# Svetlana Yakovlevna Jitomirskaya

### Quick Info

Kharkov, Ukraine

**Svetlana Jitomirskaya**is a Ukranian-born American mathematician who is known for her work on dynamical systems and mathematical physics.

### Biography

**Svetlana Jitomirskaya**was born into a Jewish family of mathematicians. Her father, Yakov I Zhitomirskii, and her mother, Valentina Mikhailovna Borok, were both professors of mathematics in Kharkov. Svetlana had an older brother Michail who was also a talented mathematician so her parents encouraged her to take an interest in subjects other than mathematics [3]:-

By the time I was born both of my parents were already full professors (in a society where this title commanded a lot of respect). My mother was certainly the most prominent female mathematician in the country. Having raised my older brother who was clearly gifted in mathematics, my parents thought that one more mathematician in our family would be too many. They encouraged me to get interested in the variety of things, and I started to lean seriously towards humanities. I wrote some prize-winning poetry and won some national high-school competitions in Russian literature. I planned a future studying (if not writing) Russian poetry.Let us quote Jitomirskaya's own description of how she ended up studying mathematics at university rather than humanities [3]:-

... at the age of 14, I fell in love with a boy I met during a summer vacation. He lived far away (in Moscow), and when, after about a year, his letters started to get shorter and more seldom, I realized that I had to go to Moscow. I was younger than my classmates, and only turned 16 after graduating from high school. The only way for me to go to Moscow was through entering Moscow State University which was an almost impossible task. Moscow State University was notorious for its limiting anti-Jewish quotas. Jewish applicants were subjected to extremely difficult questions during the oral exams to make sure that Jews did not comprise more than $\large\frac{1}{2}\normalsize$% of the student body. My chance was minuscule in any discipline, but mathematics seemed a much better bet than humanities due to a much smaller (by about a factor of three) competition and higher objectivity. As a result I spent my last year of high school preparing for that oral exam in mathematics. I think during that year I solved all the tricky elementary problems there were, and then some. I took each problem personally and attacked it as if my future happiness depended on whether I solved it or not. I was accepted at Moscow State University; however, I cannot view it as a personal victory as I would have liked. I did not get to show a fraction of my skills at that oral exam since I was not subjected to that "Jewish" treatment (perhaps, due to my parents' connections). However, something happened to me during that extensive preparation, as I started to love the process.Jitomirskaya went to Moscow to be close to Vladimir A Mandelshtam who [3]:-

... still recalls how he once had a one-day break from a month-long mandatory labour at a collective farm. He travelled all night to see me, only to have to wait for another three hours since I didn't want to miss a lecture on differential equations by Vladimir Igorevich Arnold. We did, however, get married almost as soon as I reached the legal age. Yet on the morning of my wedding, I sneaked out to listen to a lecture by Tom Spencer on his recently developed multi-scale analysis. Still, by the time I finished the undergraduate school, I was already a proud mother of a beautiful daughter, Olga.Jitomirskaya completed her undergraduate studies in 1987, graduating with distinction having written the thesis

*Localization problems in the kicked rotor model*. She continued to study at Moscow State University for her doctorate where her thesis advisor was Yakov Grigor'evich Sinai, who had also advised her during her undergraduate studies. She was appointed as a Researcher at the International Institute of Earthquake Prediction Theory and Mathematical Geophysics in Moscow in 1990, the Institute where her husband worked. Jitomirskaya was awarded a doctorate from Moscow State University in 1991 for her thesis

*Spectral and Statistical Properties of Lattice Hamiltonians*. She already had papers in print before completing her thesis, such as

*The singular spectrum and scale invariance for a Schrödinger operator with a binary almost periodic potential*(1990). Her husband Vladimir Mandelshtam was also awarded a doctorate in 1991 and in that year they had a joint paper published, namely

*The Bohm-Aharonov problem on a square lattice*. They gave the following summary of the results of this paper:-

We find an explicit expression for the Green function of the Schrödinger operator that describes the motion of an electron on a square lattice in a magnetic field with a flow that runs through a single cell. We prove that the nontrivial component of the Green function, equal to the contribution of the paths that wind around the singularity, is a compact operator. We also apply the method to find partition functions, over ensembles of paths on the lattice, that are connected with the winding number of the fixed point.In 1991 Jitomirskaya also published

*Singular spectral properties of a one-dimensional Schrödinger operator with almost periodic potential*,

*Spectral properties of one-dimensional almost periodic operators*and, with her husband Vladimir Mandelshtam,

*1D-quasiperiodic operators. Latent symmetries*. Also in 1991 with her husband, Alexander Belov and Yu E Lozovik, she published

*Anyon gas on a lattice*.

In [3] Jitomirskaya explains how she came to leave Russia and move to the United States. In 1990 Abel Klein, from the University of California at Irvine, visited Yakov Sinai in Moscow. Jitomirskaya was given the task of assisting him during his visit [3]:-

I guess I did well since he said I would be welcome to come to Irvine, to which invitation I did not pay much attention since I had no intention of leaving Moscow. Vladimir and I were expected to get our PhD's in 1991, and we had nice Moscow jobs organized for us by our advisors. Not that these jobs were paying much, but we cared even less back then. We had no idea about a world where people would actually apply for jobs. However, in 1991, Vladimir was offered an (unsolicited by him) postdoctoral position at the University of Southern California. We studied the map and realized Irvine was in Southern California too. We thought it would be fun to spend a year in California. I then happily informed Abel that I was ready to accept his "offer" from a year ago. That was in April 1991. Interestingly, he still managed to find some support for me for a year. My first job title at UCI was a "half-time lecturer". During the first couple of months on the job, I so impressed Abel with my knowledge of multi-scale analysis (remember my wedding day?) that he went on a crusade to keep me at UCI forever.Appointed as a Visiting Assistant Professor at the University of California at Irvine in 1992, Jitomirskaya published the joint paper

*Ising model in a quasiperiodic transverse field, percolation, and contact processes in quasiperiodic environments*with Abel Klein in the following year. She explained about quasiperiodic operators in [3]:-

I work on the spectral theory of Schrödinger operators. Up until the mid 70s the kind of spectra most people had in mind in the context of this theory were spectra occurring for periodic potentials and for atomic and molecular Hamiltonians. Then evidence started to accumulate that "exotic" spectral phenomena such as singular continuous, Cantor, and dense point spectrum do occur in mathematical models that are of considerable interest to theoretical physics. One area where such exotic phenomena are particularly abundant is quasiperiodic operators, and a large part of my research is centred around those. Quasiperiodic operators feature a fascinating competition between randomness (ergodicity) and order (periodicity), which is often resolved on a deep arithmetic level. The richness of the corresponding spectral theory can be breathtaking. Mathematically, the methods involved include a mixture of ergodic theory, dynamical systems, probability, functional and harmonic analysis. The interest in those models was enhanced by strong connections with some major discoveries in physics, such as integer quantum Hall effect, experimental quasicrystals, and Quantum chaos theory. Quasiperiodic operators provide central or important models for all three.After holding a Visiting Assistant Professorship for two years she became an Assistant Professor in 1994. In that year she was an invited lecturer at the XI International Congress of Mathematical Physics in Paris where she gave the lecture

*Everything about the almost Mathieu operator*. In 1996 she took leave from the University of California to spend nine months as a Visiting Assistant Professor at the California Institute of Technology. Also in 1996 she was awarded an A P Sloan Research Fellowship. Returning to the University of California at Irvine, she was promoted to Associate Professor in 1997 and to full professor in 2000.

Jitomirskaya has received prestigious awards for her outstanding contributions. She was invited to address the International Congress of Mathematicians at Beijing in August 2002, lecturing on

*Nonperturbative localization*. She summarised the lecture as follows:-

Study of fine spectral properties of quasiperiodic and similar discrete Schrödinger operators involves dealing with problems caused by small denominators, and until recently was only possible using perturbative methods, requiring certain small parameters and complicated KAM-type schemes. We review the recently developed nonperturbative methods for such study which lead to stronger results and are significantly simpler.In 2003 she received an award from the School of Physical Sciences at the University of California at Irvine for Outstanding Contributions to Undergraduate Education. In the following year she received a Distinguished Mid-Career Award for Research and then, in 2005, the Ruth Lyttle Satter Prize in Mathematics from the American Mathematical Society. The citation reads [1]:-

The Ruth Lyttle Satter Prize in Mathematics is awarded to Svetlana Jitomirskaya for her pioneering work on non-perturbative quasiperiodic localization, in particular for results in her papers (1) "Metal-insulator transition for the almost Mathieu operator", Ann. of Math. (1999) and (2) with J Bourgain, "Absolutely continuous spectrum for 1D quasiperiodicoperators", Invent. Math (2002). In her Annals paper, she developed a non-perturbative approach to quasiperiodic localization and solved the long-standing Aubry-Andre conjecture on the almost Mathieu operator. Her paper with Bourgain contains the first general non-perturbative result on the absolutely continuous spectrum.In her response she talked of the influence that many people had on her career [1]:-

I am very grateful to the American Mathematical Society for this honour and to the members of the Ruth Lyttle Satter Prize Committee for identifying and selecting me. It is humbling to be on the same list with the past recipients of this prize. I must say that I have never felt disadvantaged because of being a woman mathematician; in fact, the opposite is true to some extent. However, compared to most others, I did have a unique advantage: a fantastic role model from early on - my mother, Valentina Borok, who would have been much more deserving of such a prize than I am now, had it been available in her time. I see my receiving this prize as a special tribute to her memory. It is a pleasure to use this opportunity to say some thanks. It was great to be raised by my parents, and I was lucky to be a student of Yakov Sinai, who was both my undergraduate (since 1984) and graduate advisor. I am also very grateful to Abel Klein, whose support and encouragement in the postdoctoral years were crucial for my career. I had many wonderful collaborators, from each of whom I learned a lot. Three of those particularly stand out, as they have influenced my work in a major way. They are, in chronological (for me) order: Barry Simon, Yoram Last, and Jean Bourgain. Each of them has not only introduced new techniques to me and had a visible influence on my style and choice of topics but also provided a special inspiration and changed the way I think about mathematics. I am also grateful to Jean for entering, with his methods and ideas, the area of quasiperiodic operators. That certainly brought this field to a new level and changed how it is perceived by many others. Finally, special thanks go to my family, as I wouldn't have accomplished a fraction of what I did without patience, support, and a lot of sacrifice on their part.In January 2006 Jitomirskaya gave a plenary address to the Joint American Mathematical Society/Mathematical Association of America Annual Meeting in San Antonio and in August of that year she gave a plenary address to the XV International Congress of Mathematical Physics in Rio de Janeiro.

### References (show)

- 2005 Satter Prize,
*Notices Amer. Math. Soc.***52**(4) (2005), 447-448. - L Bruce, UCI professor honoured for mathematics research,
*Los Angeles Times*(9 January 2005). - S Jitomirskaya, Biography,
*UCI Academic Senate's Web site*. http://www.senate.uci.edu/

### Additional Resources (show)

Other websites about Svetlana Jitomirskaya:

### Honours (show)

Honours awarded to Svetlana Jitomirskaya

Written by J J O'Connor and E F Robertson

Last Update February 2010

Last Update February 2010