Thursday, November 5, 2020

2020-11-06 / 15:30 ~ 16:30

by 최규동()

The Lamb dipole is a traveling wave solution to the two-dimensional Euler equations introduced by S. A. Chaplygin (1903) and H. Lamb (1906) at the early 20th century. We prove orbital stability of this solution based on a vorticity method initiated by V. I. Arnold. Our method is a minimization of a penalized energy with multiple constraints that deduces existence and orbital stability for a family of traveling waves. As a typical case, orbital stability of the Lamb dipole is deduced by characterizing a set of minimizers as an orbit of the dipole by a uniqueness theorem in the variational setting. This is a joint work with K. Abe (Osaka City Univ).

2020-11-12 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 콜로퀴엄: Homogeneous dynamics and Diophantine approximation

by 임선희(서울대학교)

The idea of using homogeneous dynamics to Diophantine approximation has grown to an active subfield of mathematics, with numerous results on Hausdorff dimension of sets of vectors with certain Diophantine properties. In this talk, we will start from scratch, from the Gauss map of the usual continued fraction expansion for real numbers and give a "dynamical interpretation" of Diophantine properties of continued fractions in terms of the orbits of the geodesic flow on the hyperbolic plane. We will then present a series of results of the speaker with coauthors on inhomogeneous Diophantine approximation and give ideas of proofs, especially the idea related to the partial proof of Littlewood conjecture of Einsiedler-Katok-Lindenstrauss. (The latter part of the talk is based on joint works with U. Shapira-N. de Saxce, Y. Bugeaud-Donghan Kim-M. Rams, and Wooyeon Kim-Taehyung Kim.)

2020-11-05 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 콜로퀴엄: Image Segmentation : old fashioned ways are still worthy

by 김윤호(UNIST)

In this talk, I will present a recent work in collaboration with physicists on the analysis of real time Transmission Electron Microscopy (TEM) images to understand molecular transition from crystal solid state to liquid state. Molecules are deposited on graphene with multilayer structures, which are projected and overlaid in noisy 2d TEM images. The problem is to find all the molecular centers in the extremely noisy 2d images where projected molecules are overlaid and to track the centers across the image frames. Before discussing the method that we considered, I will give a brief history in the development of image segmentation techniques with some theoretical and numerical details of old fashioned methods. Then, our method of image segmentation for molecular center identification follows.

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