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
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 invariant random subgroups in rank one
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.