Incidence Theory and Uniform Distribution in Higher Dimensions

Incidence bound for points and spheres in higher dimensions generally becomes trivial in higher dimensions due to the existence of the Lenz example consisting of two orthogonal circles in ℝ4, and the corresponding construction in higher dimensions. There are several natural assumptions one can make to get around these examples. We shall survey some of these and focus on uniformly distributed sequences of points on the torus. This is joint work with Ayla Gafni and Emmett Wyman.