Dark energy and exotic R4

To develop mathematical analysis on the dark energry and accelerating universe, we should study Lorentz geometry, Riemannian geometry, nonlinear elliptic partial differentia equations on a noncompact space (space with infinite size), especially the behavior on the ends at infinity, and new framework on those issues. We took an algebraic-complex analytic approach to these problems. We investigated the behavior of the vector spaces called "conformal blocks" at the infinity of moduli spaces of compact Riemann surfaces, and developped the theory of spectral analysis of the operator algebras asssociated with these.