In very general terms, my research interests concern problems that arise in continuum mechanics. I am interested in studying physical phenomena that occur due to the presence of small length scales, for example, the structure and dynamics of defects in crystal.

Specialization

Analysis of theoretical aspects of defects (dislocation, phase boundary, and crack) in crystals using Hamiltonian mechanics (continuum elastodynamics and lattice dynamics) and analytical techniques in applied mathematics.

Research Interests

Continuum Mechanics and Thermodynamics, Lattice Dynamics, Dislocations, Brittle Fracture, Solid-Solid Phase transformation, Wave Scattering, Nonlinear Elasticity, Discrete Mechanics.

Geometric Algorithms, Symplectic Algorithms, Structure of Hamiltonian Systems, Toeplitz Operator Theory, Calculus of Variations, Difference Calculus, Fourier Analysis, Special Functions.

``Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of

physics where experiments are cheap.” - V. I. Arnold

``genuine mathematicians do not gang up, but the weak need gangs in order to survive” - I. G. Petrovskii

(for science in modern times, a relevant quote as recollected by V. I. Arnold)

``The only instruction which a teacher can give, in my opinion, is to think in front of his students.” - Henri Lebesgue