讨论班与学术活动
Kahler-Ricci Flow 讨论班
2021年春季学期，每周二、周四下午14:00-17:00
参考文献：
[1] Valentino Tosatti: Kawa Lecture notes on the Kahler Ricci Flow.
Deformation Theory
2021年秋季学期，每周三下午14:00-17:00
参考文献：
[1] Christian Schnell: Deformation of Complex Structures.
[2] Norihito Koiso: A Decomposition of the Space M of Riemannian Metrics on a Manifold.
[3] Norihito Koiso: Rigidity and Stability of Einstein Metrics - the case of complex symmetric space.
[4] Norihito Koiso: Rigidity and infinitesimal deformability of Einstein metrics.
[5] Xianzhe Dai, Xiaodong Wang, Guofang Wei: On the Stability of Riemannian Manifold with Parallel Spinors.
[6] Xianzhe Dai, Xiaodong Wang, Guofang Wei: On the Variational Stability of Kahler-Einstein Metrics.
GIT讨论班
2022年春季学期：古典GIT理论
参考文献：Nolan R. Wallach 《Geometric Invariant Theory》
2022年春季学期、2022年秋季学期：Canonical Metric on Complex Vector Bundle
Atiyah’s GIT picture:
[1] Atiyah & Bott “The Yang-Mills Equations over Riemann Surface” 主讲：游磊、周可树
Donaldson’s GIT picture:
[2] Donaldson “Lower bounds on the Calabi functional” 主讲：田珺昊
Slope Stable v.s. YHM:
[3] Donaldson “Anti self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles” 主讲：张文嘉
[4] Donaldson “Infinite determinants, stable bundles and curvature”
[5] Uhlenbeck & Yau “On the Existence of Hermitian-Yang-Mills Connection in Stable Vector Bundles”
Gieseker Stable v.s. Balanced Condition:
[6] Wang Xiaowei “Balance Point and Stability of Vector Bundles over a Projective Manifold”
[7] Wang Xiaowei “Canonical metrics on stable vector bundles”
cscK v.s Balanced condition: 【待定】
Kahler-Einstein、scsk
2021年秋季学期，
参考文献：
Calabi 猜想、Yau 定理：
[1] ShingTung Yau: On The Ricci Curvature of a Compact Kahler Manifold and the Complex Monge-Ampere Equation.
[2] HuaiDong Cao: Deformation of Kahler metrics to Kahler-Einstein metrics on compact Kahler manifolds.
Futaki 不变量：
[1] Gang Tian: On Kahler-Einstein metrics on certain Kahler manifolds with C_1(M)>0.
[2] Gang Tian: On Calabi's conjecture for complex surfaces with positive first Chern class.
[3] WeiYue Ding, Gang Tian: Kahler-Einstein metrics and the generalized Futaki invariant.
[4] Gang Tian: Kahler-Einstein metrics with positive scalar curvature.
锥奇点 K-E 度量：
[5] S. K. Donaldson: Kahler metrics with cone singularities along a divisor.
[6] Chi Li, Song Sun: Conical Kahler-Einstein Metric Revisited.
[6] Song Sun, Simon Donaldson: Gromov–Hausdorff limits of Kahler manifolds and algebraic geometry.
K稳定与K-E度量：
[7] XiuXiong Chen, Simon Donaldson, Song Sun: Kahler-Einstein metrics on Fano manifolds, I: approximation of metrics with cone singularities.
[8] XiuXiong Chen, Simon Donaldson, Song Sun: Kahler-Einstein metrics on Fano manifolds, II: limits with cone angle less than 2π.
[9] XiuXiong Chen, Simon Donaldson, Song Sun: Kahler-Einstein metrics on Fano manifolds, III: limits as cone angle approaches 2π and completion of the main proof.
csck：
[1] XiuXiong Chen: On the existence of constant scalar curvature Kahler metric: a new perspective.
[2] XiuXiong Chen, JingRui Cheng: On the Constant Scalar Curvature Kahler Metrics (I)-Apriori Estimate.
[3] XiuXiong Chen, JingRui Cheng: On the Constant Scalar Curvature Kahler Metrics (II)-Existence Results.
[4] XiuXiong Chen, JingRui Cheng: On the Constant Scalar Curvature Kahler Metrics (III)-General Automorphism Group.
