Svetlana Jitomirskaya was awarded a Sloan Fellowship by the Alfred P Sloan Foundation. The Sloan Research Fellowship Program recognises and rewards outstanding early-career faculty who have the potential to revolutionise their fields of study.

Svetlana Jitomirskaya was an Invited Speaker in the Section 13, Mathematical Physics, at the 2002 International Congress of Mathematicians in Beijing. She gave the talk Nonperturbative localization. It has the following:-

Summary.

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. Numerous applications, mainly due to J Bourgain, M Goldstein, W Schlag, and the author, are also discussed.

Awarded yearly to one faculty member from each department who has excelled in undergraduate education. The 2002-2003 awards were made to Ramesh Arasasinghm, Francois Primeau, Svetlana Jitomirskaya, Steven Ruden.

The recipients of the Distinguished Mid-Career Faculty Award for Research must be members of the Academic Senate from the rank of Associate Professor through Professor V when nominated, who have made outstanding contributions in their discipline through their research.

5.1. The American Mathematical Society awarded Svetlana Jitomirskaya the Ruth Lyttle Satter Prize in Mathematics:

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.

5.2. 2005 Satter Prize, Notices of the American Mathematical Society.

The 2005 Ruth Lyttle Satter Prize in Mathematics was awarded at the 111th Annual Meeting of the AMS in Atlanta in January 2005.

The Satter Prize is awarded every two years to recognize an outstanding contribution to mathematics research by a woman in the previous five years. Established in 1990 with funds donated by Joan S. Birman, the prize honours the memory of Birman's sister, Ruth Lyttle Satter. Satter earned a bachelor's degree in mathematics and then joined the research staff at AT&T Bell Laboratories during World War II. After raising a family, she received a Ph.D. in botany at the age of forty-three from the University of Connecticut at Storrs, where she later became a faculty member. Her research on the biological clocks in plants earned her recognition in the U.S. and abroad. Birman requested that the prize be established to honour her sister's commitment to research and to encourage women in science. The prize carries a cash award of $5,000.

The Satter Prize is awarded by the AMS Council acting on the recommendation of a selection committee. For the 2005 prize the members of the selection committee were: Karen E Smith, Jean E Taylor (chair), and Chuu-Lian Terng.

Biographical Sketch

Svetlana Jitomirskaya was born on June 4, 1966, and raised in Kharkov, Ukraine, in a family of two accomplished mathematicians (later three, counting her older brother). She received her undergraduate degree (1987) and Ph.D. (1991) from Moscow State University. Since 1990 she has held a research position at the Institute for Earthquake Prediction Theory in Moscow. In 1991 she came with her family to southern California. She was employed by the University of California, Irvine, as a part-time lecturer (1991-92) and rose through the ranks to become a visiting assistant professor (1992-94) and then a regular faculty member (since 1994). She took a leave from UCI to spend nine months at Caltech (1996). She was a Sloan Fellow (1996-2000) and a speaker at the International Congress of Mathematicians in 2002. She is married and has three children ranging in age from one to seventeen.

Response

I am very grateful to the AMS 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.

This Fellowship allowed Jitomirskaya to attend the meeting 'Mathematics and Physics of Anderson Localization: 50 Years After' (4 July to 9 December 2008) at the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge. She was an invited speaker in the concluding conference of the programme on localization theory.

The title of Chancellor's Fellow is intended for faculty with tenure whose recent achievements in scholarship evidence extraordinary promise for world-class contributions to knowledge, and whose pattern of contributions evidences strong trajectory to additional/further distinctions.

While holding the Simons Fellowship 2014-2015, Svetlana Jitomirskaya carried out an impressive research programme. The papers which came out of this programme include:

8.1. Svetlana Jitomirskaya and Rajinder Mavi, Dynamical bounds for quasiperiodic Schrödinger operators with rough potentials (2016).

Abstract.

We establish localization type dynamical bounds as a corollary of positive Lyapunov exponents for general operators with one-frequency quasiperiodic potentials defined by piecewise Hölder functions. This, in particular, extends some results previously known only for trigonometric polynomials to the case of surprisingly low regularity. On the technical level, an important part of the argument is an extension of uniform uppersemicontinuity to cocycles with discontinuities, a result of independent interest.

8.2. C A Marx and S Jitomirskaya, Dynamics and Spectral Theory of Quasi-Periodic Schrödinger-Type Operators (2016).

From the Introduction.

Quasi-periodic Schrödinger-type operators naturally arise in solid state physics, describing the influence of an external magnetic field on the electrons of a crystal. ... The intention of this article is to survey the theory of quasi-periodic Schrödinger- type operators attaining this "global" view-point with an emphasis on dynamical aspects of the spectral theory of such operators.

8.3. Svetlana Jitomirskaya and Ilya Kachkovskiy, L2-Reducibility and Localization for Quasiperiodic Operators.

Abstract.

We give a simple argument that if a quasiperiodic multi-frequency Schrödinger cocycle is reducible to a constant rotation for almost all energies with respect to the density of states measure, then the spectrum of the dual operator is purely point for Lebesgue almost all values of the ergodic parameter. The result holds in the L2 setting provided, in addition, that the conjugation preserves the fibered rotation number. Corollaries include localization for (long-range) 1D analytic potentials with dual ac spectrum and Diophantine frequency as well as a new result on multidimensional localization.

The Authors write:

We are grateful to the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Periodic and Ergodic Spectral Problems where this paper was completed.

8.4. A Avila, S Jitomirskaya and C A Marx, Spectral theory of extended Harper's model and a question by Erdös and Szekeres (2017).

From the Abstract.

The extended Harper's model, proposed by D J Thouless in 1983, generalises the famous almost Mathieu operator, allowing for a wider range of lattice geometries (parametrised by three coupling parameters) by permitting 2D electrons to hop to both nearest and next nearest neighbouring lattice sites, while still exhibiting its characteristic symmetry (Aubry-André duality). Previous understanding of the spectral theory of this model was restricted to two dual regions of the parameter space, one of which is characterised by the positivity of the Lyapunov exponent. In this paper, we complete the picture with a description of the spectral measures over the entire remaining (self-dual) region, for all irrational values of the frequency parameter (the magnetic flux in the model).

The award is a recognition of Svetlana Jitomirskaya's outstanding work in mentoring undergraduate students engaged in research.

Svetlana Jitomirskaya was appointed as Aisenstadt Chair and was at the Centre de Recherches Mathématique, University of Montreal 12-16 November 2018. Jitomirskaya's lectures were a part of the workshop on Spectral Theory of Quasi-Periodic and Random Operators (12-16 November). The first two lectures took place on 12 November and the third one on 13 November. Jitomirskaya's lectures were held on 14, 15 and 16 November 2018.

Lecture 1. Anti-concentration bounds for determinants and Anderson localization.

Abstract. We present yet another proof of Anderson localization for the Anderson model.

Lecture 2. Localization and delocalization for multidimensional quasiperiodic operators.

Abstract. We discuss recent progress on localization and delocalization for quasiperiodic operators, including the case of interacting particles. The talk is based on papers with Liu and Shi, Bourgain and Parnovsky, and Bourgain and Kachkovskiy.

Lecture 3. Sharp arithmetic transitions for 1D quasiperiodic operators.

Abstract. A very captivating question in solid state physics is to determine/understand the hierarchical structure of spectral features of operators describing 2D Bloch electrons in perpendicular magnetic fields, as related to the continued fraction expansion of the magnetic flux. In particular, the hierarchical behaviour of the eigenfunctions of the almost Mathieu operators, despite significant numerical studies and even a discovery of Bethe Ansatz solutions has remained an important open challenge even at the physics level. I will present a complete solution of this problem in the exponential sense throughout the entire localization regime. Namely, I will describe the continued fraction driven hierarchy of local maxima, and a universal (also continued fraction expansion dependent) function that determines local behaviour of all eigenfunctions around each maximum, thus giving a complete and precise description of the hierarchical structure. In the regime of Diophantine frequencies and phase resonances there is another universal function that governs the behaviour around the local maxima, and a reflective-hierarchical structure of those, phenomena not even described in the physics literature. These results lead also to the proof of sharp arithmetic transitions between pure point and singular continuous spectrum, in both frequency and phase, as conjectured since 1994. This part of the talk is based on the papers joint with W Liu. Within the singular continuous regime, it is natural to look for further, dimensional transitions. I will present a sharp arithmetic transition result in this regard that holds for the entire class of analytic quasiperiodic potentials, based on the joint work with S Zhang.

11.1. University of California Irvine News (18 April 2018).

Svetlana Jitomirskaya, professor of mathematics at the University of California, Irvine, has been named a fellow by the American Academy of Arts & Sciences. The 238th class of new members includes the world's most accomplished scholars, scientists, writers and artists, as well as civic, business and philanthropic leaders.

Jitomirskaya was born in Ukraine and earned her bachelor's, master's and doctoral degrees at Moscow State University. She came to the University of California Irvine in 1991 as a part-time lecturer and was appointed to a full professorship in 2000.

"Professor Jitomirskaya exemplifies the innovation and excellence that are the hallmarks of those elected to the American Academy of Arts & Sciences," said Enrique Lavernia, UCI provost and executive vice chancellor. "This is yet another demonstration of the tremendous strength of the University of California Irvine faculty."

Jitomirskaya is a leading expert in the interplay between mathematical physics and dynamical systems, an area of math used to describe the behaviour of an item over time. Her work involves the study of equations associated with quantum mechanics - the field in physics describing nature at the atomic and subatomic particle levels - and related mathematical inquiry.

The University of California Irvine now has 36 American Academy of Arts & Sciences members. Jitomirskaya will be officially inducted along with more than 200 other new members in an October ceremony in Cambridge, Massachusetts.

"I am honoured and pleasantly surprised to have been elected as a member of the American Academy of Arts & Sciences," Jitomirskaya said. "I didn't even know I was being considered. Having started at the University of California Irvine as a fresh PhD, I am especially proud to now be joining my University of California Irvine colleagues who are Academy fellows."

Her numerous distinctions include the Ruth Lyttle Satter Prize in Mathematics from the American Mathematical Society, an Aisenstadt Chair at Montreal's Center de Recherches Mathematiques, a Sloan Research Fellowship, a Distinguished Mid-Career Faculty Award for Research from the University of California Irvine, a Simons Fellowship and a University of California Irvine Chancellor's Fellowship.

Founded in 1780, the American Academy of Arts & Sciences is one of the country's oldest learned societies and independent policy research centres, convening elected members from the academic, business and government sectors to respond to challenges facing the nation and the world.

12.1. The American Physical Society and the American Institute of Physics awarded Svetlana Jitomirskaya the 2020 Dannie Heineman Prize for Mathematical Physics.

Citation:

"For work on the spectral theory of almost-periodic Schrödinger operators and related questions in dynamical systems. In particular, for her role in the solution of the Ten Martini problem, concerning the Cantor set nature of the spectrum of all almost Mathieu operators and in the development of the fundamental mathematical aspects of the localization and metal-insulator transition phenomena."

Background:

Svetlana Jitomirskaya received her undergraduate degree in 1987 and Ph.D. in 1991, both in mathematics, from Moscow State University. Other than spending about half a year in 1996 visiting Barry Simon at California Institute of Technology, she has been professionally associated throughout her post Ph.D. scientific career with the University of California Irvine, where she started as a part-time lecturer in 1991 and is now a Distinguished Professor of Mathematics. She is a member of the International Association of Mathematical Physics (IAMP), where she has served as the vice president in 2012-14. She is a recipient of Sloan and Simons Foundation Fellowships and is a member of the American Academy of Arts and Sciences. She has won the American Mathematical Society Satter Prize in 2005. Jitomirskaya's main accomplishments are in the area of quasiperiodic operators, where she is best known for developing the first nonperturbative methods of study of small denominators, that have influenced the future development of this field. She has also been involved, by herself and with collaborators, in the solution of several long-standing problems related to the almost Mathieu operators, also known as Harper's, Aubry-Andre, or Azbel-Hofstadter model.

12.2. University of California Irvine News (22 October 2019).

Svetlana Jitomirskaya, Distinguished Professor of mathematics at the University of California, Irvine, has been named the 2020 winner of the Dannie Heineman Prize for Mathematical Physics. She is only the second woman to receive the annual prize - and the first to receive it alone, not jointly.

The citation says Jitomirskaya was recognised "for work on the spectral theory of almost-periodic Schrödinger operators and related questions in dynamical systems. In particular, for her role in the solution of the Ten Martini problem, concerning the Cantor set nature of the spectrum of all almost Mathieu operators, and in the development of the fundamental mathematical aspects of the localization and metal-insulator transition phenomena."

Established in 1959 by the Heineman Foundation for Research, Educational, Charitable and Scientific Purposes Inc., the prize is administered jointly by the American Physical Society and the American Institute of Physics. It was first awarded to Murray Gell-Mann, and other recipients include Stephen Hawking (1976), Edward Witten (1998) and Giorgio Parisi (2005).

"To say I am honoured and humbled to receive this prize - to now be on the same list with so many of my absolute heroes - is a huge understatement," Jitomirskaya said. "The prize is relatively rarely given to pure mathematicians like me; I see it as an indication of the physics community's growing interest in the questions I've been working on - and perhaps math in general."

The Journal of Mathematical Physics defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories." An early example would be Sir Isaac Newton's invention of calculus in order to solve physics problems, such as explaining Kepler's laws of planetary motion. Some of the most significant modern advances have been in classical mechanics, quantum theory, special and general relativity, and statistical mechanics.

Jitomirskaya's main accomplishments involve quasiperiodic operators. She is best known for creating the first nonperturbative methods of studying small denominators, influencing ongoing developments in this field. She has also solved - individually and collaboratively - several long-standing problems related to almost Mathieu operators.

"The work I do that this prize recognises is in a rather narrow area, so it hasn't had a fraction of the impact the work of some of my predecessors has had," she said. "However, it did have a considerable impact in that area, and the field itself is getting more and more attention because of its relationship to the science of quantum materials."

Jitomirskaya attended Russia's Moscow State University, earning an undergraduate degree in 1987 and a Ph.D. in 1991, both in mathematics. She became a part-time lecturer at UCI in 1991 and has been professionally affiliated with the university ever since - her most extended leave being about half a year in 1996 when she was a visiting assistant professor at the California Institute of Technology with Barry Simon, 2018 winner of the Dannie Heineman Prize.

She is a member of the International Association of Mathematical Physics, serving as vice president in 2012-14, and was inducted into the American Academy of Arts and Sciences in 2018. Jitomirskaya is a recipient of fellowships from the Alfred P. Sloan Foundation and the Simons Foundation and was awarded the American Mathematical Society's Ruth Lyttle Satter Prize in 2005. She has also held an Aisenstadt Chair at Montreal's Centre de Recherches Mathematiques and received a Distinguished Mid-Career Faculty Award for Research from UCI and a UCI Chancellor's Fellowship.

"Congratulations to Professor Jitomirskaya on this outstanding accomplishment," said Enrique Lavernia, UCI provost and executive vice chancellor. "Being awarded the Dannie Heineman Prize for Mathematical Physics is indeed an exceptional honour and a recognition of her outstanding work in the field."

12.3. University of California Irvine News (22 October 2019).

"To say I am honoured and humbled to receive this prize - to now be on the same list with so many of my absolute heroes - is a huge understatement," Jitomirskaya said in this 22 October 2022 University of California Irvine news release. "The prize is relatively rarely given to pure mathematicians like me; I see it as an indication of the physics community's growing interest in the questions I've been working on - and perhaps math in general."

The prize citation shows the extremely theoretical scope of her work:

"For work on the spectral theory of almost-periodic Schrödinger operators and related questions in dynamical systems. In particular, for her role in the solution of the Ten Martini problem, concerning the Cantor set nature of the spectrum of all almost Mathieu operators and in the development of the fundamental mathematical aspects of the localization and metal-insulator transition phenomena."

For help in translating all that, I asked Professor Alfonso Agnew, who chairs the Mathematics Department at Cal State Fullerton, for his insight. Though this kind of math isn't his specialty, and he had to sacrifice some accuracy to provide an explanation in less than 100 pages, he offered the following:

1. Many problems in science can be explained with non-relativistic quantum mechanics (QM). QM describes the physics of the small (say, atomic scale and below) where the bodies involved are neither too massive, too energetic, nor moving too fast (relativity would then need to be taken into account). One formalism for doing QM uses the celebrated Schrödinger equation, which involves the use of "Schrödinger operators" to describe the energy content of the system under consideration. Different systems require different Schrödinger operators for their description. Thus, it is helpful to be able to understand as much as possible about various families of Schrödinger operators, since then we understand more about the physical systems that they are modelling, which in turn informs laboratory activity, technology and so forth. One family of operators are the "almost periodic Schrödinger operators," that tend to come up often enough in applications to warrant special attention.

2. One can tell quite a bit about an operator by studying the geometric (or topological) properties of its "spectrum"- which is in some sense its geometric "skeleton" or DNA. The term "spectrum" is directly related to the physical spectrum of light emitted by atoms, which can be predicted by the mathematical spectrum of the operators describing the atom. This goes back to studies in the late 19th/early 20th century.

As for the "Ten Martini Problem" mentioned in the citation, that was one of 15 questions on quantum operators (mathematical representations of energy, position, things like that) first posed by the mathematician Barry Simon. The name itself comes from the reward the mathematician Mark Kac offered to whoever solved it. Sadly, Kac died in 1984, so he never paid up.

Anyway, if you're really curious, click here to read the 2009 paper "The Ten Martini Problem" published in Annals of Mathematics that Jitomirskaya co-wrote with the Brazilian mathematician Arthur Avila. In 2014, Avila received the Fields Medal, an honour awarded to mathematicians under 40, partially based on this work.

"The work I do that this prize recognises is in a rather narrow area, so it hasn't had a fraction of the impact the work of some of my predecessors has had," Jitomirskaya said in the 22 October 2022 University of California Irvine news release. "However, it did have a considerable impact in that area, and the field itself is getting more and more attention because of its relationship to the science of quantum materials."

Jitomirskaya was born in Kharkov, Ukraine and got her PhD in mathematics from Moscow State University. She has taught at University of California Irvine since 1991.

13.1. The Simons Foundation awards fellowships to mathematicians and theoretical physicists with remarkable bodies of work. In December, mathematics Professor Svetlana Jitomirskaya discovered she would get a 2020 Simons fellowship. Jitomirskaya's fellowship award totals $660,000, and the windfall will fund a part of her sabbatical for the upcoming academic year. Before, she was only going to take one quarter off for the sabbatical - but now she can use the entire year to further her research, which currently focuses on the mathematics of quantum materials.

This is the second Simons Award for Jitomirskaya, who received the award for the first time in 2014 ....
"I had robust travel plans for my sabbatical," says Jitomirskaya. But with the coronavirus epidemic sweeping the world, she had to cancel some of her work trips. The one silver lining is that she now has more time to focus on her research projects. "I'm sure I'll be producing a lot more," she says.

13.2. University of California Irvine News (1 December 2021).

The award will give the math professor resources to continue her research into the properties of two-dimensional materials.

The Simons Foundation has awarded a $5 million targeted grant for a project called "Moiré Materials Magic" to a group of physicists and mathematicians that includes Distinguished Professor Svetlana Jitomirskaya of the UCI Department of Mathematics. The project centres on the unusual physical properties that occur when two-dimensional layers of crystals that are only one atom or one molecule thick - and with tiny differences in the arrangement of the atoms and molecules in the layers - are overlaid and create so-called moiré patterns. Moiré materials, Jitomirskaya explained, may potentially realise new fundamental physics as well as find valuable applications. Mathematically, they feature a new type of so-called "quasiperiodic order," wherein moiré materials have "longer and longer pieces of larger and larger structures repeated," said Jitomirskaya, who's the world's leading expert on the topic. "The emergence of moiré materials highlights new opportunities to make math progress by looking to nature, and to make physics progress by learning from math," said Jitomirskaya. "While the key objective of the overall project is the latter, to me it is equally exciting that moiré materials have the potential to lead to fundamentally new mathematical objects." Other Moiré Materials Magic grantees are at UC Berkeley, Harvard University, University of Minnesota, and the University of Texas at Austin.

14.1. The recipients of the Distinguished Senior Faculty Award for Research must be members of the Academic Senate at the rank of Professor VI or above when nominated, who have made a significant contribution through research that has had a major influence on the discipline, either through a career-long record of contributions, or through an influential/germinal contribution.

Svetlana Jitomirskaya. Distinguished Professor, Department of Mathematics.

Presentation Title: The Hofstadter's Butterfly: From Playing with Numbers to Studying Quantum Materials.

14.2. University of California Irvine News (1 September 2021).

The UC Irvine Academic Senate recently awarded Professor Svetlana Jitomirskaya of the UCI Department of Mathematics their Distinguished Senior Faculty Award for Research. The designation comes in the wake of a robust research career that focuses on mathematical physics and dynamical systems, and which is replete with honours. In 2005 Jitomirskaya received the American Mathematical Society's Satter Prize, in 2018 she became a fellow of the American Academy of Arts and Sciences, in 2019 she was awarded the American Physical Society and American Institute of Physics Dannie Heineman Prize in Mathematical Physics, and last year was selected to give a plenary talk at the International Congress of Mathematics - a meeting often called the Olympics of mathematics. She's also the recipient of two recent awards from the Simons Foundation - a foundation dedicated to the advancement of mathematics and the sciences. A targeted grant will support research into two-dimensional materials, while the other, a fellowship, gave Jitomirskaya funding to go on a sixth month-long sabbatical in 2020. "I am tremendously honoured to receive this award. It is truly humbling for me to look at the list of the past recipients, going back to Sherry Rowland in 1977," Jitomirskaya said. "All the more so because the only other mathematician previously so honoured was Don Saari in 2004, a man who revolutionised not only a big area of math, but also economics and other fields. Being on this list along with my heroes such as Don is a great distinction and a big responsibility."

15.1. University of California Irvine News (18 June 2021).

Professor Svetlana Jitomirskaya of the UCI Department of Mathematics will, come July 2022, give a plenary talk at the International Congress of Mathematics (ICM). Receiving an invitation to give one of the 20 plenary lectures to the thousands of ICM participants is a special honour in the mathematics profession, and Jitomirskaya will be the first-ever plenary ICM speaker with UCI affiliation. Often dubbed the Olympics of mathematics, the ICM happens once every four years, and it encompasses all areas of mathematics, from pure to applied, as well as computer science, with top prizes in mathematics and computer science awarded during the meeting. ICM also features talks in 19 sections - about 200 at each Congress - and receiving an invitation to give one of those talks is another hall-of-fame-level honour, one Jitomirskaya received in 2002. Other UCI faculty who gave ICM sectional talks are Richard Schoen in 1983, Matthew Foreman in 1998, Roman Vershynin in 2010, as well as professors emeriti Ronald Stern in 1998, Peter Li and Karl Rubin in 2002, and Chuu-Lian Terng in 2006. Schoen gave plenary talks in 1986 and 2010 when he was a faculty member at UC San Diego and then Stanford University. Jitomirskaya, who researches analysis problems motivated by quantum physics, expects the subject of her talk to orbit around arithmetic spectral transitions.

15.2. Svetlana Jitomirskaya gave the Plenary talk with title Small denominators and multiplicative Jensen's formula.

Abstract. Small denominator problems appear in various areas of analysis, PDE, and dynamical systems, including spectral theory of quasiperiodic Schrödinger operators, non-linear Schrödinger equations, and non-linear wave equations. These problems have traditionally been approached by KAM-type constructions. We will discuss the new methods, originally developed in the spectral theory of quasiperiodic Schrödinger operators, that are both considerably simpler and lead to results completely unattainable through KAM techniques. For one-dimensional quasiperiodic operators, these methods have enabled precise treatment of various types of resonances and their combinations, leading to proofs of sharp (arithmetic) spectral transitions, the ten martini problem, and the discovery of universal hierarchical structures of eigenfunctions. The related theory of the dynamics of corresponding linear cocycles leads to a surprising extension of the classical Jensen's formula.

16.1. University of California Irvine News (4 May 2022).

Two University of California, Irvine researchers have been elected to the National Academy of Sciences, one of the world's most respected scientific organisations. Svetlana Jitomirskaya, Distinguished Professor of mathematics, and Krzysztof Palczewski, Distinguished Professor of ophthalmology, are among 120 U.S.-based members chosen this year.

"Congratulations to Svetlana Jitomirskaya and Krzysztof Palczewski on this exceptional achievement of being elected to the National Academy of Sciences," said Hal Stern, provost and executive vice chancellor. "Their recognition serves as another indication of the innovative contributions and academic excellence of the University of California Irvine faculty."

Ukraine-born Jitomirskaya - after earning her bachelor's, master's and doctoral degrees at Moscow State University - came to University of California Irvine in 1991as a part-time lecturer. She was appointed to a full professorship in 2000. Her work involves the study of equations associated with quantum mechanics - the field in physics describing nature at the atomic and subatomic particle levels - and related mathematical inquiry.

A member of the American Academy of Arts & Sciences, she won the American Mathematical Society Ruth Lyttle Satter Prize in 2005 and the American Physical Society and American Institute of Physics Dannie Heineman Prize for Mathematical Physics in 2020.

"I am honoured and pleasantly surprised to have been elected to the National Academy of Sciences," Jitomirskaya said. "Having started at the University of California Irvine as a fresh Ph.D., I am especially proud to now be joining my University of California Irvine colleagues who are members of the academy."

The first ever Olga Alexandrovna Ladyzhenskaya Prize, celebrating the life of the noted Russian mathematician, honours outstanding contributions to the mathematics underlying previously unsolved problems in quantum physics.

The inaugural Ladyzhenskaya Prize in Mathematical Physics was awarded to Professor Svetlana Jitomirskaya "for her seminal and deep contributions to the spectral theory of almost periodic Schrödinger operators" in a session of the International Congress of Mathematicians jointly organised by the World Meeting for Women in Mathematics and the Probability and Mathematical Physics conference in Helsinki on 2 July 2022.

18.1. Nankai University News (25 August 2023).

Svetlana Jitomirskaya, a fellow of the American Academy of Arts & Sciences, a fellow of the National Academy of Sciences, and a professor at the University of California, Irvine, gave an academic report entitled "Treating small denominators without KAM" at the academic lecture hall of Fan Sun Building under the Chen Institute of Mathematics' "Chern Lecture". Professor Chen Yulu, President of Nankai University, met with Svetlana Jitomirskaya after the lecture session and exchanged views on scientific research, discipline construction and other topics.

Over 200 faculty and students from Nankai University, Tiangong University and Tianjin University of Finance and Economics listened to the wonderful report delivered by Svetlana Jitomirskaya.

In the report, Svetlana Jitomirskaya first talked about mathematics in Newton's time, and believed that Newton's main mathematical discovery was the Taylor Series.

Subsequently, Svetlana Jitomirskaya reviewed the research history of celestial mechanics systems and talked about the problem of small denominators.

She also gave basic examples of the role of small denominators.

At the end of the report, Svetlana Jitomirskaya introduced the quasi-periodic Schrödinger operator. A small denominator problem similar to the macroscopic celestial mechanics system also occurs in this basic model of quantum mechanics. Many mathematicians and physicists have made important contributions in this regard.

After the keynote speech, Svetlana Jitomirskaya interacted with the teachers and students present, answered their questions, and had a group photo with them.

Background.

Svetlana Jitomirskaya is a professor at the University of California, Irvine, a fellow of the American Academy of Arts & Sciences, and a fellow of the National Academy of Sciences. She was a Plenary Speaker at the 2022 International Congress of Mathematicians. In 2020, she received the Dannie Heineman Prize for Mathematical Physics, becoming the first female scientist to independently receive this honour since 1959. She received the first Ladyzhenskaya Prize in Mathematical Physics in 2022 in recognition of her contributions to the study of Schrödinger operator spectrum theory.

The "Chern Lectures" is the highest-level series of lectures organised by the Chern Institute of Mathematics, and is also set up in honour of Mr Chern Shiing-shen, a master of mathematics. It aims to spread scientific ideas, promote the development of science, particularly mathematics, and enable mathematical science to play a greater role in social and economic development.

19.1. University of California Irvine News (8 November 2023).

Svetlana Jitomirskaya, University of California Irvine adjunct professor of mathematics, has received a 2023 Barry Prize from the American Academy of Sciences and Letters in recognition of intellectual excellence and courage. The prize was awarded recently by academy President Donald W Landry of Columbia University and Chairman of the Board Sanjeev R Kulkarni of Princeton University in a ceremony at the Library of Congress in Washington, D.C. The Barry Prize for Distinguished Intellectual Achievement is the academy's premier award to promote excellence in scholarship. This annual prize, open to scholars across diverse fields and disciplines, honours those whose work has "made outstanding contributions to humanity's knowledge, appreciation and cultivation of the good, the true and the beautiful," according to the academy. Recipients are nominated by academy members and appointed by the board of directors. Winners of the Barry Prize receive $50,000 and become members of the academy. In their award citation, academy officials said: "Svetlana Jitomirskaya has done pioneering work in an area of mathematical physics stemming from the quantum mechanics of two-dimensional materials and lying at the fertile interplay of many exciting branches of modern mathematics. In the course of this work, she developed novel methods and new ideas to some of the central problems in the field, transforming the way mathematicians look at these problems and attracting a new generation of young researchers. The academy honours Dr Jitomirskaya for her distinguished scientific contributions and intense dedication to preserving the highest standards of academic excellence." The American Academy of Sciences and Letters promotes scholarship and honours outstanding achievement in the arts, sciences and learned professions. It supports learning by encouraging the exchange of ideas within academia and in society at large; by sponsoring occasions for scholarly interaction; and by providing platforms for the presentation and dissemination of scholarship in the humanities, social sciences, natural sciences, mathematics and engineering. Jitomirskaya was one of 10 Barry Prize recipients this year and the only one representing a public university. While continuing as an adjunct professor at the University of California Irvine, Jitomirskaya began serving this fall as the Richard and Rhonda Goldman Distinguished Chair and Professor of mathematics at University of California Berkeley.

19.2. Berkeley mathematician Svetlana Jitomirskaya awarded inaugural Barry Prize.

Svetlana Jitomirskaya, UC Berkeley professor of mathematics, has been awarded the American Academy of Sciences and Letters' inaugural 2023 Barry Prize for Distinguished Intellectual Achievement. The Barry Prize is the Academy's foremost program designed to recognise and celebrate "outstanding contributions to humanity's knowledge, appreciation, and cultivation of the good, the true, and the beautiful." The annual award is open to scholars from diverse fields and disciplines, and recipients are honoured with a $50,000 cash award and become members of the academy. Jitomirskaya and nine other scholars were presented with the Academy's Barry Prize during a ceremony at the Library of Congress in Washington, D.C. on 8 November.

Dr Jitomirskaya's award citation for the Barry Prize recognised her innovative contributions to the field of mathematics. "Svetlana Jitomirskaya has done pioneering work in an area of mathematical physics stemming from the quantum mechanics of two-dimensional materials and lying at the fertile interplay of many exciting branches of modern mathematics. In the course of this work, she developed novel methods and new ideas for some of the central problems in the field, transforming the way mathematicians look at these problems and attracting a new generation of young researchers. The Academy honours Dr Jitomirskaya for her distinguished scientific contributions and intense dedication to preserving the highest standards of academic excellence."

"I am deeply humbled and profoundly honoured to have been chosen as a recipient of the inaugural Barry Prize, alongside an extraordinary group of individuals," said Jitomirskaya. "I am especially inspired by the Academy's mission to promote not only excellence in scholarship, but also independence of mind, and intellectual courage. I hope the AASL will play a pivotal role in bolstering and upholding our society's commitment to the highest standards of honest inquiry and academic excellence."