Consider the unnormalized Ricci flow ...Richard Hamilton showed that if the curvature operator is uniformly bounded under the flow for all times ... then the solution can be extended beyond T. In the thesis we prove that ...

In this thesis, the Hilbert scheme of lines on smooth hypersurfaces is studied. The main result is that the Hilbert scheme of lines on any smooth Fano hypersurface of degree d =/< 6 in ... has the expected dimension 2n - ...

We show that for a large class of torsionfree classifying spaces, K-theory filtered ring is an invariant of the genus. We apply this result in two ways. First, we use it to show that the powerseries ring on n indeterminates ...

The Minimal Model Program (in short, MMP) aims at classifying projective algebraic varieties from a birational point of view. That means that starting from a projective algebraic variety X, [Delta] it is allowed to change ...

The category of Segal spaces was proposed by Charles Rezk in 2000 as a suitable candidate for a model category for homotopy theories. We show that Quillen functors induce morphisms in this category and that the morphisms ...

Lithium-ion battery is a family of rechargeable batteries with increasing importance that is closely related to everyone's daily life. However, despite its enormously wide applications in numerous areas, the mechanism of ...