Hello!

My name is Gentian Zavalani. I am currently a Wrap-up Postdoc at the Institute of Numerical Mathematics, TU Dresden, Germany.

I completed my PhD under the supervision of Prof. Oliver Sander and Prof. Michael Hecht.

During my PhD, I focused on the development and analysis of numerical methods for partial differential equations (PDEs) posed on smooth two-dimensional surfaces. My work is motivated by applications in biology and physics and aims at designing fast and accurate algorithms for complex geometries.

It centers on three main themes:

• High-order polynomial approximations of curved surfaces
• Accurate computation of surface integrals
• Fast direct solvers for elliptic PDEs on static and evolving surfaces

Figure: Left to right — baseline pattern, and patterns produced by linear, quadratic, and cubic coupling in an interacting Turing system.

📘 Winter Semester 2025/26 (WiSe 2025/26):
I taught a course on Approximation Theory at TU Dresden.
The course covered both the theoretical foundations and practical aspects of function approximation and interpolation, with a focus on high-order polynomials, trigonometric series, and rational functions.

📝 Lecture notes are available here “Approximation Theory”.