Much appreciated proof of Wiles and Taylor verified the Taniyama-Shimura Conjecture for semistable elliptic curves, which implied Fermat's Last Theorem. Then, the proof is generalized for all elliptic curves over rational numbers. Now, it -known as the Modularity Theorem- is lying on the heart of the modern number theory, and what I research about is related to the tools (in particular Galois Deformations) developed during the discovery of the Modularity Theorem. Roughly, Modularity Theorem states that the Galois representation attached to an elliptic curve coincides with the Galois representation attached to some special type of modular form of weight 2 of level N, where N is the conductor of the elliptic curve. This coincidence is indeed a part of a bigger picture called Langlands Program.
As of September 2024, I study Deformations of Galois Representations, Twists of Modular Curves, and Frey-Mazur Conjecture. Aside from pure math, I conduct research on Mathematical Creativity and Instructional Methods, and Mathematics Education for Gifted Students.
Papers:
(Published in Journal of Creative Behavior) Enhancing Higher Education: Customizing the Curriculum and Instruction to Foster Mathematical Creativity and Motivation (in collaboration with Melodi Ozyaprak)
(submitted) A Local-Global Study of Obstructed Deformation Problems of Galois Representations - I
Here, you can find a concise version of my CV (last update on July 23rd, 2025).