Gradient shrinking Ricci solitons play an important role in understanding the formation of singularities of the Ricci flow. In two and three dimensions, they have been fully classified by the work of Hamilton, Perelman etc. The problem becomes difficult in four dimensions and seems impossible in higher dimensions due to many "non-standard" examples. In this talk, I will present some classification results for gradient shrinking Ricci and Kahler-Ricci solitons under some invariant nonnegativity curvature conditions. This is joint work with Professor Lei Ni.

Bio: Xiaolong Li is currently a Britton Postdoctoral Fellow at McMaster University. He received his PhD from University of California San Diego in 2017 under the supervision of Prof. Lei Ni and Prof. Ben Chow. From 2017 to 2020, he was a Visiting Assistant Professor at University of California Irvine supervised by Prof. Richard Schoen. He works in geometric analysis, particularly in Ricci flow, eigenvalue estimates, and modulus of continuity estimates.