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Informal Several Complex Variables Seminar (2025.11-2026.07)
The seminar aims to be a relaxed forum for researchers and graduate students interested in several complex variables and complex geometry,
and students of all levels are encouraged to attend and ask questions.
Some talks will be on zoom.
2025 Fall
November 4, 10am (Zoom: 811 5638 1768 (msrc))
Speaker: Zhiwei Wang (BNU) Title: Recent progress on the SOS conjecture Abstract: In this talk, we will introduce our recent progress on the study of the SOS conjecture (proposed by Ebenfelt),
which is closely related to the Huang-Ji-Yin gap conjecture in the study of rational proper maps between the
complex unit balls. This is based on joint work with Chenlong Yue and Professor Xiangyu Zhou.
November 12, 10am (Zoom: 811 5638 1768 (msrc))
Speaker: Yongxin Gao (NKU) Title: Corona Problem 及相关问题的简单介绍 Abstract: 我们将对 Corona Problem 的发展历史进行简单的梳理。具体包括如下内容：1. Corona Problem 与 Banach algebra；
2. 圆盘上 Corona Theorem 的证明；3. Corona Problem in SCV；4. Corona 集的拓扑及解析结构。
November 21, 10am (in person)
Speaker: Xingsi Pu (CQUT) Title: Kobayashi distance on complex domans II Abstract: We review some properties and results of Kobayashi distance.
November 26, 10am (Zoom: 8115638 1768 (msrc))
Speaker: Fei Tao (PKU) Title: Characterization of asymptotically smooth curves Abstract: We construct an example of an asymptotically conformal chord-are curve that fails to be asymptotically smooth.
This implies that a function belonging to both the little Bloch space and BMOA does not necessarily lie in VMOA,
and that a strongly quasi-symmetric homeomorphism which is symmetric is not necessarily strongly symmetrie. We also
provide a complete characterization of asymptotically smooth curves in terms of asymptotic conformal-ity and
uniform approximability.
December 5， 10am (Zoom: 8115638 1768 (msrc))
Speaker: Yaxiong Liu (UMD) Title: Recent progress on the YTD conjecture Abstract: Given a polarized manifold (X, L), The Yau-Tian-Donaldson conjecture predicts that the existence of constant scalar curvature
Kähler (cscK) metric in \(c_1(L)\) is equivalent to algebraic K-stability. Very recently, together with works of Chen-Cheng,
Chi Li and others, Boucksom-Jonsson and Darvas-Zhang independently prove a YTD corresponding for (weighted) cscK metries on smooth
manifolds. We will summary those breakthroughs. If time permits, we also discuss the existence on singular varieties.
December 12， 10am (Qiuzhen building 323) December 23， 10am (Zoom: 8115638 1768 (msrc))
Speaker: Xieping Wang (USTC) Title: Complex Geodesics and Complex Monge-Ampere Equations with Boundary Singularity Abstract: A complex geodesic ofa complex hyperbolic manifoldis by definition a holomorphie isometry from the hyperbolic discto the manifold.
Since Lempert’s groundbreaking work in 1981, complex geodesies and their applications have become an important research topic in several
complex variables and CR geometryIn this talk, I will present some recent results concerning the existence and uniqueness of complex geodesics
with preseribed boundary value and direction on strongly linearly convex domains in \(\mathbb{C}^n\) with \(\mathbb{C}^3\)-boundary, and applications to the existence and
regularityof solutions to a homogeneous complex Monge-Ampere equation with preseribed boundary singularity. This is based on two of my papers,
one of which is joint with Professor Xiaojun Huang.
January 12， 1-2pm (Qiuzhen building 429)
Speaker: Chenghao Qing (THU) Title: On the cohomology of pseudoeffective line bundles over holomorphically convex manifolds Abstract: We present a structure theorem for cohomology groupsof pseudo-effective line bundles over holomorphically convex Kähler manifolds, which generalizes
the results of Takegoshi, Demailly-Peternell-Schneider, Meng-Zhou. As applications, we first give ananswer to a question proposed by Matsumura,
and establish an injectivity theorem for purelylog terminal pairs generalized to pseudoeffective line bundles with transcendental singularities.
Then we show a Kawamata-Viehweg-Kollár-Nadel type vanishing theoremfor higher direet images in terms ofnumerical dimension for closedpositive currents
on compact Kähler manifolds. These are basedon works with Prof, Xiankui Meng, Hongzhao Sun, and Prof. Xiangyu Zhou.
January 15， 10am (Qiuzhen building 433, Zoom: 811 5638 1768 (msrc))
Speaker: Songyan Xie (CAS) Title: A Second Main Theorem for Entire Curves Intersecting Three Conics Abstract: We establish a Second Main Theorem for entire holomorphic curves \(f:\mathbb{C}\rightarrow\mathbb{P}^2\) intersecting a generic configuration of three conics
\(\mathcal{C}_1\), \(\mathcal{C}_2\) , \(\mathcal{C}_3\) in the complex projeetive plane \(\mathbb{P}^2\). By means of invariant logarithmic 2-jet differentials
with negative twist, weprove the estimate
$$T_f(r)\leq 5\sum_{i=1}^3N_f^{[1]}(r,\mathcal{C}_i)+o(T_f(r))\ \|, $$
where \(T_f(r)\)is the Nevanlinna characteristie function and \(N_f^{[1]}(r,\mathcal{C}_i)\) is the l-truncated counting funetion. This is joint work with Lei Hou, Dinh Tuan Huynh and Joel Merker.
January 19， 10am (Qiuzhen building 433, Zoom: 811 5638 1768 (msrc))
Speaker: Lei Zhang (THU) Title: Heat approximation to psh functions and regularity of solutions to CMA Abstract: In this talk, we will concern about the regularity of solutions to the complex Monge-Ampère equation on a compact Kähler manifold when the measure belongs to certain Orlicz space. We begin by
developing heat approximation techniques for psh functions, yielding an alternative proof of Demailly's regularization theorem on a compaet Kähler manifold. By combining a detailed study of heat approximation
to psh functions with our \(L^{\infty}\) and stability estimates, we proceed to establish the modulus of continuity of solutions to the complex Monge-Ampère equation. If time permitted,
we will discuss its related geometric applications. This talk based on a joint work with my advisor Prof. Zhenlei Zhang.
2026 Spring
April 10， 14:30-15:30pm (Qiuzhen building 106)
Speaker: Jiayang Yu (SCU) Title: 无限维空间中余任意维数曲面上的测度及Stokes型公式 Abstract: In this talk, we construct explicitly measures on general co-dimensional surfaces in \(\ell^2\) which is, in some sense, the simplest infinite-dimensional space, closest to Euclidean spaces,
but the construction of related surface measures is a longstanding unsolved problem. Our surface measures are naturally induced from the usual Gaussian measures on \(\ell^2\), based on which we introduce the notion of
differential forms and establish the corresponding Stokes type theorems.
April 20， 10:00-11:30am (Qiuzhen building 433)
Speaker: Zhangchi Chen (ECNU) Title: ： 有界数列的分布与Astorg-Boe Thaler问题 Abstract: 游荡域的存在性，是高维复动力系统中有趣的研究课题。Astorg-Boc Thaler利用指数增长的正整数列，构造了带游荡域的多项式斜积映射\(P:\mathbb{C}^2\to \mathbb{C}^2\)。由多项式$P$的系数可定义两个双全纯不变量(实数)\(\alpha, \beta\)其中\(\alpha>1\)。
A-B证明了给定\( (\alpha,\beta) \)，若存在正整数列\((n_k)\)使得相序列\(\sigma_k:=n_{k+1}-\alpha n_k-\beta \ln (n_k)\)收敛，那么\(P\)有游荡域。由此引发问题：哪些\((\alpha,\beta)\)具有使\((\sigma_k)\)收敛的\((n_k)\)？
A-B证明了\(\alpha\)必须是有Pisot性质的数。并且对\(\beta\)给出一个条件：\(\theta=(\beta\ln \alpha)/(\alpha-1)\)是有理数时，存在正整数列\((n_k)\)使得\((σ\sigma_k)\)收敛到一个周期。他们提问：\(\theta\)是有理数，是否是必要条件？
我和叶子豪、郑维喆合作，在\(\alpha\)是代数数的情形下，解决了A-B问题。假设\(\alpha\)是代数数，极小多项式为\(P(x)\)，那么\(P(1)\theta\)是整数，是存在正整数列\((n_k)\)使得\((\sigma_k)\)收敛的充要条件。作为在动力系统中的应用，我们构造了新的带有游荡域的多项式斜积映射。
April 29, 10--11.30am (Qiuzhen building 433)
Speaker: Xingsi Pu (CQUT) Title: The Corona problem and related results Abstract: In this talk, we will review the proof of the Corona theorem on the unit disk and discuss some results of the Corona problem in SCV.
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