Saturday, November 23, 2024

2024-11-29 / 11:00 ~ 12:00

by 정윤모(성균관대학교)

Dimensionality reduction represents the process of generating a low dimensional representation of high dimensional data. In this talk, I explain what dimensionality reduction is and shortly mention formation control. After that, I will introduce a nonlinear dynamical system designed for dimensionality reduction. I briefly discuss mathematical properties of the model and demonstrate numerical experiments on both synthetic and real datasets.

2024-11-29 / 14:00 ~ 15:00

SAARC 세미나 - SAARC 세미나:

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We discuss on fractional weighted Sobolev spaces with degenerate weights and related weighted nonlocal integrodifferential equations. We provide embeddings and Poincare inequalities for these spaces and show robust convergence when the parameter of fractional differentiability goes to $1$. Moreover, we prove local H\"older continuity and Harnack inequalities for solutions to the corresponding nonlocal equations. The regularity results naturally extend those for degenerate linear elliptic equations presented in [Comm. Partial Differential Equations 7 (1982); no. 1; 77?116] by Fabes, Kenig, and Serapioni to the nonlocal setting. This is a joint work with Linus Behn, Lars Diening and Julian Rolfes from Bielefeld.

2024-11-25 / 11:00 ~ 12:00

학과 세미나/콜로퀴엄 - 박사논문심사: 에너지 임계성 비균질 비선형 슈뢰딩거 방정식의 해의 전역적 존재성 및 분산성

by 박동진()

2024-11-27 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 박사논문심사: 분자 및 행동 수준의 동적 생명현상 이해를 위한 수리모델의 개선 및 응용

by 송윤민()

2024-11-25 / 17:00 ~ 18:00

학과 세미나/콜로퀴엄 - 대수기하학:

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Given two relatively prime positive integers, p < q, Kunz and Waldi defined a class of numerical semigroups which we denote by KW(p, q) consisting of semigroups of embedding dimension n and type n−1 and multiplicity p by filling in the gaps of the semigroup < a, b >. We study these semigroups, give a criterion for these in terms of principal matrices or their critical binomials and generalize the notion to KW(p, q, w) and prove some results and questions. We will discuss their resolutions and Betti Numbers. Most of this is a joint work with Srishti Singh.

2024-11-25 / 15:30 ~ 16:30

학과 세미나/콜로퀴엄 - 대수기하학:

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In this talk, we consider a finite rational map determined by a linear system with base locus. The degree of such map has been studied in many situation, for instance, the degree of Gauss map of theta divisors. In principal, this degree can be computed by Segre class of the base locus. In practice, one can use Vogel's cycle to give an estimation. Associated to the base locus, one can define distinguished subvarieties, which has been used to the study of geometric Nullstellensatz by Ein-Lazarsfeld. We discuss how distinguished subvarieties and their coefficients can be used to estimate the degree of finite rational map. This is a joint work with Yilong Zhang.

2024-11-25 / 14:00 ~ 15:00

학과 세미나/콜로퀴엄 - 대수기하학:

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Let (R,m_R) be a d-dimensional, excellent, normal local ring. A divisorial filtration {I_n} is determined by a divisor D on a normal scheme X determined by blowing up an ideal on R, so that I_n are the global sections of nD. Associated to an m_R-primary divisorial filtration, we have the Hilbert function f(n)=\lambda_R(R/I_n), where \lambda_R is the length of an R-module. We discuss how close or far this function is from being a polynomial, focusing on examples which are constructed and analyzed geometrically.

2024-11-26 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Graphon branching processes and fractional isomorphism

by Eng Keat Hng(IBS 극단 조합 및 확률 그룹)

In 2005, Bollobás, Janson and Riordan introduced and extensively studied a general model of inhomogeneous random graphs parametrised by graphons. In particular, they studied the emergence of a giant component in these inhomogeneous random graphs by relating them to a broad collection of inhomogeneous Galton-Watson branching processes. Fractional isomorphism of finite graphs is an important and well-studied concept at the intersection of graph theory and combinatorial optimisation. It has many different characterizations that involve a range of very different and seemingly unrelated properties of graphs. Recently, Grebík and Rocha developed a theory of fractional isomorphism for graphons. In our work, we characterise inhomogeneous random graphs that yield the same inhomogeneous Galton-Watson branching process (and hence have a similar component structure). This is joint work with Jan Hladký and Anna Margarethe Limbach.

2024-11-29 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 박사논문심사: 계수가 주어진 델타매트로이드와 쌍선형 형식이 주어진 선형공간

by 김동규()

2024-11-28 / 16:00 ~ 18:00

학과 세미나/콜로퀴엄 - 기타: About birational classification of smooth projective surfaces III

by 김재홍(KAIST)

This is a reading seminar to be given by Mr. Jaehong Kim (a graduate student in the department) on foundations of the intersection theory and the classification theory of complex algebraic surfaces. He will give three 2-hour long talks.

2024-11-29 / 11:00 ~ 12:00

IBS-KAIST 세미나 - IBS-KAIST 세미나:

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Malignant gliomas are highly invasive brain tumors. Recent attention has focused on their capacity for network-driven invasion, whereby mitotic events can be followed by the migration of nuclei along long thin cellular protrusions, termed tumour microtubes (TM). Here I develop a mathematical model that describes this microtube-driven invasion of gliomas. I show that scaling limits lead to well known glioma models as special cases such as go-or-grow models, the PI model of Swanson, and the anisotropic model of Swan. I compute the invasion speed and I use the model to fit experiments of cancer resection and regrowth in the mouse brain. (Joint work with N. Loy, K.J. Painter, R. Thiessen, A. Shyntar).

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