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 from 4:30-5:00 PM on Thursday in 数理楼 Room 117. Refreshments will be served from 4:00-4:30 PM outside the lecture room.


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 Room TBA 孙斌勇 (中国科学院数学与系统科学研究院) "Low degree cohomologies of congruence groups"

Abstract: We prove the vanishing of certain low degree cohomologies of some induced representations. As an application, we determine certain low degree cohomologies of congruence groups. Basic theory of continuous cohomologies, and Franke's filtration of the space of automorphic forms will be reviewed. This is a joint work with Jian-Shu Li.

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Thu 04/18 4:30 PM Room TBA 聂思安 (中国科学数学与系统科学研究所) " Title TBA "

Abstract: TBA.

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Thu 05/09 4:30 PM Room TBA 朱利平 (中国人民大学) "Title TBA "

Abstract: TBA.

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Thu 05/16 4:30 PM Room TBA 杨彤 (香港城市大学) " Title TBA "

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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Last modified: 01/10/2019.