I'm finishing my undergraduate mathematics programme this summer. The graduate program at my university requires that you specify a specialization on entry. This is very difficult for me and would like some advise. I have no experience with the third set. (Courses I liked: Groups, fields and Galoistheory, algebraic topology)
The possible sets to choose from are :
Set 1 "Algebraic geometry & Number Theory":
Algebraic Geometry, Algebraic Number Theory, p-adic Numbers, Elliptic Curves, Diophantine Equations, Modular Forms, Analytic Number Theory, Riemann Surfaces.
Set 2 "Differential geometry & Topology":
Homotopy Theory, Homological Algebra, Sheaf Theory, Knot Theory, Quantum groups and Knot theory, Category Theory, Simplicial sets, K-theory and vector bundles, nalysis on Manifolds, Symplectic Geometry, Foliation Theory, Riemannian Geometry, Lie groups, Semisimple Lie Algebras, Differential Topology.
Set 3 "Logic":
Model Theory, Proof Theory, Computability Theory, Intuitionism, Category Theory, Topos Theory, Peano Arithmetic and Gödel Incompleteness, Set Theory, Type theory and $\lambda$-calculus.
Which one has the most algebraic 'flavour' to it