Tuesday, October 5, 2021

2021-10-07 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 학부생 콜로퀴엄: 수리과학 모델을 이용한 감염병 확산 예측 및 방역 정책 효과 분석

by 손우식(국가수리과학연구소)

이번 발표를 통해 수리과학 모델을 이용한 감염병 확산 예측 방법 그리고 방역 정책의 감염 확산 억제 효과 분석에 대하여 소개하겠습니다. 감염 확산 모형의 가장 기본이면서 널리 쓰이고 있는 compartment model, 그리고 지역 단위 인구 이동 자료를 반영한 metapopulation model에 대하여 논의하고, 시시각각 변화하는 감염 확산 상황을 표현하기 적합한 data assimilation method을 살펴보겠습니다. 방역 정책 효과 분석을 위한 수리과학 모델로서 microsimulation model을 소개하겠습니다. Microsimulation model은 정부의 정책 변화가 사회, 경제적으로 미치는 영향을 분석하고자 제안된 시뮬레이션 도구로 거시적 수준의 경제, 사회, 인구 변화를 각 개인과 가구 단위의 미시적 사건들로부터 기술합니다. Microsimulation model을 이용하면 가구, 직장/학교, 종교 및 친목 모임의 밀접 접촉을 통한 호흡기 감염병 확산을 시뮬레이션할 수 있습니다. 그리고 휴교령, 직장 재택 근무, 종교 시설 폐쇄 등의 비약물적 조치가 감염병 확산 방지에 어떤 효과를 지니는지 분석할 수 있다는 장점이 있습니다.

2021-10-07 / 11:00 ~ 12:00

IBS-KAIST 세미나 - 수리생물학:

by ()

Immune sentinel cells must initiate the appropriate immune response upon sensing the presence of diverse pathogens or immune stimuli. To generate stimulus-specific gene expression responses, immune sentinel cells have evolved a temporal code in the dynamics of stimulus responsive transcription factors. I will present recent works 1) using an information theoretic approach to identify the codewords, termed “signaling codons”, 2) using a machine learning approach to characterize their reliability and points of confusion, and 3) dynamical systems modeling to characterize the molecular circuits that allow for their encoding. I will present progress on how the temporal code may be decoded to specify immune responses. Further, I will discuss to what extent such a code may be harnessed to achieve greater pharmacological specificity when therapeutically targeting pleiotropic signaling hubs. NFκB Signaling: information theory, signaling codons

2021-10-07 / 17:00 ~ 18:00

학과 세미나/콜로퀴엄 - 대수기하학:

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2021-10-08 / 11:00 ~ 12:00

학과 세미나/콜로퀴엄 - 대수기하학:

by ()

2021-10-07 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 대수기하학:

by ()

For a quadratic projective variety X ⊂P_r , the locus of quadratic polynomials of rank 3 in the homogeneous ideal I(X) defines a projective algebraic set, say PHI_3(X), in P(I, (X)_2). So, it provides several projective invariants of X. In this talk, I will speak about the structure of Phi_2(C) when C ⊂P_n is a rational normal curve. This is based on the joint work with Saerom Shim.

2021-10-07 / 10:00 ~ 12:00

학과 세미나/콜로퀴엄 - 위상수학 세미나: Immersed surfaces in hyperbolic mapping tori and geodesic laminations, Part 2

by 김경로(서울대학교)

We continue our discussion on the result of Marden, Thurston and Bonahon which states that in hyperbolic 3-manifolds, every immersed surface of which the fundamental group is invectively embedded in the 3-manifold group is quasi-fuchsian or doubly degenerated. Surface subgroups of 3-manifold groups play an important rule in 3-manifold theory. For instance, some collection of immersed surfaces give rise to a CAT(0) cube complex. Especially, in the usual construction of the CAT(0) cube complex, each immersed surface composing the collection is quasi-fuchsian. In this talk, I introduce the work by Cooper, Long and Reid. In hyperbolic mapping tori, the work gives a criterion to determine whether the given immersed surface is quasi-fuchsian or not. The criterion is given in terms of laminations induced in immersed surfaces.

2021-10-05 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 대수기하학: Multiplicity-free products of Schubert divisors

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In my first talk I am going to speak about Schubert calculus. Let G/B be a flag variety, where G is a linear simple algebraic group, and B is a Borel subgroup. Schubert calculus studies (in classical terms) multiplication in the cohomology ring of a flag variety over the complex numbers, or (in more algebraic terms) the Chow ring of the flag variety. This ring is generated as a group by the classes of so-called Schubert varieties (or their Poincare duals, if we speak about the classical cohomology ring), i. e. of the varieties of the form BwB/B, where w is an element of the Weyl group. As a ring, it is almost generated by the classes of Schubert varieties of codimension 1, called Schubert divisors. More precisely, the subring generated by Schubert divisors is a subgroup of finite index. These two facts lead to the following general question: how to decompose a product of Schubert divisors into a linear combination of Schubert varieties. In my talk, I am going to address (and answer if I have time) two more particular versions of this question: If G is of type A, D, or E, when does a coefficient in such a linear combination equal 0? When does it equal 1?

2021-10-12 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Majority dynamics on sparse random graphs

by 이준경(한양대)

Majority dynamics on a graph $G$ is a deterministic process such that every vertex updates its $\pm 1$-assignment according to the majority assignment on its neighbor simultaneously at each step. Benjamini, Chan, O'Donnell, Tamuz and Tan conjectured that, in the Erd\H{o}s--R\'enyi random graph $G(n,p)$, the random initial $\pm 1$-assignment converges to a $99\%$-agreement with high probability whenever $p=\omega(1/n)$. This conjecture was first confirmed for $p\geq\lambda n^{-1/2}$ for a large constant $\lambda$ by Fountoulakis, Kang and Makai. Although this result has been reproved recently by Tran and Vu and by Berkowitz and Devlin, it was unknown whether the conjecture holds for $p< \lambda n^{-1/2}$. We break this $\Omega(n^{-1/2})$-barrier by proving the conjecture for sparser random graphs $G(n,p)$, where $\lambda' n^{-3/5}\log n \leq p \leq \lambda n^{-1/2}$ with a large constant $\lambda'>0$.

2021-10-05 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Feedback Vertex Set on Geometric Intersection Graphs

by 오은진(포스텍)

I am going to present an algorithm for computing a feedback vertex set of a unit disk graph of size k, if it exists, which runs in time $2^{O(\sqrt{k})}(n + m)$, where $n$ and $m$ denote the numbers of vertices and edges, respectively. This improves the $2^{O(\sqrt{k}\log k)}(n + m)$-time algorithm for this problem on unit disk graphs by Fomin et al. [ICALP 2017].

2021-10-06 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 정수론: Vanishing theorems for unitary Shimura varieties

by Prof. Teruhisa Koshikawa(RIMS)

The cohomology of Shimura varieties have rich structures and have been studied for many years. Some new vanishing theorems were proved in the last few years and especially the one by Caraiani-Scholze is crucial in arithmetic applications. I will survey these results, and discuss further development.

2021-10-07 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄: Derive fluid models from many-body problem of particles

by 김찬우(University of Wisconsin-Madison)

In his famous 1900 presentation, Hilbert proposed so-called the Hilbert’s 6thproblem, namely “Mathematical Treatment of the Axioms of Physics”. He mentioned that “Boltzmann's work on the principles of mechanics suggests the problem of developing mathematically the limiting processes, there merely indicated, which lead from the atomistic view to the laws of motion of continua.” In this lecture, we present some recent development of the Hilbert’s 6th problem in the Boltzmann theory when the various fluid models have natural “singularities” such as unbounded vorticity and formation of boundary layers.

Events for the 취소된 행사 포함