my peers, when a teenager, I used to play for hours football in summer and hockey in winter. Actually, I started playing hockey being quite small: my brother and I would use sofa's legs as gates in one of the two rooms in our apartment and play with small souvenir hockey sticks and an eraser (as a puck), at that time the Soviet team won all major tournaments and we would pretend to be some of the stars on the team; of course, we would produce a lot of noise,and, naturally, get in trouble with the neighbours. As I grew up, I started going out to our backyard to play hockey there, for this we needed real sticks and a real puck, but no skates, we would play on foot sliding on the snow.

Later we used to frequent a skating rink not far from our house,there you had to be able to skate, so, I spent a lot of time simply skating, however, it was not yet a real hockey since we would use as the gates' poles boots or just sweaters, neither did we use any protective gear.

In the early seventies my older brother and a friend of mine, who's also older than me, took up hockey more seriously; by the time, they were too old and lacked sufficient training to play professionally, however, they participated in tournaments where teams were composed of factory workers, researchers or students who played hockey in their spare time just for fun.

There used to be lots of teams like this in Moscow. That hockey was quite real: real fields, real gates, real injuries, even referees.

At that time I entered the college myself and joined our college hockey team: physical exercising was one of the required subjects and the students could choose either to engage in a general training where they would do, say, track-and-field or basketball in the fall and spring, and skiing in winter; or join one of the specialised training groups and practice exclusively either skiing, track-and-field, football, hockey or some other sport. So, I joined the ice-hockey team, which gave me the rare possibility of enjoying my "classes". It was for the first time in my life when I tried on hockey gear, playing in it turned out to be much different: it weighed about 10 kilos, so you had to be stronger to be able to move fast from the first to the last minute of the match. An illustration of how serious I was about my hockey is that I would spend a lot of time "improving" hockey sticks: at that time first "curved" hockey sticks started appearing in the stores (before only "straight" sticks had been available),but they were not quite to our liking, so, my friend and I would buy these sticks, which were made of wood and covered with fabric, take the fabric off, do some woodwork, mainly, to make the sticks thinner, then put the sticks in boiling water, which would make them less stiff, and curve the sticks by hand giving them the shape we needed, after the sticks had dried up, we would glue a special fabric to their surface. I, personally, liked much better the hockey sticks that I "produced", they also lasted longer.

Of course, during the season we didn't play as many matches as in NHL, I don't remember exactly but we may have had not more than ten matches per season. But every one was important, we would even say with emphasis: "I have A Game today". For the most part, we didn't have at our disposal fields with artificial ice since there were few such fields (about five for the whole of Moscow) and they were occupied by the teams who played professionally; we were only allowed to play out-doors on natural ice. That's why our season would start in late December or early January and wrap up by the end of March. In January we occasionally had to play in freezing cold with the temperature falling as low as 20 C below zero, while in March we sometimes had to play on ice covered with water because the temperature would rise up to 10 C above zero.

In the fall, before the start of the season, we used to work on improving our physical qualities such as speed, stamina, strength. Sometimes during this "preparation period" we were lucky enough to play on artificial ice: these training sessions would start at 10 or 12 p.m. and end late at night but we were really happy to have an opportunity like this. The peak of our season when we played quite often, once or twice a week, coincided with what is known in Russia as "a session". This is a period when the students take exams. Normally, they have four or five oral exams, which decide grades for the courses taken in the preceding semester, no classes are given during this period. This is the "hottest" time for the students since they have to go over the material they have studied in the semester. It's possible to get away with being lazy in the semester but you have to work hard during the session to get ready for the exams. There are two "sessions" in a school year: "the winter session" that takes place in January and "the summer session", in June. The winter session was the time I really enjoyed: since I didn't have to attend classes, I had more time for hockey. My day was divided between preparing for exams and playing hockey. During this time I would play hockey (or skate) daily: if we didn't have to play another team or didn't have a training session, I would go to the skating rink near my house and play there. On days when we had matches I would pack my bag with hockey gear, take a stick and go by subway to the stadium where the match was taking place. I would come back home four or five hours later, quite tired, but never regretted the time spent. I will never forget the feeling you experience after you have been trying very hard to score, you have been squeezing out the last drop of your strength to win, and you have succeeded: you have scored, your team has won. It is really an overwhelming feeling. Of course, I had bad moments when I didn't play the way I would like to, twice I was injured: once a puck hit my eyebrow, another time I had my ankle broken, was taken to the hospital right away from the field and spent three months with my leg in plaster. But the feelings that I was lucky to experience will stay with me forever.

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