David Urbanik, of the Institute for Advanced Study, presents a seminar talk on the geometry of abelian varieties, joint work with Greg Baldi. He defines the Bezout range: given a simple abelian variety A and subvarieties X and Y, the pair sits inside the range when the sum of their dimensions is at least the dimension of A. Urbanik shows that pairs inside the range always intersect, and that multiplying Y by a suitable endomorphism n forces a proper intersection while producing an analytically dense family of such intersections with X. He then turns to pairs outside the Bezout range, arguing that X and nY almost never meet, with torsion points as the sole exception. Delivered as part of the IAS special year learning seminar, the talk assumes familiarity with algebraic geometry and moves through definitions, theorems, and proof sketches on the chalkboard rather than slides.