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, this result, known as the Modularity Theorem, lies at 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.
I study Deformations of Galois Representations and Frey-Mazur Conjecture. Aside from pure math, I also conduct research on Mathematical Creativity and Instructional Methods, Mathematics Education for Gifted Students, and Sports Analytics.
Research Papers:
In preparation:
5. Bingol, B (2026). Skill, Luck, and Parity in College Football.
4. Bingol, B. (2026). Unobstructed Deformation Rings in the Level Aspect.
Submitted:
3. Bingol, B. (2026). A Local-Global Study of Obstructed Deformation Problems II. Submitted. arXiv:2606.23918 [math.NT].
2. Bingol, B. (2024). A Local-Global Study of Obstructed Deformation Problems I. Submitted. arXiv:2404.01414 [math.NT].
Published:
1. Bingol, B. and Ozyaprak, M. (2025). Enhancing Higher Education: Differentiating the Curriculum and Instruction to Foster Mathematical Creativity and Motivation. The Journal of Creative Behavior, 59(2).
Here, you can find a concise version of my CV (last update on July 6th, 2026).