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2025 KSCW, Capturing Additive structures via Gowers Norms
I am an undergraduate student in the Department of Mathematics at Yonsei University in Korea.
My research interests lie in additive combinatorics, especially in structure-randomness dichotomies discovered in sets with some underlying algebraic structure. I am interested in approaches using Gowers norms and other Fourier analytic techniques. I am also highly interested in higher-order Fourier analysis itself. My interest in additive combinatorics was motivated by Roth's theorem and Szemerédi's theorem, so I am interested in any type of problems related to the solution set of linear configurations inside a given set of integers. Also, I am interested in measuring the randomness of a given subset of an abelian group.
I am currently participating in DAISY, a student seminar at Yonsei University.
My emali is: jihyochae@yonsei.ac.kr
Seminars on Gowers Norms
Summer 2025
Jul 1, Intro: Modern view on the circle method, Capturing randomness in a subset of Z
Jul 11, Quadratic Fourier Analysis, I: Generalized von Neumann Theorems for k=2, 3 in the finite field model [reference]
Jul 24, Quadratic Fourier Analysis, II: Gowers Inverse Theorem for k=3 - Gowers inverse theorems in the finite field model
Fall 2025
Sep 21, Quadratic Fourier Analysis, III: Gowers Inverse Theorem - Finding a quadratic character with large correlation
Sep 26, Quadratic Fourier Analysis, IV: Gowers Inverse Theorem - concluding the proof in the finite field setting
For more details, please visit the seminar page.
Experiences
Spring 2025
Peer Tutor, Algebra (1) (Yonsei Doksuri Peer Tutoring Program)
Grants
2021-2025
Presidential Scholarship for Science, Korea Student Aid Foundation
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