We study the Iwasawa $\mu$- and $\lambda$-invariants of the non-primitive plus/minus Selmer groups of elliptic curves for supersingular primes. We prove that they are constant for a family of elliptic curves with the same residual representation if the $\mu$-invariant of any of them is 0. As an application we find a family of elliptic curves whose plus/minus Selmer groups have arbitrarily large $\lambda$-invariants.

We study global log canonical thresholds of singular cubic surfaces.

We study the structure of the moduli space of principally polarized abelian varieties in characteristic p. In this paper we determine the configuration of the central streams in the moduli space. As a corollary of our proof we obtain a new proof of the dimension formula of the central streams.

The Ricci flow on a compact four-manifold preserves the condition of pointwise 1/4- pinching of flag curvatures. Any compact Riemannian four-manifold with 1/4-pinched flag curvatures is either isometric to $\Bbb C\Bbb P^{2}$ or diffeomorphic to a space-form.

We introduce certain conformal, rotationally symmetric, real analytic perturbations of the standard Euclidean metric on $S^2$ and study the perturbed eigenvalues of the Laplace operators for the metrics sufficiently close to the Euclidean metric.