Upcoming Seminars
Dear Invited Speakers, the registration procedure consists of two steps:
- Please click on the date you are interested in to reserve it. For example, click on "November 13, 2025".
- You may submit your talk title and abstract later, once finalized, by clicking on "here" in the corresponding form.
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September 18, 2025
Introduction to modern complex dynamics
In this presentation, I will give an introduction to complex dynamics. I will start with some historical reminders in dimension 1, presenting a few tools that lie at the heart of modern techniques, such as potential theory and ergodic theory. Then, I will explain the questions that interest researchers in modern dynamics, in dimension 1 or higher, and if time permits, I will try to make a connection with famous problems that do not directly involve dynamics but for which recent progress has been made using complex dynamics methods.
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September 25, 2025
Introduction to modern complex dynamics II
This presentation will be a continuation of the one initiated last week. This time, I will focus on the case of higher dimension. We will see that the concepts introduced last week in the one-dimensional setting can be extended to higher dimensions. The main difference between dimension one and higher dimensions is essentially the emergence of a new concept: the notion of positive currents. This concept generalizes the notion of functions or measures, which are predominant in dimension one. Currents are formally differential forms, but with non-smooth coefficients, they serve as a bridge between geometry and analysis, and are particularly well-suited for addressing problems in dynamics. I will also present some new results I have recently obtained on the dynamics of endomorphisms of projective spaces.
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October 9, 2025
Hongyi Sheng
Localized Deformations and Gluing Constructions in General Relativity
Gluing constructions of initial data sets play an important role in general relativity. Earlier in 1979, Schoen-Yau used gluing constructions with conformal deformations as a crucial step in their proof of the famous positive mass theorem. Corvino later refined this approach by introducing localized deformations that preserve the manifold's asymptotic structure. In this talk, I will survey recent theorems on localized deformation and their applications regarding rigidity and non-rigidity type results. I then outline extensions of these results to manifolds with boundary, including asymptotically flat regions outside black-hole horizons, and conclude with a brief discussion of the analytic challenges that arise in this boundary setting.
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October 16, 2025
An introduction to the p-adic Riemann-Hilbert correspondence
The classical Riemann-Hilbert correspondence describes the relationship between local systems and flat connections on a projective smooth variety. In my talk, I will talk about its variant in the p-adic setting: I will elaborate all known results on p-adic Riemann-Hilbert correspondence, based on the works of Scholze, Liu-Zhu, Gao-Min-Wang and others.
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October 23, 2025
Differential-Geometric Curvature Positivity and Rational Connectedness
Recently, we proved that a compact Kähler manifold has rational dimension at least n-k+1 if its tangent bundle is BC-p positive for every p≥k. This curvature positivity, introduced by L. Ni, can be guaranteed by various differential-geometric curvature positivity of the tangent bundle, such as positive holomorphic sectional curvature, mean curvature positivity, uniformly RC-positivity and etc. We demonstrate that this positivity naturally arises in a Bochner-type formula associated with the MRC fibration. As a new application in a broader context, we answer a question posed by F. Zheng, Q. Wang, and L. Ni, namely, that any compact Kähler manifold with positive orthogonal Ricci curvature must be rationally connected. Additionally, I will introduce our earlier work, which generalizes Yau's conjecture on positive holomorphic sectional curvature to the quasi-positive case via a Bochner-type integral inequality. These works are joint with Xi Zhang.
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October 30, 2025
Recent breakthroughs on completing general period mappings
Since Griffiths' question in the 70's, it is a long-standing problem to find a completion of general period mapping with significant geometric and Hodge-theoretic meaning. The classical theories on the compactification of locally symmetric varieties by Satake—Baily—Borel and Mumford et al provide such completions to a very limited set of "classical" cases, while the problem has been almost completely open for non-classical cases until recent years. I will report the latest progress in this direction including several of my papers. Collaborators include Chongyao Chen (IMFP Shanghai), Colleen Robles (Duke), Jacob Tsimerman (Toronto).
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November 6, 2025
Mingchen Xia
The trace operator of Kähler currents
In the study of plurisubharmonic singularities on projective manifolds, it is important to make induction on the dimension of the underlying manifold. It is therefore desirable to have a well-behaved restriction operator of closed positive (1,1)-currents T from a manifold X to a divisor D. When D is in general position, the analytic Bertini theorems show that the naïve restriction is well-behaved. While for special D, the naïve restriction may fail to give useful information. I will explain how to define a correct restriction (called the trace operator) in this case. This talk is based on a joint work with T. Darvas.
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John Doe
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November 20, 2025
Liu Yuning
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November 27, 2025
Zhixin Wang
Recent breakthroughs on completing general period mappings
In this paper, we derive the first and second variation formulas for the renormalized area for static Einstein spaces along a specific direction, demonstrating that the negativity of the Neumann data implies instability. Consequently, we obtain a rigidity result for the case when the conformal boundary is a flat torus, which strengthens a previous theorem.
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December 4, 2025
Dekai Zhang
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December 11, 2025
Takumi Otani
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December 18, 2025
Yoshi
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December 25, 2025
Junhao Tian
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John Doe
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John Doe
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John Doe
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John Doe
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John Doe
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John Doe
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John Doe
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John Doe
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John Doe
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John Doe
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John Doe
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John Doe
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John Doe
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John Doe
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John Doe
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John Doe
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John Doe
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John Doe
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John Doe
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John Doe
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John Doe
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John Doe
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John Doe
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John Doe
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John Doe
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John Doe
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John Doe
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John Doe
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John Doe
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John Doe
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John Doe
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