Aner Shalev
Encyclopedia
Aner Shalev is a professor
at the Einstein Institute of Mathematics at the Hebrew University of Jerusalem
, and a writer.
. He moved to Jerusalem at 18 to study Mathematics
and Philosophy
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 and dealt with Group Rings, an area combining Group Theory
and Ring Theory
.
Shalev spent his post-doctoral period at Oxford University and at the University of London
, returned to Israel in 1992, when he was hired as a Senior Lecturer at the Hebrew University. Shalev was appointed Full Professor in 1996, and spent sabbaticals at the Universities of Chicago
, Oxford (All Souls College), and London (Imperial College). He was also a Visiting Scholar at other Institutes, such as the Australian National University
, MSRI Berkeley, the Institute for Advanced Studies at the Hebrew University, and the Institute for Advanced Study
at Princeton.
Shalev is joint editor of the Israel Journal of Mathematics, the Journal of Group Theory, and the Journal of Algebra. 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 prestigious 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.
and Probability
. 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 automorphisms of p-groups, and studied subgroup growth of profinite and discrete groups.
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’.
Professor
A professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...
at the Einstein Institute of Mathematics at the Hebrew University of Jerusalem
Hebrew University of Jerusalem
The Hebrew University of Jerusalem ; ; abbreviated HUJI) is Israel's second-oldest university, after the Technion – Israel Institute of Technology. The Hebrew University has three campuses in Jerusalem and one in Rehovot. The world's largest Jewish studies library is located on its Edmond J...
, and a writer.
Biography
Aner Shalev was born in Kibbutz Kinneret and grew up in Beit BerlBeit Berl
Beit Berl is a village and the largest academic college in Israel in number of students and the range of programs it offers. Located on the outskirts of Kfar Sava, it falls under the jurisdiction of Drom HaSharon Regional Council...
. He moved to Jerusalem at 18 to study Mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
and Philosophy
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
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 and dealt with Group Rings, an area combining Group Theory
Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...
and Ring Theory
Ring theory
In abstract algebra, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers...
.
Shalev spent his post-doctoral period at Oxford University and at the University of London
University of London
-20th century:Shortly after 6 Burlington Gardens was vacated, the University went through a period of rapid expansion. Bedford College, Royal Holloway and the London School of Economics all joined in 1900, Regent's Park College, which had affiliated in 1841 became an official divinity school of the...
, returned to Israel in 1992, when he was hired as a Senior Lecturer at the Hebrew University. Shalev was appointed Full Professor in 1996, and spent sabbaticals at the Universities of Chicago
University of Chicago
The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...
, Oxford (All Souls College), and London (Imperial College). He was also a Visiting Scholar at other Institutes, such as the Australian National University
Australian National University
The Australian National University is a teaching and research university located in the Australian capital, Canberra.As of 2009, the ANU employs 3,945 administrative staff who teach approximately 10,000 undergraduates, and 7,500 postgraduate students...
, MSRI Berkeley, the Institute for Advanced Studies at the Hebrew University, and the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
at Princeton.
Shalev is joint editor of the Israel Journal of Mathematics, the Journal of Group Theory, and the Journal of Algebra. He gave an invited talk at the International Congress of Mathematicians
International Congress of Mathematicians
The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....
(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 prestigious 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.
Research
Aner Shalev’s main area of research over the years has been Group Theory, and he often uses methods from other disciplines, such as Lie AlgebrasLie algebra
In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. Lie algebras were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" was introduced by Hermann Weyl in the...
and Probability
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
. 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 automorphisms 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 groups and (nonabelian) finite simple groups 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, were 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 groups, diameters of certain Cayley graphs, Fuchsian groups, random walks, etc.Current research
Recently Shalev (partly with Larsen) has been researching the behavior of word maps on groups, proving Waring type theorems; he also proved, together with Liebeck, O’Brian and Tiep, the celebrated Ore Conjecture from 1951, according to which every element in a finite simple group is a commutator.Selected papers
- A. Shalev, The structure of finite p-groups: effective proof of the coclass conjectures, Invent. Math. 115 (1994), 315–345.
- M.W. Liebeck and A.Shalev, Classical groups, probabilistic methods, and the (2,3)-generation problem, Annals of Math. 144 (1996), 77–125.
- M.W. Liebeck and A.Shalev, Diameters of finite simple groups: sharp bounds and applications, Annals of Math. 154 (2001), 383–406.
- A. Shalev, Asymptotic Group Theory, Notices Amer. Math. Soc. 48 (2001), 383–389.
- M.W. Liebeck and A.Shalev, Fuchsian groups, finite simple groups, and representation varieties, Invent. Math. 159 (2005), 317–376.
- M. Larsen and A.Shalev, Characters of symmetric groups: sharp bounds and applications, Invent. Math. 174 (2008), 645–687.
- M. Larsen and A.Shalev, Word maps and Waring type problems, J. Amer. Math. Soc. 22 (2009), 437–466.
- A. Shalev, Word maps, conjugacy classes, and a non-commutative Waring-type theorem, Annals of Math. 170 (2009), 1383–1416.
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 Aner 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’.