Nikolai Chernov

TALK BY ROBERTO MARKARIAN BEFORE THE CONFERENCE GIVEN IN THE DYNAMICAL SYSTEMS, ERGODIC THEORY, AND PROBABILITY CONFERENCE DEDICATED TO THE MEMORY OF NIKOLAI CHERNOV  (University of Alabama at Birmingham, May 18-20, 2015)

    In June 91 I was invited by Professor Sinai to work in the Lev Landau Institute for Theoretical Physics, Moscow, and met Kolya who was working in the Joint Institute for Nuclear Research, Dubna. There, he and Vieta were living in a beautiful dacha, with a lot of carpets hanged in the walls; some of them were of Armenian origin.  This was my first visit to an important scientific institute apart from IMPA, Rio de Janeiro, where I had studied with Jorge Lewowicz and Jacob Palis. Kolya had studied my first paper (that appeared in 1988[1]), and he knew it better than me; it was clear that he (and Sinai) had been the referees of the paper. Moreover, in a small book on billiard systems, in Russian, that Kolya wrote with Gregory Galperin, they refer to the “young Uruguayan mathematician, Roberto Markarian”, although I was already 42; confusion came from the fact that this was my first paper.

    We began to work jointly in a lot of different topics in billiards mathematical theory. Our first joint paper appeared in 1992[2].  We met again in 1994, now in Princeton University.  We began to study systems with holes and published 4 papers on this topic, some of them with Sergei Troubetzkoy, at this moment working here in Alabama. I visited  Birmingham three times before now and I stayed in Kolya’s and Vieta´s home (in the basement), very close to their sons´ rooms.

    In my last visit to Birmingham we began to work in our books. During this period we visited a lot of beautiful state Parks near by, with magnificent creeks, streams and falls. I don´t remember their names although I have a lot of pictures taken by Vieta and myself.

     In May 2003, while I was visiting my daughter Vania who was finishing her PhD (in History) in Columbia University, we worked in the Institute of Advanced Studies in Princeton. There I met for the first time Dmitry Dolgopyat. I remember well that we (Dolgopyat and me) drank one bottle of wine in a vietnamese restaurant.  I also remember very well our discussions with Kolya, walking in the beautiful gardens of the IAS, about the US invasion to Iraq that began in March 20, 2003.

     At this time we began to prepare our last book that was published by the AMS in 2006[3], whose latter versions were prepared in Montevideo and Rio de Janeiro. Kolya stayed twice in my home and we visited some of the beautiful beaches of the Rio de la Plata. In one of our joint visits to IMPA, we stayed in the hotel Flamengo where the famous Uruguayan soccer world champion´s team stayed in 1950.

     I consider myself a good friend of Kolya’s family and I am touched for being in this fully deserved commemoration. I am much in debt with him for all he helped me both personally and mathematically.

 Kolya – In Memoriam

       I first heard Kolya’s name around 1991 when I was discussing with Yasha Sinai the computer simulations of Moran and Hoover. They considered a particle moving in in a Sinai billiard subject to an external electric field and a Gaussian thermostat. The resulting stationary measure looked very fractal (see my presentation on the web page of the Chernov Memorial Conference). Yasha thought that for small electric fields this system may be considered a perturbation of the classic billiard, corresponding to a particle moving freely in a periodic array of convex scatteners. To carry out this program, we needed the expertise of someone who really understands billiards. Sinai thought that the best person for that would be his former student Kolya Chernov who had just come to the U.S. from Russia. Kolya, if I remember correctly, was then in California visiting Lai-Sang Young at UCLA.
 

Yasha and I then invited Kayla to come to Princeton and Rutgers. This was the start of a collaboration which lasted until Kolya’s premature tragic death. Kolya and his young family then moved to Princeton the place where I also live. An incident I remember from that time is my telling Kolya how to get by subway from Penn Station in Manhattan to Brighton Beach in Brooklyn where there was a concentration of Russian immigrants and many stores with Russian foods.  It was a Sunday morning and Kolya was headed there with his family. The next day I asked Kolya how the trip went and discovered that instead of ending up in Brighton Beach he took the subway north to the Bronx, ending up in a rather unsafe area. I expressed my shock but Kolya was totally unfazed.

After Kolya and his family moved to Birmingham Kolya would often drive up to Princeton/Rutgers where we would spend a couple of days working together. Kolya loved driving and at least in the beginning he did not have any car insurance, which was not required in Alabama at that time. This used to worry me a great deal but did not seem to bother Kolya at all. He was a cool guy, all right.

The last time Kolya and I met in Princeton it was together with his student Alexey Korepin and with Federico Bonetto from Georgia Tech. I remember we spent most of a Saturday working in the common room of Fine Hall – the location of the math department of Princeton University trying to figure out how to derive a stochastic differential equation to describe the slow changes in the speed of a system of N-particles moving in a Sinai billiard under influence the of a weak elective field. Later that day we went to a Chinese restaurant for dinner where we were joined by some friends. During dinner Kolya kept on sneakily looking at his notebook and scribbling away.
 

I think that is the last time I saw Kolya. Several weeks later I received an eleven page long e-mail from him beginning as follows:

“Dear Joel, Federico, Alexey, -

            I made some progress in my work on stochastic differential equations. In fact, I advanced in two directions! First, I learned something about stochastic differential equations (SDE), which is good. Not that I understood much, but the picture got clearer… Second, I managed to derive the density formula published in your paper [BDLR], at least for the system of N = 2 particles. This is something!”

I think this is very characteristic of Kolya’s approach to science: full devotion and great modesty. He was a friend and teacher and is greatly missed by all who knew him.

                                                                                                                                              Joel Lebowitz

          Kolya started his mathematical career under supervision of Ya. Sinai and in the late 1970’s became a member of the legendary Sinai’s Moscow seminar on dynamical systems. At this time the seminar served not only as a scientific meeting for those who worked on problems in dynamics, ergodic theory, and mathematical physics (in a very broad interpretation of these areas) but also as a place for spiritual and social interaction between its members, which was very important in the time of a harsh life in the former Soviet Union. With time the seminar had become something like a “close club” where despite age difference and social status, we all were friends. Kolya was one of us, our good friend and we have many good memories of him. This is why his untimely death is so painful for us.

           Participating in the seminar was the best way for Kolya to get involved into research in modern dynamics and he was very successful due to his talent and hard work. He has left behind a great deal of work in dynamical systems, most notably billiards, and in mathematical physics. His results are remarkable, innovative and deep, they will be forever attached to his name and constitute his scientific legacy.

                                                In Memory of N. I. CHERNOV (1956-2014)

The Mathematics and Mathematical Physics communities have suffered a heavy and untimely loss. After a long fight with cancer Professor Nikolai Ivanovich (Kolya) Chernov passed away on the seventh of August 2014.

     Kolya was born and grew up in the city of Kryvyi Rih in the Ukraine (former USSR). His interest in Mathematics appeared early and began to flourish already in Kolya's school years. Kolya Chernov was a winner of the State, the Republic and the International Mathematical Olympiad. In 1974 Kolya entered the Department of Mechanics and Mathematics of the Moscow State University. He had chosen the field of Probability Theory and started to work under the supervision of Professor Sinai. Kolya graduated at 1979 with Master Degree. His Master thesis was devoted to the study of kneading invariants of one-dimensional maps with an absolutely continuous invariant measure. It was the topic of the first paper out of more than a hundred research papers published by Professor Chernov. In the same year Kolya became a graduate student in the Department of Mechanics and Mathematics continuing his work with Prof. Sinai. At that time he became interested in the dynamics of chaotic billiards which remained the Love of his scientific life.

    The theory of chaotic billiards forms one of the most exiting and the most difficult areas in the modern theory of dynamical systems. A billiard dynamics is generated by the motion of a point particle with constant speed in a region Q which is called a billiard table. Upon reaching the boundary of Q the particle gets elastically reflected according to the law “the angle of incidence equals the angle of reflection”. Billiards appear as natural models in many areas of Physics, first of all in Statistical Mechanics. The study of billiards becomes especially difficult when the dimension of the billiard table is greater than two. Kolya's PhD thesis, which he defended in 1984,was devoted exactly to such billiards. In particular, he constructed there the stable and unstable manifolds for multidimensional semi-dispersing billiards.

    After defending his PhD Dr. Chernov was working as a research scientist in the Joint Institute for Nuclear research in Dubna. As a part of the team in the Information Technology lab he was working on statistical analysis of data from physics experiments. A problem they faced was how to approximate noisy data by simple curves like straight segments and circles. It was the main characteristic of Prof. Chernov's scientific style to penetrate deeply into any problem he was dealing with. Its not surprising that he became an expert in this field as well. He published many papers about this topic and several of his students in the University of Birmingham defended PhDs in this area. Kolya also published a very well received book “Circular and Linear Regression:Fitting Circles and Lines by Least Squares”, (2010) where he summarized the geometric, algebraic and numerical aspects of fitting lines and circles to data. However billiards were always the greatest of Prof. Chernov's scientific interests. Dubna is close to Moscow, and therefore he could attend the seminar on Dynamical systems in Moscow university and collaborate with Prof. Sinai.

    The most important example of a high-dimensional billiard is the celebrated Boltzmann gas of N hard spheres confined in a box (or in a torus). This system is equivalent to a semi-dispersing billiard , where the boundary of the billiard table consists of cylinders. Each such cylinder correspond to the collisions of some fixed pair of particles. The fundamental problem of ergodicity of the Boltzmann gas with two particles was settled by Sinai. However in dimensions greater than two the situation becomes technically much more complicated. In Kolya's joint paper with Sinai (1987) a general scheme was presented to prove ergodicityof the Boltzmann gas. This paper contains the celebrated Sinai-Chernov Ansatz which became a cornerstone for proving ergodicity of non-uniformly hyperbolic dynamical systems. Chaotic billiards belongs to this fundamental class of dynamical systems because of singularities which arise from the tangent collisions and/or singularities of the boundary of the billiard table.

      In 1991 Kolya moved to the US. He held visiting positions at UCLA, Georgia Tech and Princeton before joining the Mathematics Department in the University of Alabama in Birmingham at 1994. There Prof. Chernov was actively working with a large number of undergraduate and graduate students. Some of them became famous researchers in the theory of billiards. Already in 1991 Kolya started a new area of research. Together with Eyink, Lebowitz and Sinai they constructed nonequilibrium steady states and investigat ergodic and statistical properties of the Lorentz gas with a small electric field. Because the speed of the moving particle in this system goes with time to infinity, one needs to introduce some kind of dissipation. This was done with the help of the so called Gaussian Thermostat. Kolya continued to develop this important area with the same collaborators and with his students till the very end.

     Perhaps the most important and groundbreaking of Kolya's papers was the one published in 1998, where he proved a quasi-exponential rate of decay of correlations for Anosov flows. It was well known that Anosov diffeomorphisms have an exponential rate of decay of correlations . However in dynamical systems with continuous time (flows) there appears a new (time) dimension and along this dimension there is no exponential instability which one has along the stable and unstable transversal manifolds. It was the first dynamical proof of the fast decay of correlations in systems with continuous time which was based on new insights and a very delicate new technique. Before this such a result was known only for geodesic flows on compact manifolds with negative curvature. However the proof of this fact was purely algebraic and did not shed any light on the dynamical mechanism behind this phenomenon. In 2002 together with Balint, Szasz, and Toth,Kolya discovered the new types of singularities in the stable and unstable manifolds of semi-dispersing billiards, which was a fundamental result for the theory of such billiards.

   Kolya established a very fruitful collaboration with Dima Dolgopyat. They produced several remarkable papers which solved some long standing classical problems. Perhaps the most impressive of their results is a two hundred page proof of the existence and limiting distributions in the classical model of real diffusion, where a heavy particle elastically collides with a gas of noninteracting light particles. This is exactly a model of Brownian motion, as observed by Brown. For almost forty years the theory of chaotic billiards was virtually unaccessible for beginners. It was contained in research papers which were very hard to read. Kolya together with Markarian beautifully filled in this gap by producing the book “Chaotic Billiards” (2006) which has already made a great impact and allowed many gifted young mathematicians to join in the exiting game of mathematical billiards.

     Kolya had a very modest but also a very strong and determined personality. He always talked in a low voice and avoided, if possible, crowded and loud meetings. He often managed to find his own trails (not recommended in a conference bulletin), which always were less populated, more quiet,and therefore more suitable for thinking and enjoying nature. The same happened if there was quiet hotel nearby (not recommended). Travel to remote places and hiking was Kolya's passion. Together with his hobby of fixing old huge American cars and vans, it made him one of the most knowledgeable around on the beauty of (often remote and hardly accessible) US landscapes. Again, everything that Kolya did he did it very fundamentally. No wonder that the mechanics in Birmingam had the utmost respect for him It is always the case that we read and write in reference letters that somebody is an expert in the field. With Kolya's passing away the Mathematical Community lost the Expert in billiards. He was the only one whom we could completely trust to judge that some very sophisticated proof on billiards dynamics is, in fact, correct.

   The memories of Prof. Chernov as an outstanding mathematician and a wonderful person will always be with those were lucky enough to knew Kolya. His scientific contributions will have a long lasting life.

We lost a wonderful colleague and a dear friend.

                                                                                         Leonid Bunimovich

                                                                                                          Oct. 9. 2014

                                   Reminiscences about Kolya Chernov

   
    Kolya and I started to work together when Kolya became an undergraduate and later a graduate student of Mathematics Department of Moscow State University. From the very beginning he became interested in the theory of billiards. One of his remarkable property was his ability to penetrate very deeply in any subject in which he was involved. He started to work on the so-called basic theorem in the theory of hyperbolic billiard which was a subject of two previous papers by Bunimovich and myself. Later we worked with Kolya on the theory of multi-dimensionalhyperbolic billiards and published a joint paper in "Uspekhi".This topic was later in the center of interests of Kolya for many years. He was one of the authors in the famous paper by P. Balint, D. Szasz and I.P. Toth in which they discovered new types of singularities in stable and unstable manifolds.

   At that time Kolya became one of the leading experts in the theory of billiards. Kolya and R.Markarian wrote a beautiful monograph on billiards which later became a popular text-book for many generations of students.

   Slowly but steadily Kolya moved to other parts of Mathematics. Kolya, Joel Lebowiz and I worked together on problems related to the dynamics of adiabatic piston and published several papers on this field. In his own paper he included illustrations which demonstrated the actual dynamics of the piston. One should mention a deep paper by Kolya and Dima Dolgopyat in which they studied a model of Brownian particles which consisted of a passive particle surrounded by a cloud of small particle.

  Kolya was full of plans to continue his research. But his unexpected illness and death stopped these intentions. For all people who knew Kolya this was a great great loss. All his friend will remember Kolya as a great unforgettable friend.

  Kolya's wife Veta was with him and was a true friend during so many years. They were raising two sons one of which already graduated from the University. Looking at the boys one can see several features of Kolya in them. For us it will be something unforgettable about Kolya.

                                                                                                     Ya. G. Sinai
                                                                                                      09.05.2014 

To the memory of N.I.Chernov.
 

                 

On August 7, 2014, Nikolai Ivanovich Chernov (58) passed away in the U.S.A, who worked with me in the Laboratory of Information Technologies between 1983 and 1992.

He was the most outstanding of my young colleagues by his talent in all areas of mathematics in which he was involved. With truly ingenious skill, Kolya would find new approaches to solving the most difficult problems, and then move far beyond my particular tasks and give the most complete solutions to more general problems.

I remember when Yasha Sinai (who later became an academician and a winner of the Abel Prize in 2014 -- the analog of a Nobel Prize for a mathematician) called me to Dubna with a request to save Kolya, after graduating from Moscow State University, from being sent to the provinces to work, he said about Kolya: "He is the most talented of my students". Back then I managed to break the wall of the tightly closed bureaucracy of our Ministry  and have Kolya be accepted to ОИЯИ (Joint Institute for Nuclear Research). It was a lucky chance not only for Kolya, but also for me, since the work with him gave me a new creative impulse, and additionally made us close friends. During the years of his work in ОИЯИ, he became a co-author of more than 30 publications on topics of current interest, connected to reconstruction of the tracks of particles, adapting the rings of the Cherenkov detectors and processing the data of several other detectors of high energy physics, and in all these projects his input was significant.

When Kolya decided to move to the USA, I was sure that he will advancethere. So it happened, after working for one year at UCLA, he moved toPrinceton, then to Georgia Tech, and after that obtained a permanent position at the University of Alabama at Birmingham, where soon became a professor of the Department of Mathematics. For his outstanding research in statistical physics he received large grants from the NSF eight times. On one of these grants he managed to invite me to his university in 1998 to give a course about neural networks.

Even after moving to the USA, when without any explanation he was fired from ЛИТ (Laboratory of Information Technologies), he, working mostly on difficult problems of statistical mechanics and chaos, continued to work on our topic, connected to fitting conical sections, and obtained outstanding results, published in his monograph. These results were successfully used by A. Ayriyan, S. Lebedev, and me for realization of important tasks on RICH detector in the project CBM.

Professor N. I. Chernov was in the prime of his scientific activity, full of new scientific plans, beloved by his students. His untimely death is a big loss for his family, colleagues, friends and everybody whom he helped in solving difficult mathematical problems.

G. A. Ososkov, Professor, Principal Researcher at ЛИТ ОИЯИ (Laboratory of Information Technologies, Joint Institute for Nuclear Research)

August 12, 2014

I am a former head of the group where Kolya Chernov  has been working during Dubna’s period of his Russian life.

As I already wrote to Veta when she informed me about Kolya’s premature demise, it was so awfully to learn such a sad news about his intolerable death.  It is so unfairly and beyond my comprehension, – Kolya who always was  such a cheerful, overflowed by new ideas  and only began to share them with his younger colleagues, so much anxious and attentive, would be suddenly passed away.

I sent to Veta this picture where Kolya was sitting with my wife Inna when he has visited us last time  during his being in Dubna. Inna always loved and respected him, she has been glad long time ago to acquaint Kolya with Veta. We both grieve so much about him.

I wrote an obituary note to “Dubna” newspaper with my mournful feelings.



 

Kolya was well known to his friends and colleagues as a hard working, tough guy and avid reader. The following little story exemplifies this.

It happened around the turn of the millenium. Kolya attended the annual Fall Penn State Workshop on Dynamical Systems and drove there from Birmingham (cca. 880 mi), as was his usual habit, having loved driving cars. At the same time, he did not want to lose the precious time from work, so he put a mathematical book on the steering wheel and read it, almost from cover to cover, on his way to State College. His own explanation for his working habit was that this was the only way of survival (as a mathematician) in the Soviet Union. When he commuted between Moscow and his workplace in Dubna by a very densely packed electrichka (a  suburban train), so that you could only stand, he always took a mathematical paper and read it while standing in the thick crowd.

Another short story related to his driving habit: Once we (just two of us) travelled back from the annual Spring Maryland Workshop on Dynamical Systems  in Kolya's old, highly built, big Chevy van. (One of his hobbies was fixing cars, that's why he loved old, big American vehicles.) We were barrelling down the hill on I-24 in Chattanooga at a pretty high speed. (Kolya was known to have lead foot.) It came to negotiate a dreaded right curve on the Interstate, preceded by many warning signs. Well, Kolya did it, barely, but I got covered with cold sweat by fearing of a turn over. Kolya saw my face and quickly reassured me: "Nandor, don't worry! I took into account our speed, the curvature of the bend, the position of the baricenter of the van, calculated the arising centripetal acceleration..."

Dr. Chernov was my advisor while I was student at UAB at the turn of the century. He left a lasting impression on me in many ways. Much of who I am today is a result of my time spent with him.

  Dr. Chernov was very successful, yet so humble; extremely fast, yet ever patient with me. He had so deep and advanced knowledge of math, yet was so effective in communicating in an easy-to-understand way: everything he presented was elementary and intuitive.

  Dr. Chernov was kind, and had a comforting smile. I spent many hours in his office, sitting in his guest chair next to his desk, watching him draw on plain white paper with his BIC ball-point pen. I learned so many interesting things over the years I worked with him. In the end, I did not complete the Ph.D.; I switched paths to enter the business world. Dr. Chernov worked very hard to show me multiple paths that suited my background and skill set, and I gradually came to recognize that a career in business may be a better fit. He and I had several conversations about working in industry and he shared with me his relevant, personal life experiences.

  Once he humorously told me if he were not a research mathematician, he might choose grocery bagging, because of all the interesting people and conversations. What I find so inspiring about Dr. Chernov is that he always encouraged me to follow a path that suited me. He gave me fair and honest guidance: a true mentor.

  He shaped my worldview. As just one example, when it came to programming computers, I remember he used to always say that you should not program for the sole reason of obtaining the result, but you should program because you enjoy programming. It stuck with me, and now I give similar advice to my employees in my current job: pursue things in life not for the praise or the accomplishments or the money, but rather pursue what you truly enjoy and all of those other things will take care of themselves.

  Thank you Dr. Chernov for the wisdom, skills, and fond memories you gave me.

                      

I have known Kolya for a long, long while ... We first met at an all-Ukrainian Math Olympiad in 1973. At that time contestants were put in dormitories of local colleges, 12-15 students per room. Delegations from Kryvyy Rig (his native city) and Kharkiv (my native city) happen to live close to each other, and we became friends, partially because of math, partially because we shared some other interests, including history.

Later, when Kolya entered Moscow State University and I entered Kharkiv State University, we stayed in touch, exchanging letters and occasionally meeting. Kolya had friends from Kharkiv who were students in Moscow, so he visited them a few times; I recall that he was often addressed by his friends as ``chudo'', which in Russian means ``miracle'', yet I did not ask why, so now we would never know ... He would often bring Western preprints or papers from Moscow, unavailable in Kharkiv, occasionally even his handwritten notes of some of the preprints or some of the talks, given in Moscow. This was extremely helpful for my studies and I greatly appreciated Kolya's help in that.

After I moved to Moscow in 1982 we started meeting more or less regularly, in particular because we both attended Sinai seminar in Moscow State. Often we would sit next to each other. Of course, almost all the time he listened to the talks and followed them, but in rare cases when the talks were just too complicated or somewhat distant from his mathematical interests he would pull a small textbook of the French and start reading it. So did I.

In the 1990-s we both moved to the United States and visited each other a couple of times before settling in Birmingham. My family visited Kolya's family in Atlanta where he was working in Georgia Tech and we had a great time swimming in the pool and discussing a variety of topics. Eventually we moved to Birmingham and even had our offices practically next to each other. His help at that time was invaluable, including giving me first driving lessons and helping us buy our first car.

In addition to math, Kolya had a multitude of talents. His love for traveling was legendary, it is hard to even list all of the places he went to, from Europe to Utah and Iceland. He learned how to fix cars and was doing it so well, that his family practically stopped visiting auto shops. He was doing all of that with two important features of his personality: quiet determination. I always admired him for that.

All of us have our own assessment as to how much we are all worth. The ratio of this and our true value varies from person to person. For many great people this ratio is close to one, yet Kolya was different, he was extremely modest, so for him it was almost zero. To me this sets him aside from many, many of us. Rest in peace, my dear friend, you will be sorely missed ...