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Abstract: Finite type conditions arise naturally during the study of weakly pseudoconvex hypersurfaces in $\mathbb{C}^n$, which are defined to measure to degeneracy of the Levi form. Let $M$ be a pseudoconvex hypersurface in $\mathbb{C}^n$, $p\in M$, and let $B$ be a subbundle of the CR tangent bundle $T^{(1,0)}M$. The commutator type $t(B,p)$ measures the number of commutators of the sections of $B$ and their conjugates needed to generate the contact tangent vector at $p$. The Levi type $c(B,p)$ is concerned with differentiating the Levi form along the sections of $B$ and their conjugates. It is believed that these two types are the same, which is known as the generalized D'Angelo Conjecture. In this talk, I shall talk about the recent progress on this conjecture, which is based on the joint works with X. Huang and P. Yuan.
Bio: Wanke Yin is a professor at Wuhan University. He received his PhD degree from Wuhan University in 2008, and has been working there ever since. Professor Yin's primary research interest is Several Complex Variables and related fields.
