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Website of Bora Çalım

about me

• My surname is pronounced as /t͡ʃaˈɫɯm/
• A CV is available here (last updated February 2024). My email address can also be found in the CV. For any sort of mathematical discussion, do not hesitate to contact.
• As of 2024, I am a third year undergraduate student of mathematics at Koç University. I will be applying to graduate schools in fall 2024.
• I am mainly interested in additive combinatorics and its continuous analogues (“combinatorial” aspects of geometric measure theory). This means I try to understand questions of the form (stated vaguely on purpose) “how large should a set be in order to ensure it contains some configuration?”. This requires input from many different areas, including but not limited to harmonic analysis, number theory, and combinatorics.

mathematical writings (in chronological order)

• A self-contained exposition of a proof of Roth’s theorem. I wrote this as the “final report” of my independent study under Asgar Jamneshan in spring 2023. pdf. There are very few known typos, but often the correction is obvious so I didn’t bother to fix them.
• A summary of Ben Green’s notes on quadratic Fourier analysis, written for the summer school on analysis of multiple ergodic averages at Kopp in summer 2023. Joint with Nihan Tanısalı. Many details omitted due to space constraints. summary slides
• A self-contained exposition of the main result in Ben Green’s paper Arithmetic Progressions in Sumsets (GAFA 2002). Written as the final project of the course Topics in Additive Combinatorics in Spring 2024. pdf. Includes proofs of Bernstein, Khintchine, Rudin inequalities and Chang’s lemma also.