厦大数学科学学院和国家天元数学东南中心Colloquium系列报告

Colloquium at School of Mathematical Sciences, Xiamen University and Tianyuan Mathematical Center in Southeast China

Regular time and location: Unless otherwise specified each lecture is in 实验楼 105 from 4:30-5:30 PM on Thursday. Refreshments will be served from 4:00-4:30 PM outside the lecture room. Check the poster for more information.

This webpage is no longer updated, please check the official colloquium webpage at Tianyuan center for updated information.


2018-2019 2nd Semester (2019 Spring)

Schedule Rooms Topics
Thu 02/21 4:30 PM 数理楼 117 朱熹平 (中山大学) "Regularity of Harmonic Maps between Singular Spaces"

Abstract: M.Gromov and R.Schoen in 1992 initiated to study the theory of harmonic maps into singular spaces. In 1997, J. Jost and F. H. Lin, independently proved that every energy minimizing harmonic map from an Alexandrov space with curvature bounded from below to an Alexandrov space with non-positive curvature is locally H\"older continuous. Meanwhile, F.H.Lin proposed an open question: can the H\"older continuity be improved to Lipschitz continuity? J.Jost also asked a similar problem about Lipschitz regularity of harmonic maps between singular spaces. In this talk I will present an affirmative answer to it. This is a joint work with Hui-Chun Zhang.

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Thu 03/07 4:30 PM 数理楼 117 董彬 (北京大学) "Mathematical Modeling in Image Restoration, Image Analysis and Beyond"

Abstract: Image restoration, including image denoising, deblurring, inpainting, computed tomography, etc., is one of the most important areas in imaging science. In image restoration, wavelet frame based approach and PDE based approach (including variational models and PDE models) are two of the most successful approaches and are widely adopted in both academia and industry. The development of the two approaches followed rather different paths: wavelet frame based approach uses the tools from applied harmonic analysis and utilize sparsity to model images, while PDE based approach uses functions spaces and relies on geometry. Therefore, the two approaches are often considered as different approaches.

The first half of this talk is based on a series of papers, where we established rigorous and generic connections between wavelet frame and PDE based approach. This includes connections of wavelet frame based approach to total variation model, the Mumford-Shah model, and the total generalized variational model. Furthermore, connections of wavelet frame shrinkage to a rather general form of nonlinear evolution PDEs is also established, where the Perona-Malik equation, Osher-Rudin’s shock filters and Navier-Stokes image inpainting equation are special cases. Other than the establishment of the links between the two approaches, brand new models for both approaches are also discovered, which combine merits from both approaches, and thus outperform existing models in various applications in image restoration.

Our theoretical studies also enable us to connect mathematical modeling and computations with deep learning. The connections not only can provide guidance to deep network design, which is a central task in deep learning, but also enable us to tackle challenging problems in applied and computation mathematics. In the second half of my talk, I will present our recent work on bridging numerical differential equations with deep neural network design for various tasks of inverse problems, image processing and analysis.

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Thu 03/21 4:30 PM 实验楼 105 孙斌勇 (中国科学院数学与系统科学研究院) "李群的酉表示和轨道方法"

Abstract: 李群的酉表示是研究调和分析、量子力学和数论的重要工具。不可约酉表示是构成李群所有其他酉表示的基本单位。李群的不可约酉表示的构造和分类是表示论中备受关注的一个问题。Krillov等人发展的轨道方法说明李群的不可约酉表示和李群的余共轭轨道之间有密切的对应关系。我们将给出一些例子说明这个对应关系。

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Thu 04/04 4:30 PM 实验楼 105 Preda Mihăilescu (University of Göttingen) "Hilbert and the beginning of class field theory"

Abstract: In Hilbert's "Zahlbericht", the quintessence of the developments in algebraic number theory, at the end of the 19-th century were summarized by the great german mathematician. My talk will focus on the Theorems 90-94, which are known to provide the first major results of class field theory. The talk will discuss some new perspecitves on the classical theorems of Hilbert and use them for an exposition of the later developments in in one dimensional class field theory.

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Thu 04/18 4:30 PM Room 105 聂思安 (中国科学数学与系统科学研究所) "Geometric properties of affine Deligne-Lusztig varieties"

Abstract: Affine Deligne-Lusztig varieties (ADLVs) are natural analogues of classic Deligne-Lusztig varieties. The study of ADLVs arose from the field of arithmetic geometry, which plays an important role in the study of Shimura varieties. I will give a survey on the geometric properties of ADLVs, with an emphasis on recent progress.

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Thu 05/09 4:30 PM 实验楼 105 朱利平 (中国人民大学) "A two-sample test for equality of distributions in high dimensions"

Abstract: We propose a robust nonparametric two-sample test, which generalizes the Cram\'er-von Mises test through projections, to test for equality of two distributions in high dimensions. The population version of our proposed generalized Cram\'er-von Mises statistic is nonnegative and equals zero if and only if the two distributions are identical, ensuring that our proposed test is consistent against all fixed alternatives. In addition, our proposed test statistic has an explicit form and is completely free of tuning parameters. It requires no moment conditions and hence is robust to the presence of outliers and heavy-tail observations. We study the asymptotic behaviors of our proposed test under both the ``large sample size, fixed dimension" and the ``fixed sample size, large dimension" paradigms. In the former paradigm, we show that the asymptotic power of our proposed test does not depend on the size ratio of the two random samples. This ensures that our proposed test can be readily applied to imbalanced samples. In the latter paradigm, we observe that, surprisingly, the two distributions are equal if and only if their first two moments are equal. Therefore, we suggest to tailor our proposed test to detect location shifts and scale differences, which further enhances the power performance of our proposed test significantly. Numerical studies confirm that our proposals are superior to many existing tests in high dimensional two-sample test problems.

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Thu 05/16 4:30 PM Room TBA 杨彤 (香港城市大学) "Recent progress on the Boltzmann equation without angular cutoff"

Abstract: TBA.

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Thu 05/23 4:30 PM Room TBA 蔡剑锋 (香港科技大学) " Title TBA "

Abstract: TBA.

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Thu 05/30 4:30 PM 实验楼 105 程舜仁 (台湾数学研究院) " Representation Theory of Lie superalgebras in the BGG category "

Abstract: There has been much progress on the solution of the irreducible character problem for the complex simple Lie superalgebras in the so-called Bernstein-Gelfand-Gelfand category O over the last decade or so. The purpose of this talk is to first give a brief description of these simple Lie superalgebras and then to give an outline of these results.

Check the poster for more information.


Last modified: 05/09/2019.