Venue: 129-101, Sangsan Mathematical Building, Seoul National University, Seoul, Korea
Title and Abstracts
Title: Spreading fronts in an anisotropic Allen-Cahn equation
Abstracts: In this talk I will discuss the long time behavior of spreading fronts in anisotropic Allen-Cahn type nonlinear diffusion equations on R^N. Here, the term spreading fronts roughly means expanding level surfaces of solutions with compactly supported initial data. Among other things I show that the shape of the spreading front converges to the Wulff shape associated with the anisotropic term of the equation. This is joint work with Yoichiro Mori and Mitsunori Nara.
(Sophia University, Professor Emeritus; Seki Kowa Institute of Mathematics)
Abstracts: I started my academic career as a pure mathematician, majored the theory of generalize functions (distributions of Laurent Schwartz, hyperfunctions of Mikio Sato, etc.) and wrote my Ph.D. thesis on the theory of hyperfunctions in 1968. Later around 1990, I found a Japanese mathematician called Takebe Katahiro (1664-1739) very interesting and read his works seriously. In my talk, I will talk on the shift of my research interest.
Title: Construction of vector solution for elliptic systems
Abstracts: I would like to introduce recent progresses on construction of solutions for elliptic systems where all components of the solutions are positive functions and asymptotic behavior of the solutions with respect to some parameters.
Title: Synthesis of flocking and synchronization: From Winfree to Cucker-Smale
Abstracts: In this talk, we will briefly survey a recent progress on the flocking and synchronization. In particular, we present a unified framework on the emergence of collective behavior of complex systems such as flocking and synchronization.
Title: An over-determined boundary value problem arising from neutrally coated inclusions in three dimensions.
Abstracts: We consider the neutral inclusion problem in three dimensions which is to prove if a coated structure consisting of a core and a shell is neutral to all uniform fields, then the core and the shell must be concentric balls if the matrix is isotropic and confocal ellipsoids if the matrix is anisotropic. We first derive an over-determined boundary value problem in the shell of the neutral inclusion, and then prove in the isotropic case that if the over-determined problem admits a solution, then the core and the shell must be concentric balls. As a consequence it is proved that the structure is neutral to all uniform fields if and only if it consists of concentric balls provided that the coefficient of the core is larger than that of the shell.
Title: Gaussian free field, conformal field theory, and Schramm-Loewner evolution
Abstracts: Several interfaces in critical planar lattice models have been proven to have conformally invariant scaling limits, which are described by Schramm-Loewner evolution (SLE). As the remarkable achievements of complex analytic/probabilistic methods, Lawler-Schramm-Werner's work and Smirnov's work will be discussed. The main ingredient of these methods is to find SLE martingale-observables. After presenting the precise relation between SLE and conformal field theory, I will describe some SLE martingale-observables in terms of correlation functions in a family of statistical fields generated by background charge modification of the Gaussian free field. This is a joint work with N. Makarov.
Abstracts: