Alexander Lubotzky

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Alexander Lubotzky

Alexander Lubotzky ( Hebrew אלכסנדר לובוצקי; *  June 28, 1956 in Ramat Gan ) is an Israeli mathematician who studies group theory and combinatorics.

Life

Lubotzky studied at the Bar-Ilan University in Ramat Gan, where he received his bachelor's degree in 1975 (summa cum laude) and his doctorate with Harry Fürstenberg in 1979 (Pro-finite groups and the congruence subgroup problem). Afterwards he was an instructor and from 1979 a lecturer at the Bar-Ilan University. At the same time he was in the Israeli army in the research and development department from 1977 to 1982. From 1982 he was Senior Lecturer at the Hebrew University of Jerusalem , since 1985 as Associate Professor and since 1989 as Professor (Maurice and Clara Weil Professorship). From 1994 to 1996 he headed the Mathematics Faculty of the Hebrew University. He was a visiting scholar at Yale University in 1979, at the Institute for Advanced Study in 1983 and 2005/2006 , as a visiting professor at Stanford University , the University of Chicago , Yale and Columbia University .

Lubotzky deals with various aspects of group theory and the representation theory of groups , including applications in geometry, computer science, number theory and graph theory. In 1988 he introduced Ramanujan graphs with Peter Sarnak and Ralph Phillips .

In 1991 he received the Erdős Prize , in 2002 the Rothschild Prize and in 2018 the Israel Prize . He is an honorary doctor of the University of Chicago and a member of the American Academy of Arts and Sciences . From 1990 to 1995 he was editor of the Israel Journal of Mathematics. In 1994 he was invited speaker at the International Congress of Mathematicians (ICM) in Zurich (Subgroup Growth). In 2018 he is plenary speaker at the ICM in Rio (High Dimensional Expanders).

In 1996 he was a co-founder of the HaDerech HaSchlischit party , for which he was a member of the Knesset from 1996 to 1999 . There he advocated compromises in (intra-Jewish) religious questions. In the 1999 election he ran for the Mifleget ha-Merkas , but his place on the list was not enough for an election to the Knesset.

Alex Lubotzky (center) with Dan Segal (left) and Fritz Grunewald, Oberwolfach 2008

He has been married since 1980 and has six children. He lives in Efrat , which he helped found.

Fonts

  • With A. Magid: Varieties of Representations of Finitely Generated Groups. American Mathematical Society 1985.
  • Discrete Groups, Expanding Graphs and Invariant Measures. Birkhäuser, Progress in Mathematics 1994 (won the Ferran-Sunyer-i-Balaguer Prize ).
  • With Dan Segal : Subgroup Growth. Birkhäuser, Progress in Mathematics, 2003 (also won the Ferran-Sunyer-i-Balaguer Prize).
  • With Hyman Bass : Tree lattices. Birkhäuser, Progress in Mathematics, 2000.
  • Group presentation, p-adic analytic groups and lattices in . Ann. of Math. (2) 118 (1983) no. 1, 115-130.
  • With Birman, McCarthy: Abelian and solvable subgroups of the mapping class groups. Duke Math. J. 50 (1983), no. 4, 1107-1120.
  • Subgroup growth and congruence subgroups. Invent. Math. 119 (1995) no. 2, 267-295.
  • Eigenvalues ​​of the Laplacian, the first Betti number and the congruence subgroup problem. Ann. of Math. (2) 144 (1996) no. 2, 441-452.
  • Mit Mozes, Raghunathan: The word and Riemannian metrics on lattices of semisimple groups. Inst. Hautes Études Sci. Publ. Math. No. 91 (2000): 5-53 (2001).
  • Mit Farb, Minsky: Rank-1 phenomena for mapping class groups. Duke Math. J. 106 (2001), no. 3, 581-597.
  • With Pak: The product replacement algorithm and Kazhdan's property (T). J. Amer. Math. Soc. 14 (2001), no. 2, 347-363
  • With Kassabov, Nikolov: Finite simple groups as expanders. Proc. Natl. Acad. Sci. USA 103 (2006), no. 16, 6116-6119
  • With Larsen: Representation growth of linear groups. J. Eur. Math. Soc. (JEMS) 10 (2008), no. 2, 351-390.
  • With Belolipetsky, Gelander, Shalev: Counting arithmetic lattices and surfaces. Ann. of Math. (2) 172 (2010), no. 3, 2197-2221.

Web links

Individual evidence

  1. ↑ Alexander Lubotzky, Ralph Phillips, Peter Sarnak: Ramanujan graphs. Combinatorica, Vol. 8, 1988, pp. 261-277
  2. ↑ Arxiv
personal data
SURNAME Lubotzky, Alexander
ALTERNATIVE NAMES אלכסנדר לובוצקי (Hebrew)
BRIEF DESCRIPTION Israeli mathematician
DATE OF BIRTH June 28, 1956
PLACE OF BIRTH Ramat Gan