Talk 1（13:00 - 14:15）

Speaker：李子鈺 Li, Ziyu

Title:

Kobayashi Conjecture and Siu's Strategy

Abstract:

The famous conjecture of Shoshichi Kobayshi is that a generic algebraic hypersurface of dimension n and of sufficiently large degree d ≥ d_n in the complex project space \mathbb{P}^{n+1} is hyperbolic. A fundamental vanishing theorem states that any entire curve must satisfy some differential equations. If there are enough independent differential equations, then all entire curves must be constant. Based on this observation, Yum-Tong Siu presented his proof in 2015.

Talk 2 （14:30 - 15:45）

Speaker：冯境 Feng, Jing

Title:

4d N=1 AdS/CFT correspondence for three dimensional quotient singularity

Abstract:

We study the AdS/CFT correspondence induced by D3 branes probing three dimensional Gorenstein quotient singularity C^3/G. The field theory is given by the McKay quiver, which has a vanishing NSVZ beta function assuming that all the chiral fields have the U(1)_R charge 2/3. Various physical quantities such as quiver Hilbert series, superconformal index, central charges, etc. are computed from both the field theory and the gravity side. Our computation gives confirmation that the McKay quiver indeed gives one description of the SCFT on D3 branes probing the quotient singularity.

Talk 3 （16:00 - 17:15）

Speaker：缪铭昊 Miao, Minghao

Title:

Optimal Degenerations of K-unstable Fano Threefolds

Abstract:

In this talk, we will propose a question of how to explicitly determine the optimal degenerations of the K-unstable Fano manifolds as predicted by the Hamilton-Tian conjecture. We answer this question for a family of K-unstable Fano threefolds (No 2.23 in Mori-Mukai's list), which has discrete automorphism groups and the normalized Kahler-Ricci flow develops Type II singularity. Our approach is based on a new method to check weighted K-stability, which generalizes Abban-Zhuang's theory to give an estimate of the weighted delta invariant by dimension induction. Some speculative relations between the delta invariant and the H invariant will also be discussed. This is based on a joint work with Linsheng Wang.