세미나 및 콜로퀴엄

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

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

2017 제1회 정오의 수학산책

 

 

 

강연자: 한종규 (서울대)

 

 

일시: 2017년 3월 31일(금) 12:00 ~ 13:15

 

장소: 카이스트 자연과학동 E6-1 3435호

 

 

제목: Symmetry, invariants and conservation laws

 

내용: The notion of symmetry plays a central role in understanding natural laws and in solving equations.  To be symmetric means to be invariant under a group action.  In this lecture we are mainly concerned with continuous groups of the symmetries of differential equations.  I will explain Sophus Lie's ideas on solvability of an ordinary differential equation in terms of its symmetry group and Emmy Noether's theorem on conservation laws for variational problems.   As time permits I will present other viewpoints on the conservation laws.

 

 

등록: 2017년 3월 29일(수) 오후 3시까지

         https://goo.gl/forms/KllQvcZnFjp57sOk1

 

 

문의: hskim@kias.re.kr / 내선:8545

 

Host: 이지운     미정     2017-02-28 16:08:42

Imagine you want to present your collection of n coins on a shelf, taking as little space as possible – how should you arrange the coins?

 
More precisely, we are given n circular disks of different radii, and we want to place them in the plane so that they touch the x-axis from above, such that no two disks overlap. The goal is to minimize the length of the range from the leftmost point on a disk to the rightmost point on a disk.
 
On this seemingly innocent problem we will meet a wide range of algorithmic concepts: An efficient algorithm for a special case, an NP-hardness proof, an approximation algorithm with a guaranteed approximation factor, APX-hardness, and a quasi-polynomial time approximation scheme.

 

Host: 엄상일     미정     2017-03-29 15:18:29

Among the most well-known examples of L-functions are the Riemann zeta
function and the L-functions associated to classical modular forms.
Less well known, but equally important, are the L-functions associated
to Maass forms, which are eigenfunctions of the Laplace-Beltrami
operator on a hyperbolic surface. Named after H. Maass, who discovered
some examples in the 1940s, Maass forms remain largely mysterious.

Fortunately, there are concrete tools to study Maass forms: trace
formulas, which relate the spectrum of the Laplace operator on a
hyperbolic surface to its geometry. After Selberg introduced his
famous trace formula in 1956, his ideas were generalised, and various
trace formulas have been constructed and studied. However, there are
few numerical results from trace formulas, the main obstacle being
their complexity. Various types of trace formulas are investigated,
constructed and used to understand automorphic representations and
their L-functions from a theoretical point of view, but most are not
explicit enough to implement in computer code.

Having explicit computations of trace formulas makes many potential
applications accessible. In this talk, I will explain the
computational aspects of the Selberg trace formula for GL(2) for
general levels and applications towards the Selberg eigenvalue
conjecture and classification of 2-dimensional Artin representations
of small conductor.
This is a joint work with Andrew Booker and Andreas Strömbergsson.

Host: 임보해     영어     2017-03-02 11:08:35

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

2017 제2회 정오의 수학산책

 

 

 

강연자: 이윤원 (인하대)

일시: 2017년 4월 28일(금) 12:00 ~ 13:15

장소: 카이스트 자연과학동 E6-1 3435호

 

제목: Atiyah-Singer index theorem

내용: TBA

 

등록: 2017년 4월 26일(수) 오후 3시까지

        https://goo.gl/forms/0lqSboiW5A9vv9rd2

 

문의: hskim@kias.re.kr / 내선:8545

 

 

Host: 이지운     한국어     2017-02-28 16:12:46
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

There is a classical result first due to Keen known as the collar lemma for hyperbolic surfaces. A consequence of the collar lemma is that if two closed curves A and B on a closed orientable hyperbolizable surface have non-zero geometric intersection number, then there is an explicit lower bound for the length of A in terms of the length of B, which holds for any hyperbolic structure on the surface. By slightly weakening this lower bound, we generalize this statement to hold for all Hitchin representations.  This is a joint work with Tengren Zhang.

Host: 백형렬     영어     2017-03-09 09:30:25

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

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

1952년 영국의 수학자 A. Turing은 그 당시 생물학자들 조차 전혀 상상 할수 없었던, 다 같은 종류의 세포들이 각자 다른 세포로 분화할수 있는 메커니즘을  Reaction-Diffusion System(RD system)을 이용하여 수학적으로 제시했습니다.  그 이후로,  RD system은 수리해석학적으로도 많은 발전을 거듭해왔으며,  수리모델링을 통해  생명과학 분야에 있어서도 생명의 메커니즘을 밝히는 도구로서 발전을 거듭해 오고 있습니다. 

이 강연에서는 제가 최근에 연구를 진행하고 있는 다양한 생명현상을 예로 그 메커니즘을 밝히기 위해 개발한 수리모델 및 수리모델링 수법을 간단하게 소개하겠습니다.  여기에는  수학적으로 재미있는 구조를  가지고 있을 지 모르는  문제들이 숨어 있을 수 있습니다. 그런 문제들을  여러분들께서 직접 찾아 보시길 바랍니다.

Keywords: Mathematical modeling, PDE, Phase-field method 

 

Host: 변재형     한국어     2017-03-08 13:41:27

Liquid crystal is a state of matter between isotropic fluid and crystalline solid, which has properties of both liquid and solid. In a liquid crystal phase, molecules tend to align a preferred direction and molecules are described by a symmetric traceless 3x3 matrix which is often called a second order tensor. Equilibrium states are corresponding to minimizers of the governing Landau-de Gennes energy which plays an important role in mathematical theory of liquid crystals. In this talk, I will present a brief introduction to Landau-de Gennes theory and recent development of mathematical theory together with interesting mathematical questions.

 

 

Host: 권순식     영어     2017-02-21 12:07:17

A well known theorem of Grötzsch states that every planar graph is 3-colorable. We will show a simple proof based on a recent result of Kostochka and Yancey on the number of edges in 4-critical graphs. Then we show a strengthening of the Grötzsch’s theorem in several different directions. Based on joint works with Ilkyoo Choi, Jan Ekstein, Zdeněk Dvořák, Přemek Holub, Alexandr Kostochka, and Matthew Yancey.

Host: 최일규 엄상일     미정     2017-03-02 09:10:53

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