Dmitrii Zakharov


Lower bounds for incidences 

We consider a problem about lower bounding the number of incidences between points and tubes in the plane under natural spacing conditions. As a corollary of our results, we show that any collection of n points in the unit square contains three points forming a triangle of area at most n^{-7/6+o(1)}, improving on previous bounds. We discuss finite field and higher dimensional variants of the problem and the limitations of our method. Joint work with Alex Cohen and Cosmin Pohoata.