Скачать или смотреть Tristan Ozuch : 4-dimensional specific aspects of Ricci flows

Ricci flow has been extensively studied, and most results are either true only in dimension 3 or hold in every dimension. However, given the potential topological applications, a theory specific to the 4-dimensional situation is desirable. In this discussion, I will present tools and techniques that are unique to the 4-dimensional case.
Together with A. Deruelle, we introduce a notion of stability for orbifold singularities. This notion helps to explain the formation of orbifold singularities along Ricci flow. Moreover, in collaboration with K. Naff, we utilize self-duality in dimension 4 to simplify the evolution equations of curvature. This approach lets us uncover intriguing connections between Ricci flow and Yang-Mills flow.