we consider some recent applications of techniques of p-adic analysis to algebra and geometry. specifically, we consider three applications. first, we show that it gives a solution to a problem of keeler, rogalski, and stafford asking to show that if the orbit of a point under an automorphism of a complex projective variety has the property that it intersects some subvariety infinitely often then the orbit cannot be zariski dense. next, we show that one can give a new proof of a result of bass and lubotzky showing that the burnside problem has an affirmative solution for automorphism groups of quasiprojective varieties. finally, we consider an application that gives a result of bogomolov and tschinkel: a k3 surface defined over a number field $f$ with an infinite automorphism group has a dense set of $k$-points for some finite extension of $f$. this includes joint work with dragos ghioca, zinovy reichstein, daniel rogalski, sue sierra, and tom tucker.