I was born in Kharkov, Ukraine, in a family of two accomplished mathematicians. By the time I was born both of my parents were already full professors (in a society where this title commanded a lot ofrespect). My mother was certainly the most prominent female mathematician in the country. Having raised my older brother who was clearly gifted in math, 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.
This had changed when at the age of 14 I fell in love with a boy I met during 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. MSU 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 do not comprise more than 1/2 % 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 math. 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 MSU; 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.
My undergraduate years at MSU were spent in some sort of competition between the reason I came to Moscow and my newly discovered passion. Getting into MSU being a miracle as it was, I felt it was important to fully use its fantastic resources. When my husband is upset with me, he still recalls how he once had a one-day break from a month-long mandatory labor at a collective farm. He traveled 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 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. In the subsequent years the competition has turned into more of a collaboration. I am now an even prouder mother of Olga, Yelena, and Andrei. I have had my share of good times and bad times in math, and my family has been extremely supportive and understanding through both.
My undergraduate (and also graduate) advisor was Yakov Sinai, one of the very top people, worldwide, in dynamical systems. In those years he didn't travel much, and many scientists from around the world came to visit him. It was almost impossible for foreigners to be in Moscowwithout a help from the locals as everything was exclusively in Russian and the population generally did not speak English. To each of his many guests Sinai would assign a student in a related area, to help the guest around. One of my assignments in early 1990 was AbelKlein. 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 postdoc at USC. 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. So far he is succeeding. I was a VAP in 92-94 and a regular faculty since 94. Thus, my entire post-graduate career and a large part of my growing up happened at UCI. Abel has been a great friend and mentor during all these years.
I work on the spectral theory of Schroedinger 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 centered 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. I was lucky to have made some contributions to this field.