Noncollinear points in the projective plane

Abstract: We will look at the space of n points in the projective plane such that no three lie on the same line. There is an action of the symmetric group by permuting the points and we can compute the action on cohomology (for n < 7) by counting the numbers of such n tuples over the finite field F_q, with a 'twist'. Unfortunately for n > 6 such a computation is still hard and we expect the answer for large n to be arbitrarily complicated (in the sense of Mnëv's universality). This talk will be based on joint work with Ben O'Connor.

algebraic geometryalgebraic topologynumber theory

Audience: researchers in the topic

CMI seminar series

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