Author

Emrullah Akbas

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Preprint Sep 2026

Tighter bounds on Koml\'os discrepancy: existence and algorithmic results

Guo, Fang, and Lu recently proved the Koml\'os conjecture: for vectors $v_1,\ldots,v_n\in\mathbb R^d$ of Euclidean norm at most one, there are signs $\varepsilon_j\in\{-1,1\}$ with $\|\sum_j\varepsilon_jv_j\|_\infty\le3\sqrt{2\pi}$. We give a short proof of the bound $3\pi$ that keeps the geometric lifting framework of...

Emrullah Akbas, Suvrit Sra · 0 citations

Preprint Aug 2026

A Proof of the Matrix Spencer Conjecture

We develop a novel approach to matrix discrepancy based on matrix small-ball estimates. Specifically, we use a determinantal weight (obtained from the log-barrier) to scale the small-ball probability into a partition function of a tilt of the Gaussian measure. We then employ matrix-weighted Poincar\'e inequalities to c...

Emrullah Akbas, Suvrit Sra · 2 citations · ⚡1