On the connection of PDE, Probability and other Mathematics fields


2018.02.18(일) ~ 02.21(수)               곤지암리조트


Title&Abstract Home > Title&Abstract


김판기 (서울대학교)

- Title: Heat kernel estimates for symmetric jump processes with general mixed polynomial growths

- Abstract: In this talk, we discuss transition densities of pure jump symmetric Markov processes in R^d, whose jumping kernels are comparable to radially symmetric functions with general mixed polynomial growths. Under some mild assumptions on their scale functions, we establish sharp two-sided estimates of transition densities (heat kernel estimates) for such processes.

This is a joint work with Joohak Bae, Jaehoon Kang and Jaehun Lee.


선해상 (UNIST)

- Title: Dynamical study of continued fraction and its generalization

- Abstract: It is conjectured that the length of continued fraction behaves asymptotically like a random variable with the Gaussian distribution. This conjecture was proved by Baladi and Vallee in an average sense by studying spectral properties of transfer operator associated with a dynamical system for the Gauss map on the unit interval. In the talk, we generalize their work to a skewed dynamical system and obtain spectral properties of the corresponding transfer operator. As results, we present some number theoretical applications. This is joint work with Jungwon Lee.


남영우 (홍익대학교)

- Title: Renormalization and Hénon map in dynamical systems

- Abstract: Renormalization theory of one dimensional maps has been a topic in dynamical systems for decades. Hénon map is the two dimensional map to describe the perturbation of homoclinic tangency. In this talk, the period doubling renormalization of one dimensional map is introduced in view of smooth dynamical systems. More recently Hénon map and renormalization was combined by Martens and Lyubich. If the time permitted, then the renormalization of one dimensional holomorphic maps would be discussed very briefly.


강성모 (전남대학교)

- Title: Knots, 3-manifolds and Dehn surgery

- Abstract: In this talk, I introduce some background on knots and 3-manifolds and then present my current research. The two topological concepts, knots and 3-manifolds are very closely related through Dehn surgery. In other words, the complement of a knot in the 3-sphere is a 3-manifold with torus boundary. Gluing a solid torus along the common torus boundary yields a new 3-manifold. This process is called Dehn surgery. I will talk about which knots allow which 3-manifolds through Dehn srugery. Lastly, I will present my current research which is the study on hyperbolic knots admitting Seifert-fibered Dehn surgery.


권봉석 (UNIST)

- Title: A brief review of shock and rarefaction waves arising in hyperbolic system of conservation laws

- Abstract: We present a fundamental theory of shock and rarefaction waves for hyperbolic conservation laws. As a simple model, the p-system in one space dimension, which is one of the simplest hyperbolic model arising in gas dynamics, will be discussed. If time permits, we talk about some interesting issues for these waves, for instance, the stability of shock waves and the asymptotic behavior of rarefaction waves.


양종호 (고려대학교)

- Title: Difference of weighted composition operators

- Abstract: We characterize the joint Carleson measure for the difference of weighted composition operators acting on the weighted Bergman space. From Littlewood-Paley identity, the weighted composition operator on weighted Bergman space is closely related to composition operator on the classical Hardy space. In contrast to the case of weighted Bergman space, the compactness for the difference of composition operators on Hardy space is not yet characterized. As an application for the Carleson measure criterion, we show that the Moorhouse condition is equivalent to compactness of the difference of composition operator on Hardy space provided that inducing symbols are univalent.


최규동 (UNIST)

- Title: 1D Models of 2D Inviscid Boussinesq System

- Abstract: In connection with the recent proposal for possible singularity formation at the boundary for solutions of three-dimensional axisymmetric incompressible Euler’s equations (Luo and Hou, Proc. Natl. Acad. Sci. USA (2014)), we study models for the dynamics at the boundary and show that they exhibit a finite-time blowup from smooth data.