Since October 2017 I am Postdoctoral Associate in the Faculty of Mathematics of University of Vienna.
Currently, I am a Research Fellow at the Faculty of Mathematics of University of Vienna and a Docent at the Faculty of Mathematics of Samarkand State University.
My CV is here.
Research interests
My general research interests are in calculus of variations and
geometric measure theory (CVGMT) and spectral theory (ST). More precisely:
existence and regularity in CVGMT:
free boundary problems (with or without elastic energy)
including boundary discontinuities such as partitions, internal cracks,
wetting, edge delaminations, debonding, brittle fractures;
(anisotropic and crystalline) minimal surfaces;
capillarity problems; area functional;
higher order problems related to perimeter (such as Willmore problem);
evolution in CVGMT:
geometric evolution problems
such as (anisotropic and crystalline) mean curvature flow, mean
curvature flow of partitions; quasitatic evolution problems of
elastic materials; nonlocal evolution problems;
discrete Schrodinger operators in ST:
coupling constant threshold phenomenon;
multiparticle lattice systems, location of essential spectrum,
existence of discrete spectrum, Efimov effect; asymptotics of
eigenvalues.