Aner Shalev
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Aner Shalev (; born 24 January 1958) is a
professor Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other tertiary education, post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin ...
at the
Einstein Institute of Mathematics The Einstein Institute of Mathematics () is a centre for scientific research in mathematics at the Hebrew University of Jerusalem, founded in 1925 with the opening of the university. A leading research institute, the institute's faculty has inclu ...
at the
Hebrew University of Jerusalem The Hebrew University of Jerusalem (HUJI; ) is an Israeli public university, public research university based in Jerusalem. Co-founded by Albert Einstein and Chaim Weizmann in July 1918, the public university officially opened on 1 April 1925. ...
, and a writer.


Biography

Shalev was born in Kibbutz Kinneret and grew up in
Beit Berl Beit Berl () is an institutional settlement in Israel. Located on the outskirts of Kfar Saba, the village falls under the jurisdiction of Drom HaSharon Regional Council and is the location of Beit Berl College, which has around 7,000 students. I ...
. He moved to
Jerusalem Jerusalem is a city in the Southern Levant, on a plateau in the Judaean Mountains between the Mediterranean Sea, Mediterranean and the Dead Sea. It is one of the List of oldest continuously inhabited cities, oldest cities in the world, and ...
at 18 to study
mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
and
philosophy Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational an ...
at the Hebrew University, and since then, excluding some years abroad, he has been living mainly in Jerusalem. Shalev received his Ph.D. in mathematics at the Hebrew University in 1989, summa cum laude. His doctoral thesis was written under the supervision of Professors Amitsur and
Mann Mann may refer to: Arts, entertainment and media * ''Mann'' (film), a 1999 Indian Hindi-language romantic drama * Mann (chess), a variant chess piece * ''Mann'' (magazine), a Norwegian magazine * Mann (rapper), Dijon Shariff Thames (born 19 ...
and dealt with
group ring In algebra, a group ring is a free module and at the same time a ring, constructed in a natural way from any given ring and any given group. As a free module, its ring of scalars is the given ring, and its basis is the set of elements of the gi ...
s, an area combining
group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ( ...
and ring theory. Shalev spent his post-doctoral period at
Oxford University The University of Oxford is a collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the second-oldest continuously operating u ...
and at the
University of London The University of London (UoL; abbreviated as Lond or more rarely Londin in Post-nominal letters, post-nominals) is a collegiate university, federal Public university, public research university located in London, England, United Kingdom. The ...
, returned to Israel in 1992, when he was hired as a senior lecturer at the Hebrew University. Shalev was appointed
full professor Professor (commonly abbreviated as Prof.) is an academic rank at universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a 'person who professes'. Professors ...
in 1996, and spent sabbaticals at the Universities of
Chicago Chicago is the List of municipalities in Illinois, most populous city in the U.S. state of Illinois and in the Midwestern United States. With a population of 2,746,388, as of the 2020 United States census, 2020 census, it is the List of Unite ...
, Oxford (
All Souls College All Souls College (official name: The College of All Souls of the Faithful Departed, of Oxford) is a constituent college of the University of Oxford in England. Unique to All Souls, all of its members automatically become fellows (i.e., full me ...
), and London (
Imperial College Imperial College London, also known as Imperial, is a public research university in London, England. Its history began with Prince Albert, husband of Queen Victoria, who envisioned a cultural district in South Kensington that included museums ...
). He was also a visiting scholar at other institutes, such as the
Australian National University The Australian National University (ANU) is a public university, public research university and member of the Group of Eight (Australian universities), Group of Eight, located in Canberra, the capital of Australia. Its main campus in Acton, A ...
, MSRI Berkeley, the Institute for Advanced Studies at the Hebrew University, and the
Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...
at Princeton. Shalev is joint editor of the
Israel Journal of Mathematics '' Israel Journal of Mathematics'' is a peer-reviewed mathematics journal published by the Hebrew University of Jerusalem ( Magnes Press). History Founded in 1963, as a continuation of the ''Bulletin of the Research Council of Israel'' (Section ...
, the Journal of Group Theory, and the
Journal of Algebra ''Journal of Algebra'' (ISSN 0021-8693) is an international mathematical research journal in algebra. An imprint of Academic Press, it is published by Elsevier Elsevier ( ) is a Dutch academic publishing company specializing in scientific, te ...
. He gave an invited talk at the International Congress of Mathematicians (ICM) in Berlin in 1998 and at numerous other mathematical conferences all over the world. Shalev was awarded many grants from various sources, including the ERC Advanced Grant from the European Community (2010–2014). Aner Shalev is married to Donna Shalev, a senior lecturer at the Classics Department of the Hebrew University of Jerusalem, and they have two daughters. His cousin is the author
Meir Shalev Meir Shalev (; 29 July 1948 – 11 April 2023) was an Israeli writer and newspaper columnist for the daily Yedioth Ahronoth. Shalev's books have been translated into 26 languages. Biography Shalev was born in Nahalal, Israel. Later he lived ...
, and he is the brother of author
Zeruya Shalev Zeruya Shalev (; born 13 May 1959) is an Israeli author. Biography Zeruya Shalev was born on Kibbutz Kvutzat Kinneret, Kinneret. She has an MA in Bible studies and works as a literary editor at Keshet Publishing House. On 29 January 2004, when ...
.


Research

Shalev's main area of research over the years has been group theory, and he often uses methods from other disciplines, such as
Lie algebra In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi ident ...
s and
probability Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an e ...
. He has also worked on ring theory, Lie algebras, and other areas. Shalev has published around 120 mathematical articles in various international journals. The first fruits of Shalev's research solve various problems in group rings using a unified method based on dimension subgroups. Subsequently, he worked extensively in ''p''-groups and pro-''p'' groups and was among those who solved the coclass conjectures on the structure of such groups. Likewise Shalev used Lie methods to solve problems on fixed points of
automorphism In mathematics, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure. The set of all automorphism ...
s of ''p''-groups, and studied subgroup growth of profinite and discrete groups.


Probabilistic methods in group theory

From 1995 Shalev developed and applied probabilistic methods to
finite group In abstract algebra, a finite group is a group whose underlying set is finite. Finite groups often arise when considering symmetry of mathematical or physical objects, when those objects admit just a finite number of structure-preserving tra ...
s and ( nonabelian)
finite simple group In mathematics, the classification of finite simple groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of groups of Lie type, or one of 26 sporadic groups. The list below gives all finite simple g ...
s in particular. A formative result in this area shows that almost every pair of elements in a finite simple group generate the group. This result, like many others in the field, was proved by Shalev in collaboration with Martin Liebeck of Imperial College at the University of London. The probabilistic approach led to the solution of many classical problems whose formulation does not involve probability; these problems concern quotients of the modular group, conjectures of Babai and of Cameron on
permutation group In mathematics, a permutation group is a group ''G'' whose elements are permutations of a given set ''M'' and whose group operation is the composition of permutations in ''G'' (which are thought of as bijective functions from the set ''M'' to ...
s,
diameter In geometry, a diameter of a circle is any straight line segment that passes through the centre of the circle and whose endpoints lie on the circle. It can also be defined as the longest Chord (geometry), chord of the circle. Both definitions a ...
s of certain
Cayley graph In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, is a Graph (discrete mathematics), graph that encodes the abstract structure of a group (mathematics), group. Its definition is sug ...
s,
Fuchsian group In mathematics, a Fuchsian group is a discrete subgroup of PSL(2,R). The group PSL(2,R) can be regarded equivalently as a group of orientation-preserving isometries of the hyperbolic plane, or conformal transformations of the unit disc, or co ...
s, random walks, etc.


Current research

Shalev (partly with Michael J. Larsen) has been researching the behavior of word maps on groups, proving Waring type theorems; he also proved, together with Liebeck, O’Brien and Tiep, the Ore conjecture from 1951, according to which every element in a non-cyclic finite simple group is a
commutator In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative. There are different definitions used in group theory and ring theory. Group theory The commutator of two elements, ...
.


Selected papers

* * * * * * * *


Literary work


Shalev’s approach to writing

Shalev's approach to writing emphasizes language and structure. In all his literary writing he has included formal experimentation.


Opus 1

This is Shalev's first literary work which was published in 1988 in the ‘Library’ series at the Keter publishing house, and edited by the literary scholar and critic Yig’al Schwartz. The manuscript of this book was awarded the Harry Harishon Prize under the auspices of the Hebrew University, in 1986. This is a collection of four stories with a musical superstructure in which Shalev attempts to apply musical terms and concepts to language and to emotions. The book is composed of two major parts: the first part, "Legato", is characterized by a flowing mode, long sentences without much punctuation and psychologically conveys a state of openness, whereas the second part, "Staccato", is characterized by short sentences, copious punctuation and an introspective, closed mood. The first of the four stories, ‘Opus 1’, describes a boy who falls in love with his piano teacher. The second story, ‘Concussion’, portrays a relationship between two young people, and opens with an injury, providing the characters with a new perspective. The third story, ‘Scherzo’, deals with the journey to New York of an eccentric harpsichord player. The fourth story, ‘Absence’, describes the release from the army on psychiatric grounds of an AWOL interested in being the object of a search party. This story is formally structured as a crossword puzzle with two coordinates and has been described as ‘a crossword riddled with contradictions demanding solutions’.


Overtures

Shalev's second book was published in 1996 in the ‘New Library’ series (Siman Kri'a – ha-Kibbutz ha-Me'uhad) edited by Menachem Peri. The book is composed of seventy openings of stories. The book bears a major element of fragmentation and gaps, and treats openings, or overtures, in the widest sense of the term; at times the stories have an opening and no ending; at others there is only a middle part and the beginning and ending are missing. On the one hand Shalev creates an intense mode of writing, featuring a video-clip nature, and on the other hand he seduces the readers toward filling in the gaps by themselves. Large parts of the book describe many places in the world where people arrive for short, breathless periods and are constantly on the go.


Dark Matter

Shalev's third book is a novel that was published in 2004 at the Zmora Bitan publishing house. It has appeared in German (2007), Italian (2007) and Czech (2009). The book describes a love triangle between a man and two women. Shalev was influenced in this book by the modern astrophysical theory of Dark Matter and Dark Energy; he applies these ideas to relationships between women and men. Alongside physical attraction between men and women, Shalev describes forces of repulsion, which overwhelmingly overcome the forces of attraction. This is an attempt to understand why many love stories which begin so well end so badly. The protagonist of the book is a married Israeli diplomat in New York who, during a visit to Israel, falls in love with a woman doing a doctorate in Physics on Dark Matter. The text is formally divided between emails sent by the woman to the man in the period before their tryst in New York, and descriptions from the man's perspective of that tryst. As the plot progresses the emails asymptotically approach in time the meeting in New York and illuminate its background, but these two types of text and narrative never coalesce.


References


External links


Aner Shalev in The Institute for the Translation of Hebrew Literature

Aner Shalev in Mathematics Genealogy Project
{{DEFAULTSORT:Shalev, Aner 20th-century Israeli mathematicians 21st-century Israeli mathematicians Einstein Institute of Mathematics alumni Academic staff of the Hebrew University of Jerusalem Israeli Jews Jewish scientists Living people Jewish novelists Israeli novelists 1958 births Israel Defense Prize recipients People from Northern District (Israel) Kibbutzniks