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Applications of small Kakeya sets over finite fields
It was proved by Dvir that a Kakeya set in $\mathbb{F}_q^n$ has size at least $q^n/n!$, a bound which was later improved to $q^n/2^n$.
For $n = 2$ and $q$ odd the exact bound is $q(q+1)/2 + (q-1)/2$ …
8
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Where have you used computer programming in your career as an (applied/pure) mathematician?
My PhD supervisor and I discovered a new near octagon, related to the finite simple group $G_2(4)$, using a computer. From this we were able to give a construction of the full Suzuki tower, which was …