Colloquium/Seminar

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Event(s) on December 2016


  • Thursday, 8th December, 2016

    Title: Computational Quasi-conformal Geometry and Medical Imaging
    Speaker: Dr. Jeffery Ka Chun Lam, The California Institute of Technology, USA
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Quasi-conformal mapping, which was introduced by Gro¨tzsch (1928) and named by Ahlfors (1935), is a homeomorphism between plane domains which can be viewed as a generalization of conformal mapping. Intuitively, a quasi-conformal mapping takes small circles to small ellipses of bounded eccentricity. Mathematically, a function or mapping f : Ω → Ωt, where Ω and Ωt are two domains in C, is quasi-conformal if it satisfies the Beltrami equation ∂f = µ(z) ∂f for Some complex-valued Lebesgue measurable function µ satisfying 1µ1∞ < 1. Over the last 90 years, numerous important theories of quasi-conformal mappings have been discovered. Yet, computation of these mappings has not been developed or utilized in real applications. Therefore, we propose Computational Quasi-conformal Geometry on discrete surfaces (such as meshes or point clouds), develop theories and various numerical methods, which has shown to be useful in many different fields, especially for medical imaging. In this talk, some recent development about medical imaging and computational Quasi-conformal geometry techniques will be discussed.


  • Monday, 12th December, 2016

    Title: Photo-acoustic and Thermo-acoustic tomography in an inhomogeneous medium
    Speaker: Dr. YANG Yang, Department of Mathematics, Purdue University, USA
    Time/Place: 15:30  -  16:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Photo-acoustic and Thermo-acoustic tomography are hybrid medical imaging modalities where optical waves or electromagnetic waves and ultrasound waves are coupled.  The propagation of ultrasound waves is typically modeled as an inverse source problem for the acoustic wave equation. In this talk we discuss the inverse source problem in an inhomogeneous medium where the wave speed is variable. Two types of measurement are to be considered: one from pointwise detectors while the other from large planar detectors. We prove uniqueness and stability on the recovery of the source, and give reconstruction procedures for the source or its singularities. This is based on joint work with Plamen Stefanov.


  • Tuesday, 20th December, 2016

    Title: Spectral properties of the Poincaré-Neumann  operator and pointwise estimates on the gradients in 2D composite media
    Speaker: Prof. Eric Bonnetier, Universite Joseph Fourier, France
    Time/Place: 11:30  -  12:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: The Neumann-Poincare operator is an integral operator that appears in the integral representation of solutions to transmission problems in piecewise homogeneous media. We study its spectral properties for a system of 2 smooth inclusions in 2D. As the inter-inclusion distance $delta$ vanishes and as the coefficient contrast degenerates, the behavior of the spectrum is related to the possible blow-up of the solutions to the corresponding elliptic transmission problem. This is joint work with Faouzi Triki (Université Grenoble-Alpes).


  • Thursday, 22nd December, 2016

    Title: Solving steady incompressible Navier-Stokes equations by the Arrow-Hurwicz method
    Speaker: Prof. Jianguo Huang, Shanghai Jiaotong University, China
    Time/Place: 11:30  -  12:30
    Abstract: This talk is concerned with analyzing an Arrow-Hurwicz type method for solving incompressible Navier Stokes equations discretized by mixed element methods. Under several reasonable conditions, it is proved by a subtle argument that the method converges geometrically with a contraction number independent of the finite element mesh size $h$, even for regular triangulations. Several numerical examples are provided to show the computational performance of the method. Finally, it is also shown briefly that the method can also be extended as an algorithm framework to numerically solve multi-physics problems. This is a joint work with Puyin Chen, Binbin Du and Huashan Sheng from Shanghai Jiao Tong University.