David Kazhdan was awarded the Rothschild Prize in 2010. This is an Israeli prize designed to support the advancement of science and the humanities in Israel.

Israeli Education Minister Gideon Saar announced on 23 January 2012 that the 2012 Israel Prize for Mathematics and Computer Science would go to Prof David Kazhdan of the Hebrew University of Jerusalem. A Professor of Mathematics at the Hebrew University's Einstein Institute of Mathematics, Kazhdan received the prize for his important contributions to group theory research.

Established in 1953, the Israel Prize is awarded to Israeli citizens or organisations that have displayed excellence in their field or contributed significantly to Israeli culture.

The award committee, headed by computer scientist and Israel Prize recipient Prof Michael Rabin, called Prof Kazhdan "one of the world's leading mathematicians in recent decades" and noted his important contributions to group theory, a cornerstone of mathematics with applications in fields such as quantum theory and computer science.

Prof Kazhdan received the award on 26 April at an Israel Independence Day ceremony in Jerusalem attended by Israel's president, prime minister, Supreme Court president and other national leaders.

Since 2002 Prof Kazhdan has been a Professor of Mathematics at the Hebrew University's Einstein Institute of Mathematics. Born in Moscow in 1946, he studied and conducted research at Moscow University before moving in 1975 to the United States, where he taught at Harvard University. Professor Kazhdan held a MacArthur Fellowship from 1990 to 1995, was appointed to the American Academy of Sciences in 1990, was made a Fellow of the Israeli National Academy of Sciences and Humanities in 2006, became a member of the American Academy of Arts and Sciences in 2009, and won the Rothschild Prize in Mathematics in 2010.

The Einstein Institute of Mathematics is part of the Hebrew University's Faculty of Science, which encompasses research institutes and teaching departments in the major fields of Mathematics, Physics, Chemistry, Life Sciences and Earth Sciences, together with a Science Teaching Unit and a School of Engineering and Computer Science. Members of the Faculty have won the Israel Prize, Nobel Prize, Fields Medal, Fermat Prize in Mathematics, Turing Award, Wolf Prize and Rothschild Prize, among others.

The EMET Prize is awarded annually for excellence in academic and professional achievements that have far-reaching influence and significant contribution to society. The Prizes, in a total amount of one million Dollars, are sponsored by the A.M.N. Foundation for the Advancement of Science, Art and Culture in Israel, under the auspices of and in cooperation with the Prime Minister of Israel. The Prizes are awarded annually in the following categories: The Exact Sciences, Life Sciences, Social Sciences, Humanities & Judaism, Art and Culture. The A.M.N. Foundation for the Advancement of Science, Art and Culture was founded in 1999 by Alberto Moscona Nisim, a Mexican friend of Israel.

Professor David Kazhdan of the Hebrew University in Jerusalem won Israel's EMET prize for Excellence in Exact Sciences (Mathematics) in 2016 for his work in design of representation theory and its uses in algebra, algebraic geometry and number theory. It was only the fourth time the Exact Sciences prize had been awarded to mathematicians since it was inaugurated in 2002. David Kazhdan received his award on the evening of 4 December 2016 at the Jerusalem Theatre with the participation of the Prime Minister of Israel.

Established in November 2002 under the auspices of the late Mr Run Run Shaw, the Prize honours individuals, regardless of race, nationality, gender and religious belief, who have achieved significant breakthroughs in academic and scientific research or applications and whose works have resulted in a positive and profound impacts on mankind. The Shaw Prize is an international award managed and administered by The Shaw Prize Foundation based in Hong Kong. Mr Shaw has also founded two charities, The Shaw Foundation Hong Kong and The Sir Run Run Shaw Charitable Trust, both dedicated to the promotion of education, scientific and technological research, medical and welfare services, and culture and the arts. The Shaw Prize consists of three annual awards: the Prize in Astronomy, the Prize in Science and Medicine, and the Prize in Mathematical Sciences.

4.1. The 2020 Shaw Prize and COVID-19.

The 2020 Shaw Prize Award Presentation Ceremony was intended to be held in September 2020. However, due to the ongoing COVID-19 pandemic, the in-person Award Ceremony was forced to be cancelled. After thorough consideration and preparation, the Shaw Prize Foundation has decided to turn the event online. The first-ever virtual Shaw Prize Award Ceremony was held on Thursday, 20 May 2021, and was live-streamed via the Shaw Prize website. At the ceremony, the Honourable Mrs Carrie Lam Cheng Yuet-ngor, Chief Executive of the Hong Kong Special Administrative Region, People's Republic of China, sent a congratulatory message to the Shaw Laureates. The Shaw Laureates were selected by the international prize committee and the results were announced at the press conference on 21 May 2020.

4.2. The 2020 Shaw Prize announced on 21 May.

The Shaw Prize in Mathematical Sciences 2020 is awarded in equal shares to Alexander Beilinson, David and Mary Winton Green University Professor at the University of Chicago, USA and David Kazhdan, Professor of Mathematics at the Hebrew University of Jerusalem, Israel:-

... for their huge influence on and profound contributions to representation theory, as well as many other areas of mathematics.

4.3. Contribution of Alexander Beilinson and David Kazhdan.

Alexander Beilinson and David Kazhdan are two mathematicians who have made profound contributions to the branch of mathematics known as representation theory, but who are also famous for the fundamental influence they have had on many other areas, such as arithmetic geometry, K-theory, conformal field theory, number theory, algebraic and complex geometry, group theory, and algebra more generally. As well as proving remarkable theorems themselves, they have created conceptual tools that have been essential to many breakthroughs of other mathematicians. Thanks to their work and its exceptionally broad reach, large areas of mathematics are significantly more advanced than they would otherwise have been.

Group theory is intimately related to the notion of symmetry and one can think of a representation of a group as a "description" of it as a group of transformations, or symmetries, of some mathematical object, usually linear transformations of a vector space. Representations of groups are important as they allow many group-theoretic problems to be reduced to problems in linear algebra, which is well understood. They are also important in physics because, for example, they describe how the symmetry group of a physical system affects the solutions of equations describing that system and the representations also make the symmetry group better understood. In loose terms, representation theory is the study of the basic symmetries of mathematics and physics. Symmetry groups are of many different kinds: finite groups, Lie groups, algebraic groups, p-adic groups, loop groups, adelic groups. This may partly explain how Beilinson and Kazhdan have been able to contribute to so many different fields.

One of Kazhdan's most influential ideas has been the introduction of a property of groups that is known as Kazhdan's property (T). Among the representations of a group there is always the not very interesting "trivial representation" where we associate with each group element the "transformation" that does nothing at all to the object. While the trivial representation is not interesting on its own, much more interesting is the question of how close another representation can be to the trivial one. Property (T) gives a precise quantitative meaning to this question. Kazhdan used Property (T) to solve two outstanding questions about discrete subgroups of Lie groups. Since then it has had important applications to group representation theory, lattices in algebraic groups over local fields, ergodic theory, geometric group theory, expanders, operator algebras and the theory of networks, and has been recognised as a truly fundamental concept in representation theory.

After this first breakthrough Kazhdan solved several other outstanding problems about lattices in Lie groups and representation theory such as the Selberg conjecture about non-uniform lattices, and the Springer conjecture on the classification of affine Hecke algebras.

While working with George Lusztig on this last problem, Kazhdan introduced an important family of polynomials, as well as formulating a very influential pair of (equivalent) conjectures. One of Alexander Beilinson's achievements was to prove these conjectures with Joseph Bernstein. (They were also proved independently by Jean-Luc Brylinski and Masaki Kashiwara.) The methods introduced in this proof led to the area known as geometric representation theory, an area that Kazhdan also played an important part in developing, which aims to understand the deeper geometric and categorical structures that often underlie group representations. The resulting insights have been used to solve several open problems.
...

One of the central goals of mathematics, the Langlands programme ... Kazhdan has brought extraordinary mathematical insight into this circle of ideas. By pointing out that orbital integrals could be interpreted as counting points on certain algebraic varieties over finite fields, he and Lusztig opened the way to the proof of the fundamental lemma, and since then Kazhdan has had and continues to have an enormous influence on the subject.
...

Beilinson and Kazhdan are at the heart of many of the most exciting developments in mathematics over the last few decades, developments that continue to this day. It is for this that they are awarded the 2020 Shaw Prize in Mathematical Sciences

Mathematical Sciences Selection Committee
The Shaw Prize
21 May 2020
Hong Kong

4.4. About David Kazhdan.

David Kazhdan was born in 1946 in Moscow, Russia and is currently Professor of Mathematics at the Hebrew University of Jerusalem, Israel. He received a diploma in 1967 and earned his PhD under Alexandre Kirillov in 1969 from Moscow State University, Russia. After working at Moscow State University as a Researcher (1969-1975), he emigrated to USA to take up a position at Harvard University, where he was successively Visiting Professor (1975-1977), Professor (1977-2002) and Professor Emeritus of Mathematics (2002-). He then emigrated to Israel and has been Professor at the Hebrew University of Jerusalem since 2002. He is a member of the US National Academy of Sciences and the American Academy of Arts and Sciences.

4.5. Autobiography of David Kazhdan.

I was born in Moscow immediately after World War II, the only son of young academic parents. During the fifth grade of my local elementary school, I became interested in mathematics, and together with my grandfather, who had no high school education, I spent that year making my way quickly through algebra, geometry and trigonometry. I do not recall how much time, if any, was spent in regular classes that year, but that first experience showed me, and I still believe, that many mathematical subjects relegated to high school can be learned much earlier. The young mind can absorb mathematical concepts, like chess skills, at an early age.

By the beginning of the following year, I joined a maths club organised by two students from Moscow University. This was a great experience. It opened my eyes - and my heart - to the beauty of mathematics, the field that ties together ostensibly unrelated concepts.

At that time, I often shopped for mathematical texts in used bookstores and frequently met Naum Vilenkin on my wanderings. He was an excellent mathematician who attended the seminar led by Israel Gelfand. Gelfand, by then a 45-year-old outstanding scientist in many areas of mathematics (and later of biology), had begun instructing his son, Sergei, who hoped to follow in his father's mathematical footsteps. They were looking for a partner and I surmise that Vilenkin told Gelfand about meeting me on those shopping expeditions. In any case, Vilenkin gave me Gelfand's phone number and I eagerly called my future mentor. After a cursory interview, Gelfand invited me to his home and for many years thereafter I would go to his house on a weekly basis. Those meetings opened the world of mathematics to me. The fundamental lesson Gelfand imparted was the feeling that mathematics constitutes a unity, that even if in the apparent diversity of subjects falling within the discipline, such divisions should not be taken too seriously.

I enjoyed participating in various math circles throughout my school years, and later at Moscow University I met a number of excellent mathematicians - young, committed, and focused partners. We often became friends and shared mutual feelings about the beauty of mathematics. We went together to numerous seminars, living and breathing mathematics, and constantly discussing our ideas and sharing our findings and quandaries. For our group, the Moscow International Congress of 1966 provided the unique opportunity of meeting world-famous mathematicians: Michael Atiyah, a British-Lebanese mathematician specialising in geometry; Harish-Chandra, an Indian mathematician and physicist who did fundamental work in representation theory; and a little later, Pierre Deligne, a Belgian colleague of similar age who began to visit Moscow frequently. Despite the hermetically closed borders of the communist state, for young Soviet students such interactions offered access to cutting edge developments in the various realms of mathematics on an international scale.

In 1968, I married Helena Slobodkin, a fellow mathematics student - and later computer programmer. Our first three children - Eli, Dina and Misha - were born over the next five years in Moscow. Daniel, the youngest, was born in Boston in the early 1980s after our immigration in 1975. Helena and I took advantage of the brief détente in the mid-1970s between Moscow and Washington. As a young, religious Jewish family, the rigidity of the Soviet Union, and specifically the restrictions against any forms of organised religion, did not offer much hope of raising our family as we wished.

Upon arrival in the United States, I was offered a position in the Harvard Mathematics Department where I had the privilege of spending the next 27 years. Harvard was a remarkably friendly and stimulating place. The Department integrated many different mathematical minds and offered a unique platform for interactions and collaborations between the faculty and the graduate student community. And more broadly, the world of Boston academia provided an auspicious environment for my work. I collaborated with various colleagues at Harvard and was exceptionally lucky to become a friend and collaborator of Romanian-born George Lusztig. And beyond the academic satisfactions of my tenure at Harvard, my family quickly made Boston our "home". Relationships were built and long-lasting friendships forged.

In 2002, Helena and I moved to Jerusalem where I joined the Department of Mathematics at The Hebrew University and where I found a number of excellent mathematicians with whom I worked. Two of our four children were already living in Israel and our first grandchild had recently been born there. Although our family had previously spent two sabbaticals in Jerusalem, moving, yet again, to a new country and burdened with a new language (this time at the age of 55) was not trivial. And yet, I found the environment, the city, and especially my colleagues to be most welcoming. The Department allowed me to structure my teaching with allowances for my less than fluent Hebrew language skills and recognising my strengths and weaknesses. They created the atmosphere that ensured my productivity by supporting me each step of the way and facilitating interactions with people in a variety of unfamiliar areas. Even now, after my retirement, I enjoy leading three to four seminars each semester.

Throughout my career, in all three countries where I have lived, I have been extremely fortunate - and continue to be fortunate - to have worked with many highly talented people. The inherently pure beauty that we see in mathematics is the glue that continues to bring us together. Even if it is via ZOOM conferences in the time of COVID, the world of mathematics, perhaps even more than in other domains of science, allows for professional relationships and cooperation between people in different parts of the globe, who have no shared language, come from diverse backgrounds, and live by dissimilar political orientations. This global community is what makes mathematics special - at least for me.

20 May 2021
Hong Kong

4.6. David Kazhdan on receiving the Shaw Prize.

This is a great honour for me. Of course, I was very happy when I heard, and I'm more than happy to receive the award. But I didn't do anything, I've just engaged in maths my whole life - and not for my own sake. I feel as though I'm in the good company of scholars and mathematicians who have received the award thus far.