Ergys Çokaj

ESR 5:
Ergys Çokaj

My name is Ergys Çokaj and I come from Albania. I have completed my Bachelor and Master Degree in Mathematics and Applications at the University of Camerino in Italy.
Thanks to the study program I chose, I have gained a substantial knowledge base in pure mathematics and also in the applications of mathematics. During the academic years I have studied the fundamental bases of Analysis, Algebra and Geometry and then learned to illustrate their wide applications to Physics, Computer Science, Engineering, Statistics, Economics, and so on.
For my final projects I focused my research in the field of Geometry, respectively, my Bachelor’s thesis is entitled “Covering Spaces and Fundamental Group of a Topological Space” and the Master’s thesis is entitled “Generic Triangles in Hyperbolic and Spherical Geometry”.
A great important task during my Master degree was the study of probability, stochastic processes, dynamical systems, numerical methods for differential equations, machine learning and neural networks.
I have spent more than five years of studying in Italy and I do profoundly attest that I have had the chance to work and cooperate with very well prepared professors and colleagues from fascinating scientific backgrounds. This experience made me keen to enter in the tremendous world of mathematics.

I applied for the ESR5 position in the THREAD project because I see it as an extension of my study interests and I consider my background strongly related to the prerequisites for the project.
An exciting fact about THREAD is the direct opportunity to collaborate with researchers with different backgrounds, from all around the world.
I am enormously grateful for this given opportunity. My vivid qualities depend on honesty, consistency and zeal, always determined to perform the required tasks in a fruitful manner.
I am convinced that the experience of working on THREAD will strengthen my skills, increase my knowledge and change the way I see the world around me.


Host Institution
Norwegian University of Science and Technology (Norway)
Supervisor
Brynjulf Owren
Description

Study implementation issues for Lie group integrators and invariant preserving integrators. Results will include: 1) Variable step size Lie group integrators with error control; 2) Invariant preserving schemes for mechanical systems evolving on Riemannian manifolds; 3) Model reduction applied to large dynamical systems on Lie groups and manifolds.

Expected Results

New software generation for Lie group integration to be used for concrete applications from THREAD. For Lie group integrators with stepwise updated local coordinates standard error control from integrators on linear spaces can be applied. There is no such direct reference to coordinate charts for composition based Lie group integrators making them more tricky to work with (order conditions for non-commutative spaces). As for integral preserving schemes the use of retractions will be essential, in particular efficient maps based on geodesics. For large dynamical systems on manifolds the methodology for reducing the dimension will follow ideas from shape analysis, collaboration with ESR4 is natural.

Secondments

planned at TechnipFMC (industrial partner), Friedrich Alexander University Erlangen-Nuremberg and Martin Luther University Halle-Wittenberg

associated with the Industrial Challenge

IC 9 Software development


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