Study complex analysis. It is a very pretty field which certainly has connections both to algebra (in fact, complex analysis grew out of the study of roots of polynomials) and to geometry - there are a lot of fascinating geometrical results in it, such as the famous Euler's formula for angles, e^i Theta=cos Theta + i sin Theta as one of the simplest examples. There is also the theory of conformal mappings and all sorts of beautiful results for analytic functions, e.g. the fact that a complex function which is smooth (i.e. differentiable) and non-constant must take every possible complex value (except possibly one point) - certainly not true for the real numbers! Once you have a good understanding of complex analysis, you can continue to study Riemann surfaces and topology. A lot of modern geometry and number theory grows out of these studies, e.g. the Riemann hypothesis which is very important in number theory, and Riemann surfaces which are strongly connected to models of spacetime, both started as part of complex analysis. Also the field has a huge number of applied results, e.g. in the area of differential equations and Fourier analysis. Once you have a good grounding in complex analysis, you can decide if you want to move into the later results (such as Weil's), which tend to be very sophisticated.