The doctoral dissertation in the field of聽Mathematics will be examined at the Faculty of Science, Forestry and Technology, Joensuu campus.
What is the topic of your doctoral research? Why is it important to study the topic?
My doctoral research topic is Nevanlinna theory, which is classical subjects in complex analysis. It has a wide range of applications, especially in equation solving. My thesis contains several Nevanlinna theory analogues and their applications. Specifically, we mainly study the difference version, Askey-Wilson version and tropical version of Nevanlinna theory, and explore their applications in the corresponding equations.
What are the key findings or observations of your doctoral research?
At first, we studied a class of delay-differential equations by a refined Nevanlinna theory approach. Then, we introduced an Askey-Wilson version of the Wronski-Casorati determinant and then established an Askey-Wilson version of the general form of the Second Main Theorem in projective space. Our result improves Chiang and Feng's Second Main Theorem for the Askey-Wilson operator. Lastly, we extended the tropical Nevanlinna theory for piecewise polynomial continuous functions. Then, not only was the n-th version of the Second Main Theorem for tropical homogeneous polynomials obtained, but also a tropical Second Main Theorem for ordinary Fermat type polynomials was acquired. Furthermore, we obtained a strong equality, which implies that there is no natural tropical truncated version of the Second Main Theorem for shift operators.
What are the key research methods and materials used in your doctoral research?
At first, by incorporating singularity confinement analysis, we improved the original Nevanlinna approach to study a more general class of differential-difference equations. Then, based on the original results and methods about Second Main Theorem, we got our second key result by generalizing a key lemma about the number of irreducible components of hypersurfaces. Lastly, wo introduced a lot of definitions to extend the original theory. Besides, there are also some methods that appeared for the first time.
The doctoral dissertation of Chengliang Tan, MSc, entitled Nevanlinna theory analogues and their applications will be examined at the Faculty of Science, Forestry and Technology, Joensuu campus. The opponent will be Associate Professor Jun Wang, Fudan University, P. R. China, and the custos will be University Lecturer, Docent Janne Heittokangas, 91天美. Language of the public defence is English.
For more information, please contact:
Chengliang Tan, chengtan@uef.fi, tel. +358 505 954 930
- Public examination
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