Prof. Nikolay Nikolov
D.Phil 2002, Oxford University
Status
Academic Faculty
Associate Professor in Pure Mathematics
Research groups
Address
Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
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 groups
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
Jordan-Holder Theorem for profinite groups and applications
Bar-On, T Nikolov, N (12 Mar 2025) Krull-Schmidt Theorem for small profinite groups
Bar-On, T Nikolov, N (10 Dec 2024) Groups of profinite type and profinite rigidity
Bar-On, T Nikolov, N Journal of Group Theory volume 27 issue 6 1151-1169 (23 May 2024) Demushkin groups of uncountable rank
Bar‐On, T Nikolov, N Journal of the London Mathematical Society volume 109 issue 3 (18 Feb 2024) On the finite images of finitely generated perfect groups
Nikolov, N (28 Sep 2023) Prizes, awards, and scholarships
Whitehead prize of the London Mathematical Society, 2007.