Hello!

My name is Gentian Zavalani. I am a PhD student at the Institute of Numerical Mathematics, TU Dresden, Germany. My supervisors are Oliver Sander and Michael Hecht.

During my PhD, I focused on numerical methods for solving partial differential equations (PDEs) posed on smooth two-dimensional surfaces embedded in $R^3$. My work is motivated by applications in biology and physics and involves developing fast algorithms and spectral methods for solving PDEs efficiently on 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 partial differential equations on static and dynamic surfaces

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

📘 This semester I am teaching a course on Approximation Theory at TU Dresden.
The course discusses both the theoretical foundations and practical aspects of approximating and interpolating functions, with a focus on high-order polynomials, trigonometric series, and rational functions.

📝 The lecture notes on Approximation Theory are available here “Approximation Theory” and are continuously updated throughout the semester.