Noncollapsed Ricci limit spaces and the codimension 4 conjecture

Geometry Topology Student Seminar
Wednesday, March 11, 2020 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 006
Xingyu Zhu – Georgia Tech
Sarah (Sally) Collins

In this talk we will survey some of the developments of Cheeger and Colding’s conjecture on a sequence of n dimensional manifolds with uniform two sides Ricci Curvature bound, investigated by Anderson, Tian, Cheeger, Colding and Naber among others. The conjecture states that every Gromov-Hausdorff limit of the above-mentioned sequence, which is a metric space with singularities,  has the singular set with Hausdorff codimension at least 4. This conjecture was proved by Colding-Naber in 2014, where the ideas and techniques like \epsilon-regularity theory, almost splitting and quantitative stratification were extensively used. I will give an introduction of the background of the conjecture and talk about the idea of the part of the proof that deals with codimension 2 singularities.