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Explore the intersection of planar incidence geometry and projection theorems in this 49-minute lecture by Joshua Zahl. Delve into the theory of lens counting and its applications in proving projection theorems, drawing from joint research with Malabika Pramanik and Tongou Yang. Examine the Martens projection theorem, recent developments, and new problems in this field. Gain insights into the discretization process and analysis techniques used in studying arrangements of curves in the plane.