New expansion results via spectral graph theory

Polynomial expansion concerns the heuristic expectation that, for a typical polynomial P in n variables over a field F and subsets A₁,...,A_n of F, the image P(A₁,...,A_n) is substantially larger than each of the individual sets A_k. We establish new expansion results for certain classes of polynomials over finite fields, including a classification result for ternary quadratic polynomials. Our methods rely on spectral bounds for certain graphs arising from incidence geometry. This is joint work with Sam Chow.

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There will be coffee and cake after the seminar in the common room.