Thursday, May 19, 2022

2022-05-24 / 15:30 ~ 16:30

학과 세미나/콜로퀴엄 - 박사논문심사: 타원과 쌍곡선형 특이 극한을 통한 반응-확산 방정식의 파동 전파

by 박현준(KAIST)

심사위원장 : 김용정, 심사위원 : 강문진, 김재경, 임미경, 안인경(고려대학교)

2022-05-24 / 14:30 ~ 15:30

학과 세미나/콜로퀴엄 - 박사논문심사: 불균질 확산 방정식으로의 수렴 및 반응-확산 방정식에서 파동 전파

by 김호연(KAIST)

심사위원장 : 김용정, 심사위원 : 강문진, 김재경, 임미경, 안인경(고려대학교)

2022-05-25 / 16:00 ~ 17:00

IBS-KAIST 세미나 - IBS-KAIST 세미나:

by ()

We shall give an explicit estimate of the lower bound of the Bergman kernel associated to a positive line bundle. In the compact Riemann surface case, our result can be seen as an explicit version of Tian’s partial C0-estimate.

2022-05-25 / 17:00 ~ 18:15

SAARC 세미나 - SAARC 세미나:

by 김영헌(브리티시컬럼비아 대학)

2022-05-23 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - PDE 세미나:

by ()

This talk is concerned with the bifurcation and stability of the compresible Taylor vortex. Consider the compressible Navier-Stokes equations in a domain between two concentric infinite cylinders. If the outer cylinder is at rest and the inner one rotates with sufficiently small angular velocity, a laminar flow, called the Couette flow, is stable. When the angular velocity of the inner cylinder increases, beyond a certain value of the angular velocity, the Couette flow becomes unstable and a vortex pattern, called the Taylor vortex, bifurcates and is observed stably. This phenomena is mathematically formulated as a bifurcation and stability problem. In this talk, the compressible Taylor vortex is shown to bifurcate near the criticality for the incompressible problem when the Mach number is sufficiently small. The localized stability of the compressible Taylor vortex is considered under sufficiently small axisymmetric perturbations; and it is shown that the large time behavior of solutions around the Taylor vortex is described by solutions of a system of diffusion equations.

2022-05-26 / 16:00 ~ 17:30

학과 세미나/콜로퀴엄 - 박사논문심사: 깁스 그리고 가우시안 측도들의 해밀토니안 편미분 방정식들의 흐름에 따른 운송 성질들

by 성기훈(KAIST)

심사위원장 : 권순식, 심사위원 : 배명진, 남경식, Yoshio Tsutsumi(Kyoto University), Mamoru Okamoto(Osaka University)

2022-05-23 / 16:30 ~ 18:00

학과 세미나/콜로퀴엄 - 계산수학 세미나:

by 최민석()

Despite of great progress over the last decades in simulating complex problems with the numerical discretization of (stochastic) partial differential equations (PDEs), solving high-dimensional problems governed by parameterized PDEs remains challenging. Machine learning has emerged as a promising alternative in scientific computing community by enforcing the physical laws. We review some of machine learning approaches and present a novel algorithm based on variational inference to solve (stochastic) systems. Numerical examples are provided to illustrate the proposed algorithm.

2022-05-20 / 16:00 ~ 17:30

학과 세미나/콜로퀴엄 - Face the World with Mathematical Mind:

by ()

2022-05-19 / 16:30 ~ 18:00

학과 세미나/콜로퀴엄 - 박사논문심사: 기하적 복소함수론을 이용한 내포의 모양 복원 및 중립물질 설계

by 최두성(KAIST)

심사위원장 : 임미경, 심사위원 : 김동환, 김용정, 권기운(동국대 수학과), 이현대(인하대 수학과)

2022-05-26 / 14:30 ~ 15:45

SAARC 세미나 - SAARC 세미나:

by 김영헌(브리티시컬럼비아 대학)

2022-05-24 / 16:00 ~ 17:15

SAARC 세미나 - SAARC 세미나:

by 김영헌(브리티시컬럼비아 대학)

2022-05-19 / 14:30 ~ 15:45

SAARC 세미나 - SAARC 세미나:

by 김영헌(브리티시컬럼비아 대학)

2022-05-23 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: The precise diameter of reconfiguration graphs

by Stijn Cambie(IBS 극단 조합 및 확률 그룹)

2022-05-26 / 12:00 ~ 12:25

대학원생 세미나 - 대학원생 세미나: Spectrum of sparse random graphs and related problems

by 이재훈(KAIST)

Around early 2010, there was a huge success in understanding the spectrum of large random matrices, in other words, large random graphs. It was only for large but dense random graphs at first. However, as random matrix theory has been developed, there is some progress in sparse cases. In this short talk, I will review a series of results for spectral statistics of sparse random graphs and explain their implications.

2022-05-26 / 12:25 ~ 12:50

대학원생 세미나 - 대학원생 세미나: Deriving Stationary distributions from an underlying graph structure

by 홍혁표(KAIST)

Randomness of biochemical reactions is inherent in various biological systems, from DNA to organs and the human body. These stochastic dynamics are frequently modeled using a continuous-time Markov chain (CTMC). Its long-term behavior is described by a stationary distribution, corresponding to its deterministic counterpart called a steady state. Stationary distribution can be derived analytically only in limited systems such as linear or finite-state systems. In this talk, I will introduce a recent result by Anderson, Craciun, and Kurtz deriving stationary distribution from the underlying graph structure of a reaction network and how we can extend it. For those who are first told the word 'Mathematical Biology,' I will briefly introduce mathematical biology before going into the detailed topic.

2022-05-19 / 12:00 ~ 12:50

대학원생 세미나 - 대학원생 세미나: Modular forms and transcendental questions

by 이원웅(KAIST)

Modular curves for Hecke congruence groups, or more generally, for Fuchsian groups of the first kind can be seen as the moduli spaces of the isomorphism classes of elliptic curves with torsion data in some sense. In this talk, I will introduce the notion of modular curves and modular forms. If time permits, I will also introduce their applications to some transcendental questions.

2022-05-26 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by ()

Inside living cells, chemical reactions form a large web of networks and they are responsible for physiological functions. Understanding the behavior of complex reaction networks is a challenging and interesting task. In this talk, I would like to illustrate how the methods of algebraic topology can shed light on the properties of chemical reaction systems. In particular, we discuss the following two problems: (1) response of reaction systems to external perturbations and (2) simplification of complex reaction networks without altering the behavior of the system.

2022-05-19 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by ()

Helly-type theorems and problems form a nice area of discrete geometry. I will start with the notable theorems of Radon and Tverberg and mention the following conjectural extension.

For a set X of points x(1), x(2),...,x(n) in some real vector space V we denote by T(X,r) the set of points in X that belong to the convex hulls of r pairwise disjoint subsets of X.
We let t(X,r) = 1 + dim(T(X,r)).

Radon's theorem asserts that
If t(X,1) < |X| then t(X, 2) > 0.

The first open case of the cascade conjecture asserts that
If t(X,1) + t(X,2) < | X | then t(X,3) >0.

In the lecture I will discuss connections with topology and with various problems in graph theory.
I will also mention questions regarding dimensions of intersection of convex sets.

Some related material:
1) A lecture (from 1999): An invitation to Tverberg Theorem: https://youtu.be/Wjg1_QwjUos
2) A paper on Helly type problems by Barany and me https://arxiv.org/abs/2108.08804
3) A link to Barany's book: Combinatorial convexity https://www.amazon.com/Combinatorial-Convexity-University-Lecture-77/dp/1470467097

2022-05-25 / 17:00 ~ 18:00

IBS-KAIST 세미나 - 수리생물학:

by ()

I will discuss the development, analysis and applications of multi-resolution methods for spatio-temporal modelling of intracellular processes, which use (detailed) Brownian dynamics or molecular dynamics simulations in localized regions of particular interest (in which accuracy and microscopic details are important) and a (less-detailed) coarser model in other regions in which accuracy may be traded for simulation efficiency. I will discuss the error analysis and convergence properties of the developed multi-resolution methods, their software implementation and applications of these multiscale methodologies to modelling of intracellular calcium dynamics, actin dynamics and DNA dynamics. I will also discuss the development of multiscale methods which couple molecular dynamics and coarser stochastic models in the same dynamic simulation.

2022-05-25 / 16:30 ~ 16:55

IBS-KAIST 세미나 - 수리생물학:

by ()

I will introduce mathematical and computational methods for spatio-temporal modelling in molecular and cell biology, including all-atom and coarse-grained molecular dynamics (MD), Brownian dynamics (BD), stochastic reaction-diffusion models and macroscopic mean-field equations. Microscopic (BD, MD) models are based on the simulation of trajectories of individual molecules and their localized interactions (for example, reactions). Mesoscopic (lattice-based) stochastic reaction-diffusion approaches divide the computational domain into a finite number of compartments and simulate the time evolution of the numbers of molecules in each compartment, while macroscopic models are often written in terms of mean-field reaction-diffusion partial differential equations for spatially varying concentrations.

Events for the 취소된 행사 포함