My interests in mathematics and physics:

  • Topology: l2 methods in topology, low-dimensional manifolds, differential topology (Morse theory and surgery), classification of manifolds, hyperbolic geometries
  • Geometric group theory: random groups, coarse embeddings into Hilbert spaces, Kazhdan's Property (T)
  • Differential geometry: foliations, mapping class groups, exotic differential structures on manifolds
  • Quantum relativistic theory of information: what happens with the wave function of particle when it's falling into a black hole? How the curvature of space influence the quantum mechanics in this space?
  • Special and general relativity: Thomas-Wigner precession, flow of time in the curved space, black holes, geometry of the universe
Hopf fibration

Hopf fibration of the 3-dimensional sphere


Publications:
Notes and other works:
Problems I am working on:

Links to mathematical pages with content connected with my research: