Prof. Nikolay Nikolov

D.Phil 2002, Oxford University

Status

Academic Faculty

Associate Professor in Pure Mathematics

Contact form

+44 1865 273590

ORCID iD

https://orcid.org/0000-0003-1661-5467

Research groups

Algebra

Address
Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG

Highlighted publications

An infinite compact Hausdorff group has uncountably many conjugacy classes

Jaikin-Zapirain, A Nikolov, N Proceedings of the American Mathematical Society (08 Apr 2019)

On the growth of $L^2$-invariants for sequences of lattices in Lie
groups

Abert, M Bergeron, N Biringer, I Gelander, T Nikolov, N Raimbault, J Samet, I Annals of Mathematics (12 Apr 2017) http://arxiv.org/abs/1210.2961v1

Rank, combinatorial cost and homology torsion growth in higher rank lattices

Abert, M Gelander, T Nikolov, N Duke Mathematical Journal volume 166 issue 15 2925-2964 (06 Sep 2016)

On growth of homology torsion in amenable groups

Kar, A Kropholler, P Nikolov, N Mathematical Proceedings of the Cambridge Philosophical Society volume 162 issue 2 337-351 (14 Jul 2016)

Rank gradient and cost of Artin groups and their relatives

Kar, A Nikolov, N Groups, Geometry, and Dynamics (11 Feb 2015) http://arxiv.org/abs/1210.2873v4

Teaching

Prelims Group Theory and Part C Noncommutative Rings.

Research interests

Asymptotic behaviour of invariants of finite or infinite groups, for example expansion, word width, growth of rank or Betti numbers.

Recent publications

Constructing uncountably many groups with the same profinite completion

NIKOLOV, N Segal, D New Zealand Journal of Mathematics (18 Dec 2021)

Homology torsion growth in finitely presented pro-$p$ groups

Nikolov, N (27 Jun 2021)

On the growth of L2-invariants of locally symmetric spaces, II: exotic
invariant random subgroups in rank one

Abert, M Bergeron, N Biringer, I Gelander, T Nikolov, N Raimbault, J Samet, I International Mathematics Research Notices (11 May 2018) http://arxiv.org/abs/1612.09510v1

Some remarks on finitarily approximable groups

Nikolov, N Schneider, J Thom, A Journal de l'École polytechnique — Mathématiques (16 Jan 2018) http://arxiv.org/abs/1703.06092v2

Gradients of sequences of subgroups in a direct product

Nikolov, N Shemtov, Z Shusterman, M International Mathematics Research Notices (09 Oct 2017) http://arxiv.org/abs/1609.08900v2

Prizes, awards, and scholarships

Whitehead prize of the London Mathematical Society, 2007.