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Uzi Vishne

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Uzi Vishne
עוזי וישנה
Born(1972-01-19)January 19, 1972
NationalityIsraeli
Alma materBar-Ilan University
Known forDivision algebras, Gelfand–Kirillov dimension, Coxeter groups, Artin groups, combinatorial group theory, monomial algebras, arithmetic of algebraic groups
AwardsLevitzki Prize
Scientific career
FieldsMathematics
InstitutionsBar-Ilan University

Uzi Vishne (Hebrew: עוזי וישנה; born January 19, 1972) is an Israeli mathematician. He works as a professor at Bar-Ilan University. He was the Dean of the Faculty of Exact Sciences at Bar-Ilan University from 2021 to 2023.

Biography

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Vishne was born in 1972 in Israel. He received his Ph.D. from Bar-Ilan University in 2000; his dissertation, titled "Central Simple Algebras", was carried under the advisorship of Louis Rowen.

He was a postdoctoral fellow at the Hebrew University of Jerusalem (2000-2001), at the Université catholique de Louvain (2001), and at Yale University (as a Fulbright fellow, in 2001-2003), and a research fellow at the Institute for Advanced Study in Princeton (2005-2006).

Vishne joined Bar-Ilan University in 2003, where he has been a full professor since 2013. Since 2010, he has headed the Youth Academic Program at Bar-Ilan University.[1]

Vishne is the recipient of the Levitzki Prize in Algebra for 2003.[2]

Scientific Work

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His principal research area is noncommutative algebra and its applications to various mathematical fields.

His main scientific achievements are related to ring theory (especially: central simple algebras, division algebras and rings satisfying polynomial identities), combinatorics, differential geometry, quadratic forms and their invariants, Galois cohomology and algebraic geometry.[3]

Some of his most important results are:

  • The first explicit construction of Ramanujan complexes, which are higher-dimensional generalizations of Ramanujan graphs. These combinatorial objects have far-reaching applications in pure and applied mathematics -- for instance, they can be used to construct optimal codes (joint with Lubotzky and Samuels).
  • A proof of the existence of arithmetic lattices in the (real and complex) projective general linear groups , which induce isospectral but non-commensurable manifolds (joint with Lubotzky and Samuels).
  • An optimal bound (logarithmic in the genus) on the systoles of Hurwitz surfaces. This bound, which generalizes previous results of Sarnak, Busser and others, was achieved by an analysis of orders in quaternion algebras (joint with Katz and Schaps).
  • A full exposition of the solution (given by Kanel-Belov) of the Specht problem, which asserts that the set of polynomial identities of a PI algebra which is finitely generated over a Noetherian ring is finitely based (joint with Kanel-Belov and Rowen).
  • Structure-theoretic theorems and counterexamples in the theory of central simple algebras, especially in the theory of crossed products. In particular, he has solved the Roquette Problem on cyclicity of algebras with central elements (joint with Matzri and Rowen).
  • Computations of fundamental groups of Galois covers of various algebraic varieties and complements of plane curves (in a series of joint papers with Amram, Lawrence, Teicher and others).
  • Novel combinatorial constructions of monomial algebras of polynomial growth, and in particular, the first construction of primitive algebras of arbitrary Gelfand–Kirillov dimension over arbitrary base fields; and the first construction of a prime affine algebra of quadratic growth, which is neither primitive nor satisfies a polynomial identity (joint with Smoktunowicz).

In addition, Vishne has published several papers in group theory, statistics, computer science and applied algebra.

Selected publications

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  • Vishne, Uzi (1999-01-01). "Primitive Algebras with Arbitrary Gelfand-Kirillov Dimension". Journal of Algebra. 211 (1): 150–158. doi:10.1006/jabr.1998.7567. ISSN 0021-8693.
  • Vishne, Uzi (2004-09-15). "Galois cohomology of fields without roots of unity". Journal of Algebra. 279 (2): 451–492. doi:10.1016/j.jalgebra.2003.12.020. ISSN 0021-8693.
  • Lubotzky, Alexander; Samuels, Beth; Vishne, Uzi (2005), "Ramanujan complexes of type ", Israel Journal of Mathematics, 149: 267–299, arXiv:math/0406208, doi:10.1007/BF02772543, MR 2191217
  • Bar-On, Tamar; Gilat, Shira; Matzri, Eliyahu; Vishne, Uzi (2023-04-01). "Locally Finite Central Simple Algebras". Algebras and Representation Theory. 26 (2): 553–607. doi:10.1007/s10468-021-10103-4. ISSN 1572-9079.
  • Blachar, Guy; Haile, Darrell; Matzri, Eliyahu; Rein, Edan; Vishne, Uzi (2024-07-01). "Semiassociative algebras over a field". Journal of Algebra. 649: 35–84. doi:10.1016/j.jalgebra.2024.03.006. ISSN 0021-8693.

References

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  1. ^ ברמלי, דפנה (2014-07-12). "מתלבטים אם לשלוח את התיכוניסט לאקדמיה? תקראו את זה". Globes. Retrieved 2025-02-14.
  2. ^ "Levitzki Prize Recipients". Israeli Mathematical Union.
  3. ^ "Uzi Vishne's homepage". u.math.biu.ac.il. Retrieved 2025-02-17.
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