Incidences: Lower Bounds (part 8)

We continue to survey the known lower bounds for incidence problems (the previous post in this series can be found here). After a couple of posts in {\mathbb R}^3  we now return to {\mathbb R}^2  , to introduce a new technique that I recently learned about. This technique was discovered by Jozsef Solymosi, and is described in a work of Solymosi and Endre Szab√≥ that is unpublished at this point. As seems to often be the case with results of Solymosi, it is quite simple and elegent. In {\mathbb R}^2  this technique yields bounds that can also be obtained from Elekes’ technique (discussed in a previous post), but in higher dimensions it leads to new bounds that are also tight (which would hopefully discuss in a future post). I would like to thank Jozsef Solymosi for allowing me to describe his technique in this blog, and to Frank de Zeeuw for discussions that led to this post.

Jozsef Solymosi.

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