Geometry:
metric geometry, including Riemannian and Finslerian geometry, theory of singular spaces and asymptotic geometry.
Key words:

	asymptotic geometry,
	hyperbolic spaces,
	Alexandrov spaces,
	boundary rigidity,
	Finslerian geometry,
	minimal fillings,
	graph-manifolds,
	geometric aspects of dynamical system and inverse problems of mathematical physics.

Topology:
algebraic geometry, including topology of algebraic manifolds, low-dimensional topology, general topology.
Key words:

	real and complex algebraic manifolds,
	tropical geometry,
	homotopic groups,
	Vassiliev invariants,
	low-dimensional topology,
	groups of braids and links,
	knot theory,
	space structures.