세미나 및 콜로퀴엄

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구글 Calendar나 iPhone 등에서 구독하면 세미나 시작 전에 알림을 받을 수 있습니다.

Consider a simple symmetric random walk $S$ and another random walk $S'$ whose $k$th increments are the $k$-fold product of the first $k$ increments of $S$.
The random walks $S$ and $S'$ are strongly dependent. Still the 2-dimensional walk $(S, S')$, properly rescaled, converges to a two dimensional Brownian motion. The goal of this talk is to present the proof of this fact, and its generalizations. Based on joint works with K. Hamza and S. Meng.

Host: paul jung     영어     2017-02-21 14:37:05

Originated from applications in signal processing, random evolution,
telecommunications, risk management, financial engineering,
and manufacturing systems, two-time-scale Markovian systems have
drawn much attention. This talk discusses asymptotic
expansions of solutions to the forward equations, scaled and unscaled
occupation measures, approximation error bounds, and associated
switching diffusion processes. Controlled dynamic systems will also
be mentioned.

Host: paul jung     영어     2017-02-21 13:21:06

Many problems in control and optimization require the treatment

of systems in which continuous dynamics and discrete events

coexist. This talk presents a survey on some of our recent work on such

systems. In the setup, the discrete event is given by a random

process with a finite state space, and the continuous component is the

solution of a stochastic differential equation. Seemingly similar

to diffusions, the processes have a number of salient features

distinctly different from diffusion processes. After providing

motivational examples arising from wireless communications,

identification, finance, singular perturbed Markovian systems,

manufacturing, and consensus controls, we present necessary and

sufficient conditions for the existence of unique invariant

measure, stability, stabilization, and numerical solutions of

control and game problems.

 

 

Host: 김재경     영어     2017-02-21 12:23:17
The Siegel series is the local factor of the Fourier coefficient of the Siegel-Eisenstein series. It is also a crucial ingredient in Kudla's program to compare it with intersection numbers.
In this talk, I will explain a conceptual reformulation of the Siegel series. As the first application, I will explain a conceptual (and simple) proof of the equality between intersection number and the (derivative of) Siegel series. As the second application, I will explain a newly discovered identity between them. This is a joint work with T. Yamauchi.
Host: 임보해     미정     2017-02-10 12:42:59

재미로 풀어보는 퀴즈에나 등장할 법한 추상적인 수학적 개념이 기계공학(예, 응용역학) 연구에 도움을 줄 수 있을까? 수학과 역학 사이의 간극이 가장 좁았던 때는 언제였고, 수학과 역학이 만나는 지점에서 두 학문을 두루 섭렵했던 수리과학자는 누구였을까? 이와 같은 질문에 대한 답변의 일환으로, 본 발표의 전반부에서는 수학과 역학(유체역학, 고체역학, 열역학, 파동학)의 역사가 공존했던 시절을 인물 중심으로 살펴보고자 한다. 본 발표의 후반부에서는, 역학적 파동과 메타물질에 관한 발표자의 연구주제(음향 투명망토, 음향 블랙홀, 생물음향학 등)를 간략하게 소개한다.

 

 

 

Host: 임미경     한국어     2017-02-21 12:27:23

In this talk, we summarize results concerning anomalous behaviour of random walks and diffusions in disordered media. Examples of disordered media include fractals and various models of random graphs, such as percolation clusters, random conductance models, ErdH{o}s-R'enyi random graphs and uniform spanning trees.

Geometric properties of such disordered media have been studied extensively and their scaling limits have been obtained. Our focus here is to analyze properties of dynamics in such media. Due to the inhomogeneity of the underlying spaces, we observe anomalous behaviour of the heat kernels and obtain anomalous diffusions as scaling limits of the random walks. We will give a chronological overview of the related research, and describe how the techniques have developed from those introduced for exactly self-similar fractals to the more robust arguments required for random graphs.

 

 

Host: 폴정     영어     2017-02-21 12:35:16