Petr Naryshkin’s Homepage

I am now a Member at the Institute for Advanced Study. Before that, I was a postdoc in the DYNASNET project at Alfréd Rényi Institute of Mathematics. I did my PhD at the University of Münster (supervised by David Kerr). I am interested in various properties of infinite groups and their actions on measure spaces, topological spaces, and C*-algebras. So far, I have worked on the following topics:

  • Topological versions of the Rokhlin Lemma; classifiability of crossed products; mean dimension and shift embeddability
  • Hyperfiniteness of countable Borel equivalence relations
  • Quantitative orbit equivalence

CV (updated 04.10.24)

Publications

  1. with S. Petrakos, Quantitative orbit equivalence for \mathbb{Z}-odometers, preprint
  2. with A. Vaccaro, Hyper-u-amenability and Hyperfiniteness of Treeable Equivalence Relations, preprint
  3. URP, comparison, mean dimension, and sharp shift embeddability, preprint
  4. with E. Gardella, S. Geffen, R. Gesing, G. Kopsacheilis, Essential freeness, allostery and \mathcal{Z}-stability of crossed products, preprint
  5. with S. Petrakos, Almost finiteness and groups of dynamical origin, Int. Math. Res. Not. IMRN 2025(3), rnaf016, preprint
  6. with A. Vaccaro, Hyperfiniteness and Borel asymptotic dimension of boundary actions of hyperbolic groups, Math. Ann. 392(2025), p. 197–208, preprint
  7. Group extensions preserve almost finiteness, J. Funct. Anal. 286(7) (2024), 110348, preprint
  8. with E. Gardella, S. Geffen, J. Kranz, A. Vaccaro, Tracially amenable actions and purely infinite crossed products, Math. Ann. 390(2024), p. 3665–3690, preprint
  9. with E. Gardella, S. Geffen, A. Vaccaro, Dynamical comparison and \mathcal{Z}–stability for crossed products of simple C*-algebras, Adv. Math. 438 (2024), preprint
  10. with E. Gardella, S. Geffen, J. Kranz, Classifiability of crossed products by nonamenable groups, J. Reine Angew. Math. 797 (2023), p. 285–312, preprint
  11. Polynomial growth, comparison, and the small boundary property, Adv. Math. 406 (2022), preprint
  12. with D. Kerr, Elementary amenability and almost finiteness, preprint
  13. with L.M. Lerman, A.I. Nazarov, Abundance of entire solutions to nonlinear elliptic equations by the variational method, Nonlinear Anal. 190 (2020)
  14. A remark on the isomorphism between the Bernoulli scheme and the Plancherel measure, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 468 (2018); translation in J. Math. Sci. (N.Y.) 240 (2019)

Contact info

penaryshkin at ias dot edu