Borcherds Products Everywhere Theorem

This is a report on my joint results with Cris Poor and David Yuen about
Borcherds Products on groups that are simultaneously orthogonal and symplectic,
the paramodular groups  of degree two and the elementary divisors (1,t).
This work began as an attempt to make Siegel paramodular cusp forms
that are simultaneously Borcherds Products and additive Jacobi lifts
(or Gritsenko lifts). We prove the Borcherds Products Everywhere
Theorem, that constructs holomorphic Borcherds Products from all
Jacobi forms that are theta blocks without theta denominator.