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Joint Chinese-Russian Mathematical Online Colloquium

Organizing Committee

  • Huijun Fan (SMS PKU)
    symplectic geometry and mathematical physics, geometric analysis
  • Sergey Gorchinskiy (MI RAS)
    algebra and geometry: algebraic geometry, K-theory
  • Hailiang Li (SMS CNU)
    fluid mechanics, partial differential equations, analysis
  • Jinsong Liu (AMSS)
    algebraic geometry: singularity theory
  • Yi Liu (BICMR)
    Topology of 3-manifolds, hyperbolic geometry
  • Denis Osipov (MI RAS)
    algebraic geometry, number theory, integrable system
  • Ye Tian (UCAS, AMSS)
    Number Theory, Arithmetic Geometry, Iwasawa Theory
  • Alexey Tuzhilin (MSU)
    geometry: Riemannian and metric geometry
  • Yue Yang (CE PKU)
    computation mathematics and mechanics
  • Ping Zhang (AMSS)
    P. D. E.: fluid equation and semi-classical analysis
  • Alexander Zheglov (MSU)
    geometry: algebraic geometry, integrable system


11:00 (GMT+3)
  Sheng Rao
Wuhan University

Bio: Sheng Rao received his PhD from Zhejiang University in 2011 and spent two more years there as a postdoctoral fellow. Then, he joined Wuhan University as a lecturer and has been a full professor since 2019. He is interested in several complex variables and complex geometry, especially deformation theory of complex structures.

Geometry of logarithmic forms and deformations of complex structures.

We present a new method to solve certain dbar-equations for logarithmic differential forms by using harmonic integral theory for currents on Kahler manifolds. As applications, we generalize the result of Deligne about closedness of logarithmic forms, give geometric and simpler proofs of Deligne's degeneracy theorem for the logarithmic Hodge to de Rham spectral sequences at E1-level, as well as certain injectivity theorem on compact Kahler manifolds. Our method also plays an important role in Cao--Paun's recent works on the extension of pluricanonical sections and proof of Fujino's injectivity conjecture.

Furthermore, for a family of logarithmic deformations of complex structures on Kahler manifolds, we construct the extension for any logarithmic (n,q)-form on the central fiber and thus deduce the local stability of log Calabi--Yau structure by extending an iteration method to the logarithmic forms. Finally we prove the unobstructedness of the deformations of a log Calabi--Yau pair and a pair on a Calabi--Yau manifold by differential geometric method. Its projective case was originally obtained by Katzarkov--Kontsevich--Pantev in 2008.

This talk is based on a joint work with Kefeng Liu and Xueyuan Wan.



12:00 (GMT+3)
  Sergey Suetin

Bio: Sergey Suetin is Doctor of physico-mathematical sciences and a Leading Scientific Researcher at Steklov Mathematical Institute of RAS. He is an expert in rational approximation of analytic functions, Pade approximation, inverse theorems, general orthogonal polynomials.

On extension of a power series outside of its disk of convergence.

The problem of computer extension of power series came from the papers by Milton Van Dyke in the 1970s and is related to the theory of perturbations in fluid mechanics. The seminal Stahl's Theory (1985-1986) provided the theoretical basis for the use of Pade approximations in solving this problem. The culmination of using Stahl's Theory is the development of HELM by Antonio Trias in 2012.

In the talk, we propose to discuss some other methods of power series extension based on rational Hermite-Pade approximations.

 The meeting will be held in the form of a webinar on the Voov platform.

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Meeting ID:638-406-013