# 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

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

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

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.