I am an applied mathematician primarily interested in real-life problems whose treatment requires analysis of a model / justification of the approximation or those that can be effectively tackled with analytical tools such as asymptotic methods or closed-form solution reducibility.

I enjoy learning new things while working on diverse subjects analyzing a problem, devising a constructive solution approach and verifying / implementing it numerically. The topics I have previously worked on include:

**wave propagation in porous media**(fluid / solid inclusion scattering for Biot elastodynamics equations);**nonlinear PDEs**(analysis of one NLS model for laser beams in photopolymers; Darboux transformation);**approximation theory**(approximation of square-integrable functions by traces of analytic functions with certain properties such as pointwise constraints);**integral equations**and**optimal bases construction**(spectral theory for compact one-dimensional self-adjoint integral operators with convolution kernels);**inverse magnetization problem**(analytical estimation of net magnetization moment components from partial measurements of magnetic field);**inverse obstacle problem**(determining domain geometry for transient wave equation from partial Dirichlet+Neumann data).

At the present time, I am a postdoctoral researcher (project assistant) at Insitute of Analysis and Scientific Computing, TU Wien, Austria.

Together with Anton Arnold, we are working on development and investigation of **hybrid asymptotic-numerical methods** aimed at efficient treatment of **high-frequency problems for wave equations**, in particular, using **long-time behaviour analysis** for **time-domain problems with variable coefficients**.

You can **contact me** by *email*: dmvpon@gmail.com / dmitry.ponomarev@asc.tuwien.ac.at, or find me at:

*Office DA 06 L14*, Institute of Analysis & Scientific Computing, Vienna University of Technology, Wiedner Hauptstrasse 8, Vienna, Austria.