research related information:
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Most of my papers and preprints are available from the
mathematics
arXiv. The versions at the arXiv may have minor differences with
the published articles but are essentially the same.
Reviews of my publications can be found at
Zentralblatt and
MathSciNet (subscription required).
Some of the papers are written in collaboration with
I. Agol,
J. Ellenberg,
V. Emery,
W. T. Gan,
T. Gelander,
G. Gromadzki,
P. Gunnells,
G. Jones,
B. Linowitz,
A. Lubotzky,
J. Mcleod,
R. Scott,
A. Shalev,
P. Storm,
S. Thomson,
A. Venkatesh, and
K. Whyte.
articles in conference proceedings:
- Some estimates for the number of automorphisms of Riemann surfaces, Novosibirsk 1996 (in Russian).
- Volumes of arithmetic hyperbolic n-manifolds, Arbeitstagung 2003.
- On volumes of arithmetic locally symmetric spaces, Oberwolfach 2003.
- Counting lattices, Arbeitstagung 2009.
- Kazhdan-Lusztig cells in infinite Coxeter groups, with Paul Gunnells, Proceedings of the Workshop on Algebra, Combinatorics and Dynamics 2009. The Russian version pdf is here.
- Geodesics, volumes and Lehmer's conjecture, Oberwolfach 2010.
- Free subgroups of arithmetic 3-manifold groups, Oberwolfach 2012.
- Hyperbolic orbifolds of small volume, ICM 2014.
- Expansores Geométricos, AGRA II: Aritmética, grupos y análisis, Cusco 2015 (in Spanish).
some conference talks with slides in pdf:
- Counting manifolds and class field towers talk at Geometric and Asymptotic Group Theory Conference with Applications (September 2006, Barcelona, Spain).
- Euler-Poincare characteristic of arithmetic hyperbolic n-orbifolds talk at 26 Coloquio Brasileiro de Matematica (August 2007, Rio de Janeiro, Brazil).
- Cells in Coxeter groups talk at Workshop on Algebra, Combinatorics and Dynamics (August 2009, Belfast, UK).
- Some computational problems from geometry of lattices talk at The 5th William Rowan Hamilton Geometry and Topology Workshop (September 2009, Dublin, Ireland).
- On volumes of arithmetic hyperbolic n-orbifolds talk at the BMC 2010 Geometric Group Theory Section (Edinburgh, UK) and the LMS Northern Workshop (Newcastle, UK).
- Grupos cristalográficos hiperbólicos a palestra na Conferência de Academia Brasileira de Ciências (Outubro 2013, Rio de Janeiro, Brazil).
- Hyperbolic orbifolds of small volume talk at the ICM 2014 Geometry Section (August 2014, Seoul, Korea).
- Arithmetic hyperbolic reflection groups talk at CLAM V (July 2016, Barranquilla, Colombia).
- Growth of lattices talk at CLA - XXII (August 2017, Quito, Ecuador) and Mathematics in the Modern World (August 2017, Novosibirsk, Russia).
- Prasad’s volume formula and its applications talk at Gopal Prasad’s Day Arithmetic in Geometry (30 July 2020, ICTS, India – Online).
- Subspace stabilisers in hyperbolic lattices talk at Zariski dense subgroups, number theory and geometric applications (January 2024, ICTS, India – Online).
conferences organized:
- LMS Durham Symposium "Geometry and Arithmetic of Lattices"
organized together with M. Kapovich, J. Parker and A. Reid on July 4-14, 2011 (Durham, UK).
The conference webpage contains, in particular, the videos from the talks and a transcript of the problem session.
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Conference "Algebraic Geometry and Hyperbolic Geometry - New Connections",
together with C. Araujo, M. Kapovich and J. Kollar (Cabo Frio, Rio de Janeiro, Brazil, 17/06 - 21/06/2013).
- Conference "Hyperbolic Geometry and Minimal Surfaces", together with M. Bridgeman, J. Brock and H. Rosenberg (IMPA, Rio de Janeiro, 04/01 - 10/01/2015).
- ICM 2018 Satellite Conference "Group Theory", together with N. Nikolov, D. Osin and I. Snopche (Cabo Frio, Rio de Janeiro, Brazil, 07/23 - 07/27/2018).
- AIM Workshop "Arithmetic reflection groups and crystallographic packings", together with A. Kontorovich and A. Mark (San Jose, California - Online, 14/12 - 18/12/2020).
- AGRA IV – Aritmética, Grupos y Análisis (Part I, Part II), Rio de Janeiro, 16/08 – 20/08/2021 (online), 20/06 – 25/06/2022 (presential).