We extend tropicalization and tropical compactification of subvarieties algebraic tori to spherical homogeneous spaces. Given a subvariety, we show that the support colored fan ambient variety agrees with subvariety. The proof is based on our equivariant version flattening by blow-up theorem. provide many examples.

In this thesis, we develop methods for efficient simulation of biomolecular electrostatics based on Poisson-Boltzmann equation. Current techniques using finite-difference solution of differential formulation have many drawbacks. We present an integral formulation that resolves these difficulties and enables an efficient implementation using a recently developed fast solver. The new approach can...