University of Birmingham > Talks@bham > Analysis Seminar > How big is the set of values of a bilinear form on a point set in 2D?

How big is the set of values of a bilinear form on a point set in 2D?

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One of my favourite open questions in discrete geometry is: given a set P of N points in the plane and a non-degenerate bilinear form B, what is the minimum cardinality, in terms of N, of the set (if non-empty) of nonzero values of B(p,q), with p,q in P. The same question can be asked in geometric measure theory in terms of dimension. The conjectured answer is N, possibly up to logarithms, but the state of the art is far from it. The question may seem similar to the renown problem of Erdos/Falconer about distances, but at a closer look turns out to be different, and probably more difficult—the latter problem has been resolved. The talk will focus on the machinery used, results available, and connections to other questions of geometric/arithmetic combinatorics.

This talk is part of the Analysis Seminar series.

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