Friday, May 28, 2021

2021-06-04 / 16:00 ~ 17:00

by 변순식(서울대)

We discuss sharp regularity results for a larger class of of elliptic and parabolic equations in divergence form and present new and interesting features from the view point of regularity theory

2021-06-03 / 09:30 ~ 10:30

학과 세미나/콜로퀴엄 - 박사학위심사: 데이터 기반 시뮬레이션 모델링, 불확실성 정량화 그리고 최적화

by 김태호(KAIST)

심사위원장 김경국, 심사위원 황강욱, 전현호, 정연승, 송은혜(Department of Industrial & Manufacturing Engineering, Pennsylvania State University)

2021-06-01 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - Discrete Math:

by 고두원()

Let $\mathbb{F}_q$ be a finite field of order $q$ which is a prime power. In the finite field setting, we say that a function $\phi\colon \mathbb{F}_q^d\times \mathbb{F}_q^d\to \mathbb{F}_q$ is a Mattila-Sjölin type function in $\mathbb{F}_q^d$ if for any $E\subset \mathbb{F}_q^d$ with $|E|\gg q^{\frac{d}{2}}$, we have $\phi(E, E)=\mathbb{F}_q$. The main purpose of this talk is to present the existence of such a function. More precisely, we will construct a concrete function $\phi: \mathbb{F}_q^4\times \mathbb{F}_q^4\to \mathbb{F}_q$ with $q\equiv 3 \mod{4}$ such that if $E\subset \mathbb F_q^4$ with $|E|>q^2,$ then $\phi(E,E)=\mathbb F_q$. This is a joint work with Daewoong Cheong, Thang Pham, and Chun-Yen Shen.

2021-05-28 / 10:00 ~ 12:00

학과 세미나/콜로퀴엄 - SAARC 세미나:

by ()

One famous conjecture in quantum chaos and random matrix theory is the so-called phase transition conjecture of random band matrices. It predicts that the eigenvectors' localization-delocalization transition occurs at some critical bandwidth $W_c(d)$, which depends on the dimension $d$. The well-known Anderson model and Anderson conjecture have a similar phenomenon. It is widely believed that $W_c(d)$ matches $1/\lambda_c(d)$ in the Anderson conjecture, where $\lambda_c(d)$ is the critical coupling constant. Furthermore, this random matrix eigenvector phase transition coincides with the local eigenvalue statistics phase transition, which matches the Bohigas-Giannoni-Schmit conjecture in quantum chaos theory. We proved the eigenvector's delocalization property for most of the general $d>=8$ random band matrix as long as the size of this random matrix does not grow faster than its bandwidth polynomially. In other words, as long as bandwidth $W$ is larger than $L^\epislon$ for some $\epislon>0$, and matrix size $L$. It is joint work with H.T. Yau (Harvard) and F. Yang (Upenn).

2021-06-04 / 14:00 ~ 15:00

학과 세미나/콜로퀴엄 - 박사학위심사: 시간 지연이 있는 생물 시스템 연구를 위한 이론적 분석 체계 및 수리 모델

by 김대욱(KAIST)

심사위원장 김재경, 심사위원 김용정, 황강욱, 정연승, 이승규(고려대 세종캠퍼스 응용수리과학부)

2021-06-04 / 15:00 ~ 16:00

학과 세미나/콜로퀴엄 - 응용수학 세미나:

by 박원광(국민대학교)

MUltiple SIgnal Classification (MUSIC) is a well-known, non-iterative imaging technique in inverse scattering problem. Throughout various researches, it has been confirmed that MUSIC is very fast, effective, and stable. Due to this reason MUSIC has been applied to various inverse scattering problems however, it has not yet been designed and used to identify unknown anomalies from measured scattering parameters (S-parameters) in microwave imaging. In this presentation, we apply MUSIC in microwave imaging for a fast identification of arbitrary shaped anomalies from real-data and establish a mathematical theory for illustrating the feasibilities and limitations of MUSIC. Simulations results with real-data are shown for supporting established theoretical results.

2021-06-03 / 10:00 ~ 11:00

학과 세미나/콜로퀴엄 - 정수론:

by 차병철()

Diophantine approximation is a branch of number theory where one studies approximation of irrational numbers by rationals and quality of such approximations. In this talk, we will consider intrinsic Diophantine approximation, which deals with approximating irrational points in a closed subset $X$ in $\mathbb{R}^n$ via rational points lying in $X$. First, we consider $X = S^1$, the unit circle in $\mathbb{R}^2$ centered at the origin. We give a complete description of an initial discrete part of the Lagrange spectrum of $S^1$ in the sense of intrinsic Diophantine approximation. This is an analogue of the classical result of Markoff in 1879, where he characterized the most badly approximable real numbers via the periods of their continued fraction expansions. Additionally, we present similar results for approximations of $S^1$ by a few different sets of rational points. This is joint work with Dong Han Kim (Dongguk University, Seoul). (Contact Bo-Hae Im if you plan to join the seminar.)

2021-06-04 / 17:00 ~ 18:00

학과 세미나/콜로퀴엄 - 대수기하학: Near-rationality properties of norm varieties

by Anand Sawant(Tata Institute of Fundamental Research, Mumbai, In)

I will discuss various near-rationality concepts for smooth projective varieties. I will introduce the standard norm variety associated with a symbol in mod-l Milnor K-theory. The standard norm varieties played an important role in Vovedsky's proof of the Bloch-Kato conjecture. I will then describe known near-rationality results for standard norm varieties and outline an argument showing that a standard norm variety is universally R-trivial over an algebraically closed field of characteristic 0. The talk is based on joint work with Chetan Balwe and Amit Hogadi.

2021-06-03 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄: Infinite order rationally slice knots

by 박정환(KAIST)

A knot is a smooth embedding of an oriented circle into the three-sphere, and two knots are concordant if they cobound a smoothly embedded annulus in the three-sphere times the interval. Concordance gives an equivalence relation, and the set of equivalence classes forms a group called the concordance group. This group was introduced by Fox and Milnor in the 60's and has played an important role in the development of low-dimensional topology. In this talk, I will present some known results on the structure of the group. Also, I will talk about a knot that has infinite order in the concordance group, though it bounds a smoothly embedded disk in a rational homology ball. This is joint work with Jennifer Hom, Sungkyung Kang, and Matthew Stoffregen.

Events for the 취소된 행사 포함