# Questions tagged [discrepancy-theory]

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### Partial crepant resolution in codimension 2

Let $\xi_5$ be a 5-root of the unity. We consider $\mathbb{C}^4/G$, where $G=\left\langle \sigma,\tau\right\rangle$, with $\sigma$ and $\tau$ the automorphisms given, respectively, by the following ...
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### Source request: Optimal bounds on signings of points from a convex body

I recently came across an old survey of problems in discrete geometry: https://pdfs.semanticscholar.org/c350/f4d4a9466fa6708d99ec1187c63d89bed20f.pdf Problem 2.1 from the list caught my eye. It states ...
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### Discrepancy bounds for moderate points counts in dimensions from d=2 to 32?

In one dimension d=1 an equally-spaced set of N points in [0,1) has the lowest possible (star) discrepancy D=0.5/N. Unfortunately, I found only asymptotic bounds for other dimensions (e.g. acc. to ...
3answers
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### Current state of the Komlos conjecture on vector balancing

Komlos Conjecture: the exists an absolute constant $K>0$ such that for all $d$ and any collection of vectors $v_1,\ldots, v_n\in \mathbb{R}^d$ with $\left\lVert v_i\right\rVert _2=1$ we can find ...
1answer
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### Quantified imbalance in signed graphs

Let $G=(V,E)$ be an $n$-vertex simple undirected graph. A signing of the graph is a function $s:E \to \{1,-1\}$, and $(G,s)$ is a signed graph. That is, we label each edge of the graph with $1$ or $-1$...
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1answer
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