Ilia Smilga: Homepage

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Photo I am currently a Postdoctoral Research Associate at the Mathematical Institute of the University of Oxford, financed by the Simons Foundation through Vladimir Marković's grant.

Office number: N3.04
Physical address:
Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
United Kingdom
Phone: (+44) 1865 615143
E-mail: firstname.lastname AT maths.ox.ac.uk (current)
       or firstname.lastname AT normalesup.org (permanent)
My research touches several different fields: discrete subgroups of Lie groups, low-dimensional geometry/topology, representation theory...

My Ph.D. thesis, defended on 12 November 2014 under the supervision of Yves Benoist, is entitled "Tilings of the affine space".

Here is my CV (latest update on 13 February 2024).

Publications and preprints

  1. I. Smilga. New sequences of non-free rational points, Comptes Rendus Mathématique 359:8 (2021) 983–989
  2. J. Kahn, V. Marković, I. Smilga. Geometrically and topologically random surfaces in a closed hyperbolic three manifold, submitted.
  3. I. Smilga. Action of w0 on VL: the special case of so(1,n), submitted.
  4. I. Smilga. Action of w0 on VL for orthogonal and exceptional groups, in V. Dobrev, editor, Proceedings of the XIV International Workshop "Lie Theory and Its Applications in Physics" (Sofia, Bulgaria, June 2021), volume 396 of Springer Proceedings in Mathematics and Statistics, pages 297–303. Springer Singapore, 2023.
  5. I. Smilga. Representations having vectors fixed by a Levi subgroup, Journal of Algebra 597 (2022) 75–115
  6. I. Smilga. Action of the restricted Weyl group on the L-invariant vectors of a representation, in V. Dobrev, editor, Proceedings of the XIII International Workshop "Lie Theory and Its Applications in Physics" (Varna, Bulgaria, June 2019), volume 335 of Springer Proceedings in Mathematics and Statistics, pages 365–372. Springer Singapore, 2020.
  7. B. Le Floch, I. Smilga. Action of Weyl group on zero-weight space, Comptes Rendus Mathématique 356:8 (2018) 852–858
  8. J. Danciger, T. A. Drumm, W. M. Goldman, I. Smilga. Proper actions of discrete groups of affine transformations (a survey paper), in D. Fisher, D. Kleinbock and G. Soifer, editors, Dynamics, Geometry, Number Theory: the Impact of Margulis on Modern Mathematics, pages 95–168. University of Chicago Press, 2022.
  9. I. Smilga. Construction of Milnorian representations, Geometriae Dedicata 206 (2020) 55–73
  10. I. Smilga. Proper affine actions: a sufficient criterion, Mathematische Annalen 382 (2022) 513–605
  11. I. Smilga. Proper affine actions in non-swinging representations, Groups, Geometry and Dynamics 12:2 (2018) 449–528
  12. I. Smilga. Proper affine actions on semisimple Lie algebras, Annales de l'Institut Fourier 66:2 (2016) 785–831
  13. I. Smilga. Fundamental domains for properly discontinuous affine groups, Geometriae Dedicata 171 (2014) 203–229
  14. I. Smilga. Harmonic functions on the Sierpinski triangle, 2012 (preprint).

Other productions

Teaching

I currently have no teaching load, but have done a lot of teaching previously. See my CV for an exhaustive list of courses I have taught.