Geometry Seminar

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On forbidden configurations in point-line incidence graphs

Speaker: Nora Frankl, Open U UK

Location: Online

Date: Tuesday, November 25, 2025, 2 p.m.

Synopsis:

The celebrated Szemeredi-Trotter theorem states that the maximum number of incidences between n points and n lines in the plane is \(O(n^{4/3})\), which is asymptotically tight.

Solymosi conjectured that this bound drops to \(o(n^{4/3})\) if we exclude subconfigurations isomorphic to any fixed point-line configuration. We describe a construction disproving this conjecture. On the other hand, we prove new upper bounds on the number of incidences for configurations that avoid certain subconfigurations.

Joint work with Martin Balko.

Notes:

On Zoom.  Please contanct Boris Aronov to be put on the email announcement list and obtain Zoom details.