4-dimensional specific aspects of Ricci flows

Abstract: 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.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

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CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

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