Differential and integral equations, boundary-value problems: solvability and uniqueness, examples of non-uniqueness, eigenfrequencies bounds;

Water waves and wave-body interaction: ship waves, wave resistance, sea-keeping problems, sloshing problems, stratified fluids, trapped modes;

Numerical evaluation of special functions, numerical integration of rapidly oscillating functions.

Scientific and publishing software, open source software: Linux (my favorite distributions are Debian and Linux Mint), TeX, Octave, Maxima, etc.

Some open source software projects and publications:

• Matlab/Octave code for evaluation of the Heun functions;
• refcheck — a package for LaTeX2e, which shows label's keys on margins and checks unused labels, unlabelled equations;
• tex4cream — A set of macros to improve usage of Vim + Cream as a LaTeX editor;
• ttf2mf — a converter of TrueType fonts to MetaFont source (sources of the program);
• i-v-p-cups — a set of interactive virtual printers (pdf, ps, djvu, gtklp) through a CUPS backend;
• search4gvim — enhanced Search and search&replace dialogs for GVim;
• showcmnd — a LaTeX2e style file to show definitions of TeX document in the typeset;
• WinEdt+Wine — Instruction for installation of WinEdt in Unices with Wine (in Russian, in English).