Misha Rudnev "Erdös distance problem in positive characteristics"
Misha Rudnev from University of Bristol gave the talk "Erdös distance problem in positive characteristics" on the labs' Big Seminar.
Password: first 6 decimal places of $\pi$ after the decimal point
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Abstract:
We'll review the state of the art of the finite field version of the Erdös distinct distance problem and its variations. Recently there has been some interesting work in two and three dimensions. In particular, it was shown that in order that a point set in $F_p^2$ define a positive proportion of the feasible $p$ distances, its cardinality needs to be bigger than $p^{5/4}$. This improved the earlier lower bound $q^{4/3}$, which holds over $F_q$, and for $q$ non-prime cannot be improved. Coincidentally, the same quantitative improvement was recently made as to the Falconer problem in $R^2$, using decoupling, which seems to be very far from the incidence geometric approach over $F_p$ to be outlined.
Watch the video:
Everyone is invited to attend. The language of the lecture is English. The event is aimed at master and graduate students, as well as researchers in the field of combinatorics.