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Website of Bora Çalım

about me

• My surname is pronounced as /t͡ʃaˈɫɯm/
• A CV is available here (last updated November 2024). My email address can be found in the CV. For any sort of mathematical discussion, do not hesitate to contact.
• As of fall 2024, I am a fourth year undergraduate student of mathematics at Koç University, and I am applying to graduate schools.
• I describe my mathematical interests as "developing and using techniques for estimating quantities, especially of combinatorial interest". This includes but is not limited to quantitative aspects of additive combinatorics, "real-variable" harmonic analysis, combinatorial aspects of geometric measure theory.

Publication(s)

1. Popular differences in primes along fractional powers, joint with I. Iakovakis, S. Long, J. Moffatt, D. Wooton, preprint, 2024. Slides (many details skipped due to time constraint)

informal mathematical writings (in reverse chronological order)

• 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.
• 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 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.