Hi, I'm Jalil!
A CS & Math undergraduate student at National University of Singapore.
The Problem I'm working on
Erdös Problem 106
Draw \( n \) squares inside the unit square with no common interior point. Let \( f(n) \) be the maximum possible sum of the side-lengths of the squares. Is \( f(k^2 + 1) = k \)?
Current thoughts / Sketch:
It's easy to show \(f(k^2 + 1) \geq k\) with a simple example and it's conjecture that \(f(k^2 + 1) = k\) holds. Baek et al. showed that if we further assume that sides of all squares are parallel to the sides of the unit square, then the maximum total side length of \(k^2 + 1\) squares is \(k\). See https://arxiv.org/abs/2411.07274.
Date: Dec 25, 2025
Random Updates
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May 2026: Started the RIPS 2026 summer research program.
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May 2026: Completed my UROP project on the Polynomial Freiman–Ruzsa Theorem.
About Me
A quick peek into my academic journey and research interests.
Education & Interests
I am currently a final-year Computer Science and Mathematics student at the National University of Singapore (NUS). My academic focus is on Theoretical Computer Science, Distributed Algorithms, and Mathematics.
GPA: 4.86 / 5.00 (Highest Distinction)
Honors & Awards
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2x Dean's List
National University of Singapore (NUS) - AY24/25 Sem 2, AY25/26 Sem 1 View Certificates ↗
Teaching Experience
I have served as a Teaching Assistant for undergraduate courses at NUS.
Teaching Assistant
Aug 2024 - May 2025National University of Singapore
- Parallel and Distributed Algorithms (AY 25/26 Sem 2) : Conducting weekly consultation sessions for students to help them to understand the topics better.
- Introduction to AI & ML (AY 24/25 Sem 2) : Conducted weekly tutorials and graded weekly problem set submissions.
- Linear Algebra for Computing (AY 24/25 Sem 1) : Conducted weekly tutorials and created challenging quiz questions.
Math Outreach & Problem Setting
- ●Math Proofs Expert (Mercor): Worked with leading AI Research Labs on improving LLM performance on advanced mathematical problem solving by reviewing 1,000+ model-generated responses.
- ●Problem Author: Authored an original geometry problem that was shortlisted for the Junior Balkan Mathematical Olympiad (JBMO) 2023.
- ●National Team Coach: Coached the Azerbaijan National Team for Junior Balkan Math Olympiad 2024 (Team achieved 2nd place among 20+ countries).
My Research & Projects
- Blockchain Protocols: Researching novel blockchain protocols under the supervision of Assoc. Prof. Haifeng Yu as part of my Final Year Project.
- Polynomial Freiman–Ruzsa Theorem (UROP Project): Proposed an alternative formulation of the Polynomial Freiman–Ruzsa Theorem under Assoc. Prof. Divesh Aggarwal.
- Sparse Autoencoders in LLMs: Applied Sparse Autoencoders to improve LLM performance for low-resource languages. See paper.
Major Courses
CS Courses
- CS1101S: Programming Methodology A-
- CS1231S: Discrete Structures A+
- CS2030S: Programming Methodology II B+
- CS2040S: Data Structures & Algorithms A
- CS2100: Computer Organisation A-
- CS2109S: Introduction to AI & Machine Learning A
- CS3230: Design & Analysis of Algorithms A
- CS3231: Theory of Computation A-
- CS3263: Foundations of Artificial Intelligence A+
- CS4231: Parallel & Distributed Algorithms A
- CS4234: Optimisation Algorithms A+
- CS4261: Algorithmic Mechanism Design A+
Math Courses
- MA1521: Calculus for Computing A
- MA1522: Linear Algebra for Computing A+
- MA2101: Linear Algebra II A
- ST2334: Probability and Statistics A+
- MA2214: Combinatorics & Graphs I A+
- MA3233: Combinatorics and Graphs II A+
- MA2108: Mathematical Analysis I A+
- MA3210: Mathematical Analysis II A-
- MA3209: Metric and Topological Spaces A+