Nikolai V. Ivanov (russian: Николай Владимирович Иванов, born 1954) is a Russian
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
who works on
topology
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...
,
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...
and
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 ...
Vladimir Abramovich Rokhlin
Vladimir Abramovich Rokhlin ( Russian: Влади́мир Абра́мович Ро́хлин) (23 August 1919 – 3 December 1984) was a Soviet mathematician, who made numerous contributions in algebraic topology, geometry, measure theory, ...
in 1980 at the
Steklov Mathematical Institute
Steklov Institute of Mathematics or Steklov Mathematical Institute (russian: Математический институт имени В.А.Стеклова) is a premier research institute based in Moscow, specialized in mathematics, and a part o ...
.
According to
Google Scholar
Google Scholar is a freely accessible web search engine that indexes the full text or metadata of scholarly literature across an array of publishing formats and disciplines. Released in beta in November 2004, the Google Scholar index includes ...
, on 5 July 2020, Ivanov's works had received 2,376 citations and his
h-index
The ''h''-index is an author-level metric that measures both the productivity and citation impact of the publications, initially used for an individual scientist or scholar. The ''h''-index correlates with obvious success indicators such as ...
was 22.
He is a fellow of the
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
since 2012.
He is the author of the 1992 book ''Subgroups of Teichmüller Modular Groups''.
Among his contributions to mathematics are his classification of
subgroup
In group theory, a branch of mathematics, given a group ''G'' under a binary operation ∗, a subset ''H'' of ''G'' is called a subgroup of ''G'' if ''H'' also forms a group under the operation ∗. More precisely, ''H'' is a subgroup ...
s of surface
mapping class group
In mathematics, in the subfield of geometric topology, the mapping class group is an important algebraic invariant of a topological space. Briefly, the mapping class group is a certain discrete group corresponding to symmetries of the space.
Mo ...
s, and the establishment that surface
mapping class group
In mathematics, in the subfield of geometric topology, the mapping class group is an important algebraic invariant of a topological space. Briefly, the mapping class group is a certain discrete group corresponding to symmetries of the space.
Mo ...
s satisfy the
Tits alternative In mathematics, the Tits alternative, named for Jacques Tits, is an important theorem about the structure of finitely generated linear groups.
Statement
The theorem, proven by Tits, is stated as follows.
Consequences
A linear group is not a ...
*"Automorphisms of complexes of curves and of Teichmuller spaces" (1997), ''
International Mathematics Research Notices
The ''International Mathematics Research Notices'' is a peer-reviewed mathematics journal. Originally published by Duke University Press and Hindawi Publishing Corporation, it is now published by Oxford University Press.Inventiones mathematicae'' 135 (2), pp. 425–486.
*"On the homology stability for Teichmüller modular groups: closed surfaces and twisted coefficients" (1993), ''Contemporary Mathematics'' 150, pp. 149–149.