Kudla's modularity conjecture for cycles of codimension 2

We establish Kudla's modularity conjecture for the generating function 
of special cycles of codimension 2.  The proof is based on a 
convergence result for formal Fourier Jacobi expansions.  We define 
such expansions in some simple cases, and outline the approach taken to 
show that they always converge.  Finally, we showcase the connection to 
previous results by Zhang, which yields the desired proof of Kudla's 
conjecture.