I am interested in mathematical methods in fluid dynamics, biology and other areas of science, nonlinear PDEs, optimal transport, gradient flows, metric geometry, geometric flows, nonlinear functional analysis, attractors.

 

The major part of my publications is related to functional analysis and/or PDEs. Here is the full list, and below are the links to the lists by particular areas.

!! indicates the areas on which I am working right now.

 

Optimal transport, gradient flows, metric geometry !!

 

Inextensible string and non-standard variants of the mean curvature flow !!

 

Imaging

 

Mathematical  analysis of viscoelastic fluids

 

Mathematical  analysis of anomalous diffusion in polymers

 

Brownian motors

 

Trajectory attractors

 

Dissipative solutions to PDEs

 

1-, p(x)- and infinity-Laplacian

 

Bioconvection 

 

Singular directions in crystals

 

 

 

 

 

Other topics