People

Masashi ISHIDA

Email	ishida(@math.sci.osaka-u.ac.jp)
Research	Differential geometry
Keywords	Einstein metrics, Ricci flow
URL

My research interest is in geometry, particularly,interaction between topology and differential geometry. For instance, I am studying the nonexistence problems of Einstein metrics and Ricci flow solutions on 4-manifolds by using the Seiberg-Witten equations. I am also interested in the geomery of the Yamabe invariant. The computation of the Yamabe invariant for a given manifold is a difficult problem in general. By using the Seiberg-Witten equations, I determined the exact value of the Yamabe invariant for a large class of 4-manifolds which includes complex surfaces as special cases. Furthermore, I am also interested in both the Ricci flow in higher dimension and some generalized versions of the Ricci flow like the Ricci Yang-Mills flow. The Ricci flow was first introduced by R. Hamilton in 1981 and used as the main tool in G. Perelman's solution of the Poincare conjecture in 2002. Perelman introduced many new and remarkable ideas to prove the conjecture. The theory developed by Hamilton and Perelman is now called the Hamilton-Perelman theory. One of my recent interests is to investigate geometric analytical properties of the generalized versions of the Ricci flow from the Hamilton-Perelman theoretical point of view.