The Matrix Spencer Conjecture for Finite Groups
Prior state unknown→proved
the group case; the full Matrix Spencer conjecture remains open
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probability-statistics / Discrepancy theory
The Matrix Spencer Conjecture for Finite Groups
The group version of the Matrix Spencer conjecture holds: for every finite group $G$ there are signs $\varepsilon \in \{\pm 1\}^G$ with $\left\|\sum_{g \in G} \varepsilon_g \rho(g)\right\| \le C\sqrt{|G|}$, where $\rho$ is the left regular representation and $C$ is universal.
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The group version of the Matrix Spencer conjecture holds: for every finite group $G$ there are signs $\varepsilon \in \{\pm 1\}^G$ with $\left\|\sum_{g \in G} \varepsilon_g \rho(g)\right\| \le C\sqrt{|G|}$, where $\rho$ is the left regular representation and $C$ is universal.
the group case; the full Matrix Spencer conjecture remains open
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