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Website of Bora Çalım

about me

• A CV is available here (last updated June 2025). My email address can be found in the CV. For any sort of mathematical discussion, do not hesitate to contact.
• I will start my PhD in mathematics at Rutgers University in Fall 2025. Prior to this, I was an undergraduate at Koç University.
• I describe my mathematical interests as "developing and using techniques for estimating quantities, especially of combinatorial interest". This includes but is not limited to "real-variable" harmonic analysis, quantitative aspects of additive combinatorics, analysis of boolean functions, and 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, submitted, 2024. [1.1] Slides (many details skipped due to time constraint) Comments: There is not much in the slides. A highlight in the paper is bounding an exponential sum involving the floor function using the Erdos-Turan inequality.

informal mathematical writings (in reverse chronological order)

• [A4] Slides from a private presentation on amenability with a view towards pointwise ergodic theorems, including a proof of equivalent characterizations of amenability (following Kerr and Li) and a counterexample of Emerson.
• 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. [A3] pdf. Includes proofs of Bernstein, Khintchine, Rudin inequalities and Chang’s lemma also. Comments: The definition of dissociativity here can be weakened to "every element of S and 0 (zero) can be written in at most one way as a ±1-linear combination of elements of a subset of S" (so from the definition in the text we are allowing a ±2 coefficient in at most one element) without changing any of the proofs.
• 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. [A2.1] summary, [A2.2] slides. Comments: The summary contains a 1-page synopsis of the U³ inverse theorem, with some elaboration in the 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. [A1] pdf. There are very few known typos, but often the correction is obvious so I didn’t bother to fix them. Comments: There is not much to learn here unless you are looking for a "speedrun" towards Roth.

A remark on pronunciation: My surname is pronounced as /t͡ʃaˈɫɯm/. If you cannot pronounce /ɯ/, the schwa /ə/ is an acceptable substitute, however it might be awkward to pronounce that in the stressed syllable for native English speakers. In this case even /ɪ/ is an acceptable substitute. In any case, it is more important to NOT pronounce the first letter as /k/ or /s/.