Title: Arithmetic Dynamics, the geometric Frey-Mazur conjecture, and monodromy representations

Abstract: Which representations of the fundamental group of a complex quasiprojective variety X arise from geometry, i.e. appear inside of the monodromy representation on the cohomology of a family of varieties over X? I'll discuss new results on this topic arising from arithmetic dynamics, p-adic transcendence theory, and the geometric Langlands program. The talk will not assume familiarity with any of these topics.